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Section 02 – Cattle Milk Recording

2026-08-11T18:19:06Z

Cmosconi: /* Calculation of daily fat percentage from single samples by Jenko et al., 2008, 2010 */

= Overview =
<div class="mw-collapsible mw-collapsed">
<div>
== Introduction ==
Information about milk production traits is very important for managing and breeding dairy herds. The milk recording process starts with the collection of animal identification, a calving date of milking cows, the amount of milk given and the date with time or time frame of a day. A milk sample may be taken. The obtained milk sample is analysed for milk constituents. The results of the analysis plus the data about milk yield and time of milking are stored in a database. Subsequently a number of parameters, cumulative yields and indices are calculated and stored in the database and, finally, reported to the farmer

This Section 2 of the ICAR Guidelines focuses on the milk recording process for dairy cattle.

== Scope ==
Figure 1 gives a pictorial summary of the main elements of this guideline.

In summary, this section of the ICAR Guidelines covers the milk recording process from the enrolment of a herd for milk recording, through to the delivery of information which a herd owner can use to assist in a range of decisions.
[[File:Scope of Section 2 - Dairy cattle milk recording..png|thumb|Figure 1. Scope of Section 2 -Dairy cattle milk recording.|center|524x524px]]

Not covered in this section are:
# Standards and guidelines for ICAR approval of milk recording devices. Please consult [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices|Section 11]] for this subject.
# Standards and guidelines for ICAR approval of ID devices. Please consult [[Section 10 – Identification Device Certification|Section 10]] for this subject.
# Standards and guidelines for preparation of milk samples and for quality assurance of milk analysis. Please consult [[Section 12 – Milk Analysis|Section 12]] for this subject.
# Standards and guidelines for in-line milk analysis on the farm. Please consult [[Section 13 – On-farm Milk Analysis|Section 13]] for this subject.

== Enrolment ==

Enrolment of new herds in the recording process should involve an agreement between the farmer and the recording organisation regarding technical and financial questions such as:

# General information about the recording programme itself, i.e.
#* Herd and cow identification.
#* Scope of recorded data, including database setup as required by the user.
#* Scheduling recording.
#* Data capture and processing.
#* Recording methods and intervals.
#* Milk measuring and meters.
#* Sampling and sample transport.
#* Reports (outcomes) and supporting decisions.
# Definition of supervision scheme and other quality assurance and plausibility checking steps.
# Fee structure and invoicing.
# Approval of technicians by milk recording organisations (MROs) so as to give them free access to farms for all recording and supervision actions.

In cases where the owner of the recorded cows or his employees carry out the recording itself, it is up to the organisation to decide upon, and provide for, any necessary training.

== Standard and Guidelines for Milk Recording ==
These standards and guidelines for milk recording are valid for all milking systems, including AMS where applicable.
====General Standards and Guidelines for milk recording====
#ICAR-approved (electronic) milk meters and sampling devices must be used on the recording day (see [https://wiki.icar.org/index.php/Section_11_%E2%80%93_Testing,_Approval_and_Checking_of_Measuring,_Recording_and_Sampling_Devices#Procedure_1:_Procedure_for_Application_for_Testing_of_Measuring,_Recording_and_Sampling_Devices_or_Sensor_Systems Procedure 1 of Section 11 - Guidelines for Testing, Approval and Checking of Milk Recording Devices]). The list of approved milk meters, jars and AMS and automatic milk sampler/tray combinations sampling devices can be found on the [https://www.icar.org/index.php/certifications/icar-certifications-for-milk-meters-for-cow-sheep-goats/ ICAR web page].
#Milk weights are recorded for each milking of the recording period. The measurement may be done using any of the ICAR approved recording devices, or by weighing. The minimum accuracy of the measurement is 0.2 kg.
#Where milk constituents are analysed, the equipment used must meet ICAR standards for accuracy. Please consult [[Section 12 – Milk Analysis|Sections 12]] and [[Section 13 – On-farm Milk Analysis|Section 13]] of the Guidelines for details.
#The accuracy of the equipment used for milk recording and sampling must be checked by an agency approved by the member organisations, on a regular and systematic basis using methods approved by ICAR. The list of methods is given in [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices#Procedure 6: Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices|Procedure 6 of Section 11]] - Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices.
#All analyses of the constituents of a milk sample must be carried out on the same milk sample.
#These samples should ideally represent the 24-hour milking period.
#If milk samples do not represent a 24-hour period, the results of milk analyses must be corrected to a 24-hour period by a method approved by ICAR (see [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]).
#In cases where the duration of recording deviates from 24 hours, the results must be converted into 24-hour yields. Only approved 24-hour yield calculation methods can be used. The appropriate methodology is described in [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]
#As date of recording, we recommend to use the date on which the last sample was taken. As alternative, the date of the first sample can be used.
#Calculation methods
##The quantities of milk and milk constituents shall be calculated according to one of the methods outlined in this section of the ICAR Guidelines (see [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Standard methods for calculating 24 hour yields]).
##Member organisations should keep the ICAR Secretariat informed about the calculation methods being used by the records processing operations in their organisation or country and shall be responsible for ensuring that the records are corrected and calculated as specified in this section of the ICAR Guidelines.
====Standards and Guidelines for milk recording using AMS====
This subsection covers systems where milk weights, milk quality or other traits of the cows are monitored constantly and automatically. This can be done in both automatic and manually operated milking systems.

Requirements:
*Animal identification is automatic and reliable. Farm transponders can also be used for automatic identification if they are linked to the cow’s official identification in farm software.
*All individual milkings must be recorded from all AMSs in the farm and transmitted to the recording database for calculation, interrupted milkings included.
*For official milk recording purposes, the data file obtained from electronic milk meters must contain the following: 1) Cow ID, 2) Milking time stamp, 3) Milk weight and 4) Sampling stamp to mark the milking where the sample comes from.
*All milkings within the recording period may be sampled, and in this case the samples should be analysed separately. Alternatively, a one-milking sample can be taken for each cow, followed by fat correction calculation.
*All cows in milk on the recording day have to be sampled. The sampling device must remain in operation until all cows are sampled. When the number of available sampling devices is smaller than the number of AMS units, sampling may need to be prolonged beyond one day to allow complete sampling of all cows. In that case, the sampling device has to be moved between AMS units.
*During sampling, the automatic sampler must be monitored to make sure there are vials left for the next cows.
*24-hour yield calculations must be carried out by a MRO, independently of the AMS manufacturer. This is done in order to guarantee harmonisation of calculation methods between the different brands of equipment and software.
*Data of all milkings over a given time period must be collected for the 24-hour milk yield calculation. A 96-hour data collection period is recommended.
Recommendations:
#Ideally, data of all milkings should be collected and used to compute lactation yield.
#Description of formats to exchange data recorded by an AMS can be requested from the manufacturer or the ICAR ADE data exchange standard for milking data can be used.
#In the case of milk recording method B (see [[Section 02 – Cattle Milk Recording#Recording|chapter 1.4 "Recording]]") with AMS, the milk recording organization should make sure that the farmer knows how to load or transfer data.
#Data can be extracted by: 1) manual operation by MRO Technician’s or Farmer (file extraction), 2) automated system and data transfer through an Application Programming Interface (API), 3) another data transfer and exchange system.
#Raw milk recording data from the AMS must be easily accessible for MRO data processing.
#For official milk recording purposes, the data file obtained from electronic milk meters may also contain the following: 1) Vial ID (this is obligatory with M sampling scheme), 2) Milking duration, 3) Milking speed, 4) Incomplete milking in automatic milking systems and 5) Other relevant data measured or reported by the equipment.
#Individual milkings should be tested for milk secretion rate in order to detect interrupted and unrecorded milkings, which in turn have an effect on the calculated 24-hour yields. If there is an interrupted milking or a milking that follows an interrupted milking at the beginning of the recording period, these two milkings must be excluded from the calculations. During the recording period they can be excluded but do not need to be.
#It is recommended to individually sample all milkings within the 24-hour recording period for 24-hour fat content calculation due to the high variability of milking frequency and milk fat content. In cases where sampling all milkings is not possible, please consult Chapter 2 of [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 - Computing 24-hour Yields] (for approved correction calculation methods).
#It is recommended to sample only milkings with a preceding interval longer than 4 hours.
====Authorisation to record====
It is recommended that professional milk recording technicians are trained and certified before they carry out recordings on their own. Ideally, such training includes a period of supervised work with a certified technician. Where such a certification system is in place, it is not allowed to record without an authorisation.

It is also recommended that frequent training is given to milk recording technicians on new technologies and equipment, safety instructions and data quality issues.

In B and C recording, farmers or their employees doing the practical recording need to be capable of operating the recording equipment correctly (e.g. milk meters, data capture tools) and are familiar with recording techniques.

It is recommended to have a conformation test from a certified recording agency and that frequent training take place.
====Cows to be recorded====
In a recorded herd, all milk-producing cows must be recorded. If a herd is divided into groups, all animals in the group have to be recorded on the same recording scheme. If different recording schemes are practiced on the farm all cows must be recorded according to the standards for recording and sampling intervals in table 3.

Acceptable reasons for missing data are discussed below, in 5.5. Missing results and/or abnormal intervals are reported [[Section 02 – Cattle Milk Recording#Missing results|here]].

===Identification (ID)===
====Herd ID====
Each herd in milk recording must be allocated a unique permanent identification number.
====Animal ID====
An official milk recording system must be based on a clearly identifiable and unique animal ID. It is recommended that one identification scheme for the whole country is used. Animal identification must also be in accordance with national and international regulation (e.g. EU member countries with EU legislation - 1760/2000 for cattle), and with relevant parts of currently valid ICAR Guidelines. The animal must be marked with an ICAR approved identification device or system. If the ID of imported animals is changed, the connection to the original ID must be maintained. Management numbers for cows can be used aside the official ID.
====Identification of the sample vial====
The sample, the milk weight and the cow ID must be linked at the milking.

Vials can be identified according to:
#Vial placement in the sampling unit.
#Cow or sample ID written on the vials.
#Barcoded vial with printed cow ID.
#Barcoded vial with cow ID registered at the milking.
#RFID vial with cow ID registered at the milking.
=====Sample identification without electronic equipment=====
Samples are identified according to their placement in the sampling unit. Additionally, sample or cow numbers can be written on the vials with a waterproof marker. If this marking is not done, there must be a sure and efficient way to identify sample No. 1 (e.g. different colour) and the sequence of other samples.

Each sampling unit must be connected to a list of samples where cow ID is given for each sample. Each transportation box also has to carry the relevant herd ID’s and, preferably, the sampling dates.
=====Barcoded vials=====
Samples are identified according to the barcode on the vial label.

If the label contains cow and/or herd ID, no electronic equipment is needed at the recording. The samples can be sent to the laboratory without accompanying sample lists or herd ID markings on the box.

If the label contains a random sample ID number, the cow ID must be connected with it on the farm. This is done with a barcode reader and computer programmes making the connection possible.
=====Vials with RFID=====
Samples are identified according to the RFID chip in the vial. This system requires the use of RFID readers and specific computer programmes creating a file where the cow and vial ID’s are connected.
=====Automatic sampling systems=====
In automatic milking systems (AMS), ICAR approved automatic samplers have to be used. Sample identification in these systems can be based on vial placement, barcode or RFID. The file with corresponding cow ID is in the management programme of the milking system. Data transfer is carried out with specific software and via a specific interface from the AMS to the MRO.
=====Sample ID in the laboratory=====
For impartiality and better quality, it is recommended that the samples are identified without cow ID and sent to the laboratory anonymously and the analysis results are merged afterwards in the data processing centre.
====Connection of the sample to milking and 24 h yield====
=====Sample and milk weight from the same milking=====
The ideal situation is that the sample and milk weight represent the same milking.
=====Sample from one milking, milk weight from two=====
A corrected analysis is routinely attached to the 24-hour yield.
=====Sample from one milking, milk weight from two or more, corrected by intervals=====
In this case, a 24-hour-yield is also combined with a one-milking sample, but the 24‑hour yield is obtained by correcting the recorded milkings according to the length of the preceding milking intervals. For example, if a cow has produced 20 kg milk in two milkings and the preceding intervals total 20 hours, her 24-hour yield is calculated as 20 kg * (24 h/20 h) = 24 kg. A corrected analysis is attached to this 24‑hour yield.
=====Sample from one milking or day, milk weight from several days=====
With electronic milk meters, it is possible to use the milk production from several days. This gives better accuracy of milk yield estimation; the highest accuracy with uncorrected milk weights is reached using a 4-day average. The problem is that the sample results become disconnected from the milk yield and a loss in fat and protein yield accuracy will occur. Ideally, fat and protein production should be connected to the recording day even in AMS.

In this case, there are three options to connect samples to the 24-hour yield:
#Milk weight is estimated from a longer measurement period but for fat and protein yield estimation only the milk yield on sampling day is used.
#Information only from the recording day for constituents in milk and milk yield estimation.
#Combination of multiple day milk yield with constituents from sampling. See ICAR procedures for using data from more than one day (Lazenby ''et al''., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>, estimation of fat and protein yield (Galesloot and Peeters , 2000)<ref name=":1">Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>.
The analysis data are merged with milk weights in the laboratory or data processing centre and the date of the analysis must be known.

=== Traits to be recorded ===

==== Definition of milking speed and box time ====

===== Introduction =====
Automated Milking Systems (AMS) do measure many traits. The definition of these traits might be different per brand of AMS. Data of these traits is often used by e.g. milk recording organisations, herdbooks or management software providers. When organisations store these data in their databases and use for certain services, it is important to know how these traits are defined.

These definitions could be used by milk recording organisations etc. to take into account differences between traits measured by different brands of AMS. These definitions could also be used by manufacturers of AMS to take into account for product development, to get more alignment in trait definitions between different brands of AMS.

Aim of this document is to propose a harmonized definition of some traits measured by AMS.

At this stage, the traits milking speed and box time are taken into account. Traits related to teat coordinates are described in Section 5 (Conformatoin Recording) of the ICAR guidelines.

==== Average milking speed ====
Definition = AverageMilkingSpeed (gr/min) = {TotalMilkYield / TotalMilkingTime}

* Total milk yield (kg) = Sum of all quarter level milk yields (kg)
* Total milking time = Last Take-off time (of any teat) - Begin of milk flow (of any teat)

Recommendations for manufacturers:

* Exclude any pre-treatment time from milking time.
* Provide take-off settings (threshold in gr/min at take-off, user-defined or default) and settings for the beginning of the measurement period, as milking time will be influenced by take-off settings and by the definition of the beginning of the milk flow.

Recommendations for data users:

* Don't report milking sessions with kick-off´s, interrupted and re-attached milkings because milking time will vary for these milkings.

==== Box time ====
Different types of box time:

* Milking
* Feed-only
* Pass-through
* Selection
* Training

Definition = {End box time - Begin box time} (HH:MM:SS)

* Begin box time = datetime of recognition of animal
* End box time = datetime when cow has exited the box (which might be different from opening of the gate), best to detect when cow has actually left the box

Additional data is needed to understand the status and completeness of the milking visit (Wethal and Heringstad, 2019). Registered issues during the milking are e.g.

* ff: at least 1 teat cup kicked off
* TeatNotFound: unable to find at least 1 of the teats for milking
* IncompleteMilking/FailedMilking: Minimum of 1 teat was registered as incompletely milked.
* The expected milk yield for a milking session depends on previous milkings. Settings like yield less than 80% of expectation for a teat, the milking session would be recorded as having an incompletely milked teat.
* Manual interaction like teat manually attached or milking finished manually.

Recommendations for manufacturers:

* Make the codes available that express if a milking was successful and the cause if the milking was not successful.
* Uniform names and definitions for interrupted, incomplete or failed milkings as well.

Recommendations for data users:

* Check the availability of a code that expresses if a milking was successful and the cause if the milking was not successful. The meaning of the code can be used to consider if the box time record has to be used for the intended purpose or not.
* To check if there is any extra box time due to feeding concentrates, e.g. through user specific settings such as 'PriorityFeeding'.

=== Traits to be recorded ===
In official milk recording, the following data have to be recorded, wherever available:

# Identification of each cow in the herd, even if they remain in the herd for a very short time.
# Birth date, sex, breed and parents of each animal when known.
# All services and embryo flushings and transfers: date, recipient, sire, dam of the embryo.
# All animal deaths and movements between farms and owners.
# Recording dates and locations.
# Milk yields for each cow and recording date.
# Fat content in milk for each cow and sampling date.

It is recommended to record also the following:

# Protein content in milk for each cow and sampling date.
# Milk somatic cell count for each cow and sampling date.
# Other results obtained from milk analysis.
# Milking duration and milking speed where possible.
# Milking times during recording.
# Recording methods and respective symbols used in records.
# Information about cow during the rearing period.

=== Recording method ===
The recording method for the herd consists of using five different symbols for:

# Responsibility for the practical recording.
# Sampling scheme.
# Recording interval.
# Sampling interval (if different from the above).
# Number of milkings per day (especially any deviation from 2x milking).

The symbols in Table 2 should be used:<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Symbols for milk recording schemes.''
|- style="background-color:#efefef; text-align:center;"

|'''Responsibility for recording'''
|'''Sampling scheme'''
|'''Recording interval (weeks)'''
|'''Sampling interval (weeks)'''
|'''Number of milkings per day'''
|-
| style="text-align:center;" | A
| style="text-align:center;" | P
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | B
| style="text-align:center;" | E
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | C
| style="text-align:center;" | Z
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" |
| style="text-align:center;" | T
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" |
| style="text-align:center;" | M
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:center;" | R x
|-
| style="text-align:center;" |
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | S x
|}
</center>

As an example: Recording method is CP36, 2x means that this is a recording where records/ samples are taken partly by the owner (farmer), and partly by a technician from the MRO, where the recording frequency is every 3 weeks, where the sampling frequency is every 6 weeks, and where the number of milkings per day is 2. If a national nomenclature system is used, it should be possible to transfer this system into ICAR nomenclature.

The reference milk recording method is by a representative of the recording organisation, measuring and sampling every four weeks, with proportional sampling and two milkings per day (AP44, 2x).

Recording other than by the reference method must be indicated using the appropriate symbols.

It is recommended that a limit is set for changing the recording method e.g. so that normally it is only possible to change the method twice per year.

It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

In the next sections the symbols are explained:
====Responsibility for the recording====
This symbol indicates who is responsible for measuring the milk yields and taking samples in the herd.
#Representative of the MRO (Method A; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Farmer or his/her representative (Method B; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Mixed responsibility (Method C; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
====ICAR Standards for sampling schemes====
=====Proportional sampling (P)=====
Samples and milk weights are taken at each milking during the recording day. The sampled amount corresponds to the milk yield of each milking. This is achieved by the use of a pipette in equal number of pipetting at each milking or of a specially designed tool which ensures proportional sampling to create one mixed sample. This is the default sampling scheme with no necessary correction to the analysis results, all other schemes must be reported.
=====Equal measure sampling (E)=====
Samples and milk weights are taken at each milking during the recording day. The amount of the sample is measured to be equal at each milking and mixed into one sample. The analysis results for fat should be corrected if one of the milking intervals is shorter than 10 or longer than 14 hours.
=====Multiple sampling (M)=====
Samples are taken at more than one milking during the recording day while milk weights are taken at each milking or over several days. Samples from different milkings are not mixed but they are kept in distinct vials so that each cow has at least two samples. The analysis results must be corrected to correspond to the 24-hour fat and protein yields. For example: a cow is milked 3x during 24 hours and 2 or 3 separate samples are taken, kept and analysed in different vials. This is the gold standard for AMS. It produces the most accurate results but is more expensive.
=====One-milking sampling with milk weights from more than one milking (Z)=====
Samples are taken from one milking during the recording day while milk weights are taken at each milking or over several days. The analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Alternated one-milking recording (T)=====
Samples and milk weights are taken during one milking, alternating between morning and evening milkings. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Constant one-milking recording (C)=====
Samples and milk weights are taken during one milking, constantly during morning or evening milking. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====In-line analysis recording (I)=====
Milk is not sampled but its constituents are continuously analysed by a stationary analyser.
====ICAR Standards for recording and sampling intervals====

<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Standards for recording and sampling intervals.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| rowspan="2" style="text-align:center;" |'''Recording or sampling interval (weeks)'''
| rowspan="2" style="text-align:center;" |'''Minimum number of recordings or samplings per year'''
| colspan="2" style="text-align:center;" |'''Interval between recordings or samplings (days)'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| rowspan="10" style="text-align:center;" |Reference method
| style="text-align:center;" |1
| style="text-align:center;" |44
| style="text-align:center;" |4
| style="text-align:center;" |10
|-
| style="text-align:center;" |2
| style="text-align:center;" |22
| style="text-align:center;" |10
| style="text-align:center;" |18
|-
| style="text-align:center;" |3
| style="text-align:center;" |15
| style="text-align:center;" |16
| style="text-align:center;" |26
|-
| style="text-align:center;" |4
| style="text-align:center;" |11
| style="text-align:center;" |22
| style="text-align:center;" |37
|-
| style="text-align:center;" |5
| style="text-align:center;" |9
| style="text-align:center;" |32
| style="text-align:center;" |46
|-
| style="text-align:center;" |6
| style="text-align:center;" |8
| style="text-align:center;" |38
| style="text-align:center;" |53
|-
| style="text-align:center;" |7
| style="text-align:center;" |7
| style="text-align:center;" |44
| style="text-align:center;" |60
|-
| style="text-align:center;" |8
| style="text-align:center;" |6
| style="text-align:center;" |50
| style="text-align:center;" |70
|-
| style="text-align:center;" |9
| style="text-align:center;" |5
| style="text-align:center;" |55
| style="text-align:center;" |75
|-
| style="text-align:center;" |Daily
| style="text-align:center;" |310
| style="text-align:center;" |1
| style="text-align:center;" |3
|}
</center>

====ICAR standards for number of milkings per day====

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 3. Symbols for number of milkings per day.''
|- style="background-color:#efefef; text-align:center;"
|'''Number of milkings per day'''
|'''Symbol'''
|-
| style="text-align:center;" | Once per day milking
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | Two milkings
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | Three milkings
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" | Four milkings
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" | Continuous milking (e.g. AMS)
| style="text-align:center;" | R x
|-
| style="text-align:center;" | Regular milkings not at the same times on each day (e.g. 10 milkings per week)
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" | Shown as the average number of milkings per day.
| style="text-align:center;" |
|-
| style="text-align:center;" | Animals that are both milked and suckled. (Number of times milked to prefix the S)
| style="text-align:center;" | S x
|}
</center>

Where a herd is dry for a period of the year, the minimum number of recordings should be adjusted proportionately to the production period.

Minimum number of herd recordings should be at least 85% of the normal number of recordings.

=== Missing results and/or abnormal intervals ===
{{anchor|Missing_results}}A recorded 24-hour yield is the best estimate of the yield and the constituents of the milk, weighed, sampled and recorded within 24 hours on the day of recording.
#When herds are normally milked at intervals such that the recording day is other than 24 hours, the yields shall be adjusted to a 24-hour interval using the following procedure (or other procedures approved by the ICAR):
#*Divide 24 by the interval, then multiply by the yield. For example:
#**For a 25 hour interval (24/25) x 35 kg = 33.6 kg
#**For a 20 hour interval (24/20) x 35 kg = 42.0 kg
#A recording is a set of daily test values for a given animal on a given day of recording, one or some or all of them can be missed (missing values)
#Missing values can be due to:
#*Out of range.
#*Sickness.
#*Disaster.
#*No sample analysis results.
#The number of the official and complete (milk, fat and protein) recordings in the lactation or other accumulated yield should be reported.
#Permitted range of the daily recorded values is given in Table 5. Outside of these ranges, the daily recorded<ref>'''Note:''' High fat breeds have breed average higher than 5.0 for fat %.</ref> value will be considered as a missing value.

<center>
{| class="wikitable"
! colspan="7" style="text-align:left;" | ''Table 5. Permitted range of the daily recorded values.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| colspan="2" style="text-align:center;" |'''Milk (kg)'''
| colspan="2" style="text-align:center;" |'''Fat %'''
| colspan="2" style="text-align:center;" |'''Protein %'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| style="text-align:center;" | Main Dairy Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 1.5
| style="text-align:center;" | 9.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 7.0
|-
| style="text-align:center;" | High Fat1 Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 2.0
| style="text-align:center;" | 12.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 9.0
|}
</center>1Note: High fat breeds have breed average higher than 5.0 for fat %The true daily recorded values collected from animals labelled by the farmer as sick, injured or under treatment must be used in the computation of the lactation record unless the milk yield is less than 50% of the previous milk yield or less than 60% of the predicted yield. In such a case, the whole set of daily recorded values may be considered as missing.

Estimates of the missing values of a daily recording can be computed by using interpolation procedures or by more sophisticated procedures approved by ICAR

== Samples ==

=== Representative sample ===
The milk sample has to represent the complete milking linked to it. This is achieved by mixing the milk thoroughly or pouring it into another vessel right before sampling.

Sampling scheme P requires using a pipette for making the sample proportional between different milkings.

With sampling scheme E, it is advisable to use a measuring cup to make sure the sample parts actually are equal.

Immediately after sampling, the vials have to be preserved, capped, shaken and marked. Samples should be stored cool and dark.

=== Transport ===
Samples should be transported for analysis to a laboratory as soon as possible after sampling.

The samples need to be packed for transport and handled during transport in a manner that guarantees that sample IDs are not compromised or mixed. It is also recommended to protect the packages from external interference.

The packing material must be clean and disposable or easy to clean.

During transportation, it is recommended that the temperature of the samples stays below +10°C.

== Database ==
Storing the recorded data in a milk recording database is an indispensable part of the recording. It is recommended to use the quickest possible means to store the data in the database in order to ensure up-to-date breeding values and management applications. Where computerised data capture is possible, it should not take more than five days after the recording to have the complete recording data set in the database.

The application of the Guidelines in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield], together with other parts of the Guidelines, ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

The guidelines on storage of data collected by the milk recording process are:

# For every recording, cow identification (ID), 24-hour milk yield or individual milk yields with a minimum of 0.2 kg (or the equivalent thereof) milk accuracy and recording date have to be stored.
# Where possible, it is advisable to store each milking separately. The data stored can include milk yield, time and date of milking, and milking scheme.
# Analysed results of the milk sample are stored, namely: sample ID, fat content (or percentage), sample status, sample type. Optional data can be stored on protein and/or lactose content, somatic cell count and additional analyses.
# Analysis results can be linked to one or more milkings of the cow.
# In case of storage or performance problems it might be necessary to remove old data of individual cow milkings from the database.
# Recording day information is the yield over 24 hours and should at least be kept in the database for the current lactation and the previous lactation.
# If recording day information is changed after batch processing it should be marked with a user-ID and time stamp.
# Yields are stored in kg or lbs or, in the case of fat and protein contents, in percent units.

The necessary additional information about how the results have been obtained include:

# Who did the recording (certified technician, farmer etc.).
# Herd and/or cow milking frequency.
# How many milkings were measured.
# How many milkings were sampled.
# Sampling scheme when sampling.
# Daily yield calculation method used.
# Recording and sampling intervals.
# It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

Basic checks for recording data:

# Farm (herd) ID: identified by a unique key.
# Animal ID: has to be unique in database.
# Format of animal ID: compliant to international standards of identification and registration.
# Recording date: less than or equal to today, greater than last recording date.
# Milk yield: stored with one decimal.
# 24 hour milk yield within range ( Table 5).
# Fat and protein content: e.g. within a range of +/- 3 standard deviation of population average (Table 5).
# Calving date: greater than birthday of cow (e.g. greater than birthday of cow + 20 months).
# Calving date: less than or equal to today.
# Sample analysis

This section of the ICAR Guidelines examines how observations are performed on farms and how data are collected, analysed and reported back to farmers. It forms an integral part with other sections of the ICAR Guidelines. It ensures that samples are analysed to the relevant degree of accuracy for the purposes of milk recording, breeding value prediction and other areas of usage. ICAR members operate in a range of situations, ranging from places with almost fully automated recording systems to areas with no roads and electricity. Therefore, the guidelines only demand standards that can be followed, irrespective of production situations and recommend more advanced options, where possible or required. Under the guidelines some practices might not be permitted while other practices are tolerated but not recommended.

== Yield calculations ==
This section covers 24-hour yields and accumulated yields for milk, fat, protein and somatic cells. It also describes the procedure for acceptance of new methods not previously mentioned in the guidelines.

The basic requirements for all calculation methods are that rounding shall only take place at the last step of the computation.

=== Lactation period ===

==== Commencement of the lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, is considered to commence is:

# The day that the cow calves (calving date), or
# In the absence of a calving date, the best estimate of the day that the cow commenced milk production.

A (valid) calving is defined as a parturition taking place:

# After the mid-point of the gestation period if a service has been recorded, or,
# After at least 75% of the normal gestation period has elapsed since the previous calving recorded if no service event has been recorded.

Any parturition falling outside the above definition shall be recorded as an abortion and shall not start a new lactation period.

For cows of dairy breeds the normal gestation length shall be deemed to be 280 days unless more specific breed information is available for use.

If the first recording is done on the calving date or within the first 4 days after calving, the milk yield and constituents at the first recording should not form part of the official lactation record, especially for automated milking systems (AMS) with multiple recorded days.

==== Completion of lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, has been completed is or:

# The day that the cow ceases to give milk (goes dry) or
# The day the cow gives less than 3.0 kg/day or 1.0 kg/milking in a recording (unless recorded sick) or
# When it is common practice not to record the dry-off date, the day of the midpoint between the last recording with the cow in milk and the first recording day with the animal dry may be assumed to be the dry-off date.

The lactation period ends on whichever date above occurs first.

Cows may be recorded as absent or sick on the recording day, without the lactation period being defined as terminated.

=== Production period ===
In the case where yield records are calculated on the basis of a period of production, usually a year, the record should be expressed as a ‘production period record‘ (symbol PP).

The production period begins the day after the end of the previous production period and ends as defined by the length (in days) of the production period.

=== Additional notes ===
For any ICAR method the interval between two consecutive recordings must routinely fulfil the value for the acceptable range on the herd level.

If the first recording occurs within 14 days from calving, then no adjustment is required to the first recorded value when computing the accumulated record. If the first recording occurs 15 to 95 days from calving, then an adjustment procedure may be applied.

If the 305th day of a lactation falls before the last recording, the interpolation method should be used also for the last period to compute the yields.

=== Standard methods for calculating 24 hour yields ===
The ICAR approved methods are presented in '''[https://www.icar.org/Guidelines/02-Procedure-1-Computing-24-Hour-Yield.pdf Procedure 1 of Section 2]'''. They include:

1. Methods for calculating daily yields from AM/PM milkings:

# Method of Delorenzo and Wiggans (1986)<ref>Delorenzo, M.A., and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. [https://www.journalofdairyscience.org/article/S0022-0302(86)80678-6/pdf J Dairy Sci 69; 2386]</ref>
# Method of Liu et al. (2019). Please note that in 2022 the method of Liu et al. (2000)<ref name=":0">Liu, Z., R. Reents, F. Reinhardt and K. Kuwan. 2000. Approaches to Estimating Daily Yield from Single Milk Testing Schemes and Use of a.m.-p.m. Records in Test-Day Model Genetic Evaluation in Dairy Cattle. [https://www.journalofdairyscience.org/article/S0022-0302(00)75161-7/pdf J. Dairy Sci. 83:2672-2682].</ref> has been updated to the method of Liu et al. (2019). We recommend to organisations that currently have implemented the method of Liu et al. (2000)<ref name=":0" /> to update to method of Liu et al. (2019).
# Method of Kyntäjä et al. (2021)<ref name=":3">1. Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. [https://www.icar.org/Documents/technical_series/ICAR-Technical-Series-no-25-Virtual-Meeting/Kyntaja.pdf ICAR Technical Series no. 25: 171-175.]</ref>

2. Methods to estimate 24h yield from Automatic Milking Systems:

# Using data on more than one day (Lazenby et al., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Using data on 1 day (Bouloc et al., 2002)<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Estimation of fat and protein yield (Galesloot and Peeters, 2000)<ref>Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>
# Sampling period (Hand et al., 2004<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D.F. 2004. Comparison of Protocols to Estimate 24 Hour Percent Fat and Protein. Presented at 34th ICAR session, Sousse, Tunisia, June, 2004. Proceedings of the 34th ICAR Meeting EAAP Publication No. 113:219-224</ref>; Bouloc et al., 2004)

3. Standard methods to estimate 24h yield from electronic milk meters:

# Estimation of 24-hour milk yield
# Using data on more than one day (Hand et al., 2006)<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. [https://doi.org/10.3168/jds.S0022-0302(06)72240-8 J. Dairy Sci. 89:1723-1726]</ref>
# Estimation of 24-hour fat and protein yield

=== Standard methods for calculating accumulated yields ===
The ICAR approved methods are presented in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_2_%E2%80%93_Computing_of_Accumulated_Lactation_Yield Procedure 2 of Section 2]. They include:

# Test Interval Method (TIM) (Sargent, 1968)<ref>Sargent, F.D., V.H. Lyton, and O.G. Wall, Jr . 1968. Test interval method of calculating Dairy Herd Improvement Association records. [https://doi.org/10.3168/jds.S0022-0302(68)86943-7 J. Dairy Sci. 51:170].</ref>
# Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987)<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. [https://doi.org/10.1016/0301-6226(87)90049-2 Livest. Prod. Sci. 17:l].</ref>
# Best prediction (VanRaden, 1997)<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. [https://doi.org/10.3168/jds.S0022-0302(97)76268-4 J. Dairy Sci. 80:3015-3022].</ref>
# Multiple-Trait Procedure (MTP) (Schaeffer and Jamrozik, 1996)<ref>Schaeffer, L.R. and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. [https://doi.org/10.3168/jds.S0022-0302(96)76578-5 J. Dairy Sci. 79:2044-2055.]</ref>

=== Procedure to approve new methods ===

# All parties interested in seeking approval for any new accumulated yield calculation method will notify the ICAR Secretariat and provide a description of the proposed method.
# These parties will provide a detailed report including statistical details, scientific references and other relevant data to the ICAR Dairy Cattle Milk Recording Working Group.
# The ICAR Dairy Cattle Milk Recording Working Group will then consider the proposal and recommend that it be conditionally approved, approved or rejected.
# The final steps will consist of approval by the General Assembly and publication in the guidelines. .

== Reporting ==
This subsection covers reports, data files, statistics and calculated key figures provided to farmers for breeding and management purposes.

It is recommended that farmers are given reports after each recording and at the end of the recording year or another longer recording period. These reports should contain data on both cow and herd level. In bigger herds, it is also advisable to present results by management groups or otherwise chosen cow groups within the herd. The reporting may be done on paper, through web pages and/or in the form of data files or electronic reports.

Where data files are distributed or direct access given to the results in the database, care must be taken that data ownership is clearly defined. This also includes defining who has access to data and how this access can be authorised.

ICAR members are advised to prepare annual statistics in a reasonable timeframe after closing the recording year. The minimum data requirements are what is needed for the ICAR [https://my.icar.org/stats/list Dairy Cattle Yearly Enquiry on-line database].

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 5. Examples of key figures for herd to be used by farmers and other users.''
|- style="background-color:#efefef; text-align:center;"
|style="text-align:left |'''Key figure'''
|style="text-align:left |'''Explanation'''
|-
| style="text-align:left;" | 12-month rolling average yield
| style="text-align:center;" | Total milk, fat and protein produced during the 365 (366) days preceding the recording divided by the average number of cows for the same period.
|-
| style="text-align:left;" | Average 305-day yield
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations finished during the reporting period divided with the number of finished 305-day lactations.
|-
| style="text-align:left;" | Average 305-day yield within a period
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations during the reporting period divided with the average number of cows on a 305-day lactation within the reporting period.
|-
| style="text-align:left;" | Average annual yield
| style="text-align:center;" | Total milk, fat and protein produced during the recording year divided by the average number of cows for the same recording year.
|-
| style="text-align:left;" | Average calving interval
| style="text-align:center;" | The average preceding intervals of all calvings second and more during the reporting period.
|-
| style="text-align:left;" | Average fat, protein or lactose contents in milk
| style="text-align:center;" | Total fat, protein and lactose yields divided by the total milk yield, usually expressed with two decimals.
|-
| style="text-align:left;" | Average lactation yield
| style="text-align:center;" | Total milk, fat and protein produced within lactations of any length finished during the reporting period divided with the number of finished lactations.
|-
| style="text-align:left;" | Average lactation yield within a period
| style="text-align:center;" | Total milk, fat and protein produced during the reporting period divided with the average number of cows in milk within the reporting period.
|-
| style="text-align:left;" | Average number of cows
| style="text-align:center;" | Average number of cows in the herd (or group) on a given day during the reporting period. Usually expressed with one decimal.
|-
| style="text-align:left;" | Average somatic cell count
| style="text-align:center;" | The average of all individual cow somatic cell counts weighted for individual milk yields.
|-
| style="text-align:left;" | Daily milk, fat and protein yields
| style="text-align:center;" | 1) Total daily milk, fat and protein yields divided by number of cows, or 2) Total daily milk, fat and protein yields divided by number of cows in milk.
|-
| style="text-align:left;" | Energy Corrected Milk (ECM)
| style="text-align:center;" | Calculated according to a national standard.
Example from the Nordic countries:

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + milk yield, kg * 0.7832)/3.14

or, if lactose has been analysed

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + lactose yield * 16.54 + milk yield, kg * 0.0207)/3.14.

From solids expressed as %:

ECM = [(fat content, % * 383 + protein content, % * 242 + 783.2)/3140]* milk yield, kg

or, if lactose has been analysed

ECM = [(fat content, % * 383 + protein content, % * 242 + lactose content, % * 165.4 + 20.7)/3140]* milk yield, kg.
|-
| style="text-align:left;" | Number of lactations
| style="text-align:center;" | Total number of finished lactations in the herd (or group) during the reporting period.
|-
| style="text-align:left;" | Reporting period
| style="text-align:center;" | The period presented in the given report. The most usual options are: one day, one recording interval, lactation, rolling 365 days, recording or calendar year, and the cow’s lifetime.
|}
</center>

== Decisions ==

As a result of the recording process and reports prepared on the basis of its results, decisions can be made on one or more of the following:

=== Short term impact: day-to-day management decisions taken on farms ===

# Decisions about bulk milk quality.
# Feeding decisions - daily diet based on group or individual performance.
# Pasture management decisions.
# Grouping decisions - placing cows in different management or feeding groups.
# Culling decisions - decisions on the sale or slaughter of cattle.
# Mating decisions.
# Decisions regarding programmes of certification for milk and milk products.
# Decisions based on data flow from MRO’s to farms and vice versa.

=== Medium-term impact ===

# Farmers’ decisions based on advisory services, veterinarians, independent experts and other services.
# Decisions about production planning on farms (herd development).

=== Long-term impact ===
# Breeding programme and selection decisions - breeding partners informed by genetic evaluation ([[Section 09 – Dairy Cattle Genetic Evaluation|Section 9)]] based on milk recording results.
# Decisions based on herd book and breeder association activities and deciding on business actions related to breeding animals, i.e. in some countries animal recording data are required for international trade with breeding animals.

=== Strategic decisions ===
# Research programmes concerning management, recording and breeding.
# Political decisions about possible subsidies in dairy cattle breeding at the governmental level and implementing measurements according to agriculture policy.

== Quality control ==
This Section together with other parts of the Guidelines ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

=== Bulk tank data comparison ===
It is a recommended practice to compare milk recording data with dairy deliveries and bulk tank milk contents. This can be done on the recording day or over a longer period of time. The calculation is done as follows:

# Comparison ratio = Total recorded milk yield, kg /Total milk produced, kg. This comparison is used where there is a reliable estimate of the farm use of milk.
# Quick comparison ratio = Total recorded milk yield, kg/ Total milk delivered, kg. This comparison is used where farm use of milk is not estimated.
# Content comparison = Recorded average fat / Bulk tank average fat
# Comparison ratio for fat = Total recorded fat yield, kg/ Total fat produced, kg
# Total recorded milk yield, kg = Ʃ (Individual milk yield, kg)
# Total milk delivered, kg = Total milk delivered, litres * milk density kg/litre
# Total milk produced, kg = (Total milk delivered, litres + Milk used or discarded on the farm, litres) * milk density kg/litre
# Total fat produced, kg = Total milk produced, kg x (Bulk tank fat percent/100)
# Recorded average fat = Ʃ [Individual milk yield kg x (Individual fat percent/100)]/Ʃ (Individual milk yield, kg)

The recommended acceptable range for comparison ratios is 0.95 - 1.05, and for quick comparison ratios 0.90 - 1.00, with due regard to herd size.

=== One day bulk tank data comparison ===
Milk yields and fat yields or contents are compared on the recording day. Comparing the contents is routinely possible where every delivery is sampled or by taking a bulk tank sample (see point [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Bulk_tank_data_comparison 1.10] above for how the comparison is done.)

=== Bulk tank data comparison over a longer period ===
Milk yields and fat yields or contents are compared over a longer period of time, e.g. 4 months or 12 months. This option requires a routine to obtain the applicable data from the dairies or milk buyers. Farm use of milk may be taken into account where applicable.

=== Bulk tank sample ===
Bulk tank samples can be used to verify the milk contents analysis obtained in milk recording. A sample is taken from a well-mixed bulk tank on the recording day. It must represent the milk of the whole 24-hour period. Bulk tank fat and protein contents are then compared to the weighted averages of the fat and protein percent obtained from milk recording. Normally, the difference between the values should not be more than 5%.

=== Supervised or repeated recording ===
Supervised recording is a tool designed to verify that individual cow records are reliable. It is based on repeating the herd recording as soon as possible after the original recording, and the obtained results are compared with the original recording. It is obligatory for ICAR Certificate of Quality (CoQ) holders to practice regular supervision, irrespective of recording methods used.

It is recommended that the supervised recording will follow immediately after the original recording, but for a good reason it can be postponed for up to 7 days.

The farmer and any other staff doing the original recording must not know that a supervised recording will follow. The technician who performs the supervised recording should not be the same person who did the original recording.

Usually supervised recording is done by recording the whole herd again, using the same sampling scheme and recording method (or a reference method) as in the previous recording. When herd size exceeds 200 cows, it is also allowed to do a supervised recording to selected, or randomised groups of animals in the herd.

Choosing the herds for supervised recording may be random or based on preselection. Traits for this preselection may include high yield, great increase in yield, presence of bull dams in the herd, and general suspicions about the correctness of herd results.

The traits compared in supervised recording must include milk and fat. Comparing protein is also recommended.

=== Supervision - example of comparison calculations ===

# Milk, fat and protein yields per cow are calculated for both the original and the supervised milking.
# Individual cow records where results between supervised recording and the original recording differ outside the norms might be excused where a good explanation can be given for exclusion (illness, heat, missed milking)
# Deviations (%) are calculated for each cow and yield constituent according to the formula: deviation = (supervised yield/unsupervised yield)*100-100
# Herd averages of the absolute values for each yield constituent are calculated.
# If the supervised recording occurs within 2 days of the original recording, the acceptable difference in herd averages are 7% for milk and protein and 9% for fat.
# If the supervised recording occurs between 3 and 7 days after the original recording, the acceptable difference of the aforementioned herd averages are 9% for milk and protein and 12% for fat.

The limits mentioned in these examples are typically applied by some of the member organisations, and are not meant to be understood as exact norms. Such norms should be laid down by each member organisation.

=== Evaluation of recording data ===
It is recommended that data quality is evaluated for each herd recording day. When such an evaluation is applied, the following features of the data have to be included:

# Person responsible for the recording.
# ICAR approval and calibration status of the recording equipment if owned by the farmer.
# Number of herd recordings per time period and/or recording interval.
# Number of herd samplings per time period and/or sampling interval.

The following features are also recommended to be included if possible:

# Deviation of milk and fat yields from dairy deliveries.
# Deviation of milk and fat yields from previous or predicted yields.
# Standard deviation of individual cow records.
# Number of recorded and/or sampled milkings within the recording day.
# Number of cows missed or not recorded in the recording.
</div>
</div>
= Procedures =
== Procedure 1: Computing 24-hour Yields ==

<div class="mw-collapsible mw-collapsed">
<div>

=== Methods to calculate 24-hour yield for milk yield and fat percentage from a single milking ===

==== Method of Delorenzo & Wiggans (1986)<ref>Delorenzo, M.A. and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. J. Dairy Sci. 69: 2386-2394.</ref> ====
Daily milk (DMY) and fat yield (DFY) estimates are based on measured yield and milking frequency. An adjustment factor accounts for differences in the average milking interval (expressed in decimal hours) between the preceding milking and the measured milking, and the time of day of the measured milking (started in a.m. or p.m.). For 2X milking, an additional adjustment is applied to milk yield for the interaction between milking interval and stage of lactation, with mid lactation (158 DIM) set to zero. Milking interval does not affect protein and solids non fat (SNF) percentages and so the percentages for the sampled milking are used for test-day estimates. Protein yield is calculated from the measured percentage and the adjusted milk yield.

The prediction of DMY and DFY from single milking on morning or evening in herds milked twice a day requires factors, that are the reciprocal of the proportion of total yield expected from single milkings in relation to the milking interval.

We propose to derive these coefficients (intercept, slope, etc.) for each country separately.

===== Adjustment of milking interval =====
The milking interval is the interval between milking time for the observed milking and the milking time preceding the observed milking. The milking interval is divided into 15-minutes classes. Factors for milk and fat yields may be calculated to each class using Equation 1:

''Equation 1. Factors for milk and fat yields.''
[[File:Equation 1.png|none|thumb|397x397px]]

===== Adjustment of lactation stage =====
Because the lactation stage of the cow has an influence on the effect of different milking intervals on milk production a second adjustment is made for every interval class through a covariate of days in milk as addition:

Covariate x (days in milk - 158)

===== Estimating sample day yields =====
Formulas for prediction sample day yields and percentages in herds with two milkings are:

''Equation 2. Equation for predicting 24-hour milk yield.''
[[File:Equation2.png|none|thumb|428x428px]]

''Equation 3. Equation for predicting 24-hour fat percentage.''
[[File:Equation3.png|none|thumb|431x431px]]

''Equation 4. Equation for predicting 24-hour fat yield.''
[[File:Equation4.png|none|thumb]]

''Equation 5. Equation for predicting 24-hour protein yield.''
[[File:Equation5.png|none|thumb|316x316px]]

===== Calculation examples =====

====== Practical Application ======
Two sets of factors are available for estimating DMY from a single milking, each for morning or evening milking sampling. The factors are calculated from the formula as described above and given in Table 1.
<center>
{| class="wikitable"
| colspan="5" align="left" |'''''Table 1. Factor of milk yield and covariate for herds milked twice a day.'''''
|- style="background-color:#efefef;"
| rowspan="2" align="center" |'''Length of milking interval in hours (minutes in decimal)'''
| colspan="2" align="center" |'''Morning milking'''
| colspan="2" align="center" |'''Evening milking'''
|- style="background-color:#efefef;"
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
|-
| align="center" |< 9.00
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.594
| align="center" |0.00378
|-
| align="center" |9.00-9.24
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.534
| align="center" |0.00485
|-
| align="center" |9.25-9.49
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.477
| align="center" |0.00486
|-
| align="center" |9.50-9.74
| align="center" |2.411
| align="center" |0.00716
| align="center" |2.423
| align="center" |0.00511
|-
| align="center" |9.75-9.99
| align="center" |2.359
| align="center" |0.00726
| align="center" |2.370
| align="center" |0.00473
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |10.00-10.24
| align="center" |2.310
| align="center" |0.00458
| align="center" |2.321
| align="center" |0.00337
|-
| align="center" |10.25-10.49
| align="center" |2.262
| align="center" |0.00399
| align="center" |2.273
| align="center" |0.00214
|-
| align="center" |10.50-10.74
| align="center" |2.217
| align="center" |0.00294
| align="center" |2.227
| align="center" |0.00000
|-
| align="center" |10.75-10.99
| align="center" |2.173
| align="center" |0.00223
| align="center" |2.183
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |11.00-11.24
| align="center" |2.131
| align="center" |0.00000
| align="center" |2.140
| align="center" |0.00000
|-
| align="center" |11.25-11.49
| align="center" |2.091
| align="center" |0.00000
| align="center" |2.099
| align="center" |0.00000
|-
| align="center" |11.50-11.74
| align="center" |2.052
| align="center" |0.00000
| align="center" |2.060
| align="center" |0.00000
|-
| align="center" |11.75-11.99
| align="center" |2.014
| align="center" |0.00000
| align="center" |2.022
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |12.00
| align="center" |2.000
| align="center" |0.00000
| align="center" |2.000
| align="center" |0.00000
|-
| align="center" |12.01-12.24
| align="center" |1.978
| align="center" |0.00000
| align="center" |1.986
| align="center" |0.00000
|-
| align="center" |12.25-12.49
| align="center" |1.943
| align="center" |0.00000
| align="center" |1.951
| align="center" |0.00000
|-
| align="center" |12.50-12.74
| align="center" |1.910
| align="center" |0.00000
| align="center" |1.917
| align="center" |0.00000
|-
| align="center" |12.75-12.99
| align="center" |1.877
| align="center" |0.00000
| align="center" |1.884
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |13.00-13.24
| align="center" |1.846
| align="center" |0.00000
| align="center" |1.852
| align="center" |-0.00190
|-
| align="center" |13.25-13.49
| align="center" |1.815
| align="center" |0.00000
| align="center" |1.822
| align="center" |-0.00231
|-
| align="center" |13.50-13.74
| align="center" |1.786
| align="center" |-0.00167
| align="center" |1.792
| align="center" |-0.00308
|-
| align="center" |13.75-13.99
| align="center" |1.757
| align="center" |-0.00258
| align="center" |1.763
| align="center" |-0.00339
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |14.00-14.24
| align="center" |1.730
| align="center" |-0.00347
| align="center" |1.736
| align="center" |-0.00509
|-
| align="center" |14.25-14.49
| align="center" |1.703
| align="center" |-0.00363
| align="center" |1.709
| align="center" |-0.00471
|-
| align="center" |14.50-14.74
| align="center" |1.677
| align="center" |-0.00332
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |14.75-14.99
| align="center" |1.652
| align="center" |-0.00316
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |≥ 15.00
| align="center" |1.628
| align="center" |-0.00235
| align="center" |1.683
| align="center" |-0.00454
|}
</center>

For estimating daily fat percentage there is only one table independent of morning or evening sampling – refer to Table 2.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" |'''''Table 2. Factor of fat percentage for herds milked twice a day.'''''
|- style="background-color:#efefef;"
|'''Length of milking'''

'''interval in hours'''
|'''Fat (percentage'''

'''factor)'''
|-
|< 9.00
|0.919
|-
|9.00-9.24
|0.927
|-
|9.25-9.49
|0.934
|-
|9.50-9.74
|0.941
|-
|9.75-9.99
|0.948
|-
|
|
|-
|10.00-10.24
|0.955
|-
|10.25-10.49
|0.961
|-
|10.50-10.74
|0.968
|-
|10.75-10.99
|0.974
|-
|
|
|-
|11.00-11.24
|0.980
|-
|11.25-11.49
|0.986
|-
|11.50-11.74
|0.992
|-
|11.75-11.99
|0.997
|-
|
|
|-
|12.00
|1.000
|-
|12.01-12.24
|1.003
|-
|12.25-12.49
|1.008
|-
|12.50-12.74
|1.013
|-
|12.75-12.99
|1.018
|-
|
|
|-
|13.00-13.24
|1.023
|-
|13.25-13.49
|1.028
|-
|13.50-13.74
|1.033
|-
|13.75-13.99
|1.037
|-
|
|
|-
|14.00-14.24
|1.042
|-
|14.25-14.49
|1.046
|-
|14.50-14.74
|1.050
|-
|14.75-14.99
|1.054
|-
|≥ 15.00
|1.058
|}
</center>

Milking-interval factors are calculated using Equation 1, where the intercept and slope are as in Table 3.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 3. Slope and intercept for milk yield and fat yield.'''''
|- style="background-color:#efefef;"
| rowspan="2" |'''Trait'''
| colspan="2" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started in a.m.'''
|'''For measured milking started in p.m.'''
|-
|Milk yield
|0.0654
|0.0634
|0.0363
|-
|Fat yield
|0.1965
|0.1939
|0.0254
|}
</center>
The milking interval has no significant influence on protein percentage. Therefore, the protein percentage of the sampled milking is used as the daily protein percentage.

====== Calculation of daily yields from morning milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Data for a cow from morning milking.'''''
|-
|Begin of recording:
|6:15
|(Morning milking)
|-
|Start of preceding milking:
|17:25
|
|-
|Length of milking interval:
|12 hours 50 minutes
|(Expressed as decimal 12.83)
|-
|Milk results at morning:
|12,0
|Milk-kg
|-
|
|4,12
|Fat-percentage
|-
|
|3,45
|Protein-percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 5. Factors for morning milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.877
|-
|The covariate is
|0
|-
|The factor for fat percentage from Table 2 is
|1.018
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 6. Example calculations for morning milking.'''''
|-
|The sample-day milk yield:
|1.877 x 12,0 kg + 0 x (120 - 158) = 22,5 kg
|-
|The sample-day fat percentage:
|1.018 x 4,12 = 4,19
|-
|The sample-day fat yield:
|22,5 kg x 0,0419 = 0,94 kg
|-
|The sample-day protein yield:
|22,5 kg x 0,0345 = 0,78 kg
|}
</center>

====== Calculation of daily yields from evening milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 7. Data for a cow from evening milking.'''''
|-
|Begin of recording:
|16:48
|Evening milking
|-
|Start of preceding milking:
|6:35
|
|-
|Length of milking interval:
|13 hours 47 minutes
|Expressed as decimal 13.78
|-
|Milk results at evening:
|14,0
|Milk kg
|-
|
|4,00
|Fat percentage
|-
|
|3,40
|Protein percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 8. Factors for evening milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.763
|-
|The covariate is
|<nowiki>-0,00339</nowiki>
|-
|The factor for fat percentage from Table 2 is
|1.037
|}
{| class="wikitable"
| colspan="2" |'''''Table 9. Example calculations for evening milking.'''''
|-
|The sample-day milk yield:
|1.763 x 14,0 kg - 0,00339 x (120 - 158) = 24,8 kg
|-
|The sample-day fat percentage:
|1.037 x 4,00 = 4,15
|-
|The sample-day fat yield:
|24,8 kg x 0,0415 = 1,03 kg
|-
|The sample-day protein yield:
|24,8 kg x 0,0340 = 0,84 kg
|}
</center>

====== Alternate recording of components and milk yield at both milkings ======
For this plan only the sample-day fat yield has to be calculated with regard to milking interval. The milk yield is the sum of evening and morning milk results.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 10. Example data for a cow from both milkings.'''''
|-
|Begin of recording evening:
|17:25
|
|-
|Milk results at evening:
|10:00
|Milk kg (only milking-yield)
|-
|Begin of recording morning:
|6:15
|
|-
|Milk results at morning:
|12:00
|Milk kg
|-
|
|4:20
|Fat percentage
|-
|
|3:50
|Protein percentage
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 11. Factor for fat percentage.'''''
|-
|Length of milking interval:
|12 hours 50 minutes (expressed

as decimal 12.83)
|-
|The factor for fat percentage from Table 2 is
|1.018.
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 12. Example calculation of daily yields.'''''
|-
|The sample-day milk yield:
|10,0 kg + 12,0 kg = 22,0 kg
|-
|The sample-day fat percentage:
|1.018 x 4,20 = 4,28
|-
|The sample-day fat yield:
|22,0 kg x 0,0428 = 0,94 kg
|-
|The sample-day protein yield:
|22,0 kg x 0,0350 = 0,77 kg
|}
</center>

====== Calculation for 3X Milking ======
For 3X herds, a single milking or two consecutive milkings may be weighed. The sample may be collected at one or both of these milkings. Stage of lactation × milking interval adjustments are not used for greater than 2× milking. These AM/PM factors for estimating daily yields in 3X herds should not be confused with factors that adjust 3X records to a 2X basis. Milking-interval factors are calculated using the same formula with the intercept and slope as in Table 13.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" align = "left" |'''''Table 13. Slope and intercept factors for 3X milking.'''''
|- style="background-color:#efefef;"
| rowspan="2" | '''Trait'''
| colspan="3" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started between 2 a.m. and 9:59 a.m.'''
|'''For measured milking started between 10 a.m. and 5:59 p.m.'''
|'''For measured milking started between 6:00 p.m. and 1:59 a.m.'''
|-
|Milk yield
|0.077
|0.068
|0.066
|0.0329
|-
|Fat yield
|0.186
|0.186
|0.182
|0.0186
|}
</center>
When two milkings are included for sampling, the intercepts and intervals for both milkings are included in determining a factor for calculated estimated milk yield that is applied to the total yield from both milkings as in Equation 6.

''Equation 6. Milking interval factor for 3X milking.''
[[File:Equation6.png|none|thumb|536x536px]]
Milk and fat percent factors are calculated separately based on the number of milkings weighed or sampled.

====== Calculation for 4X - 6X Milking ======
The intercept terms for calculating 3X factors (0.077, 0.068, and 0.066) are multiplied by the factor [3 / (milkings per day)] for use in calculating factors for milking frequencies greater than 3X.

==== Method of Liu et al. (2019) ====
A multiple regression method (MRM) is used for estimating 24-hour daily milk yield (DMY), daily fat yield (DFY) and daily protein yield (DPY) based on partial yields from either morning (AM) or evening (PM) milking. Fat percentage (DFP) or protein percentage (DPP) on a 24-hour daily basis are then derived using the estimated 24-hour daily yields. The MRM can be used as a reference method for estimating daily yields and component percentages.

The method of Liu et al. (2019) is an updated version of the method of Liu et al. (2000). The model is only used for farms with 2 time milkings during 24 hours.

The following formula is used to estimate DMY, DFY, DPY based on partial yields (PMY, PFY,PPY) from either morning (AM) or evening (PM) milking:

''Equation 7. Model for predicting 24-hour yield.''

''yijk = a + bijk * xijk''

where:

yijk is the estimated 24-hour daily yield (DMY, DFY or DPY);

xijk is AM or PM partial daily yield on a test day (PMY, PFY, or PPY).

Subscript '''''i''''' represents class of parity effect with 2 levels: first and higher parities.

Subscript '''''j''''' represents class of length of preceding milking interval with 8 levels for AM milking: < 720 minutes, < 740 minutes, < 760 minutes, < 780 minutes, < 800 minutes, < 820 minutes, < 840 minutes, >= 840 minutes and 8 levels for PM milking: < 600 minutes, < 620 minutes, < 640 minutes, < 660 minutes, < 680 minutes, < 700 minutes, < 720 minutes, >= 720 minutes.

Subscript '''''k''''' represents class of lactation stage with 7 classes: < 60 days, < 120 days, < 180 days, < 240 days, < 300 days, < 360 days, >= 360 days.

'''''a''''' is the estimated intercept for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

'''''b'''''ijk is the estimated slope for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

The factors for '''''a''''' and '''''b'''''ijk can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Appendix_1_-_Adjustment_factors_to_calculate_24-hour_yields_using_the_Liu_method Appendix 1].

For a given yield trait a total number of 112 formulae are to be estimated for calculating 24-hour daily yield based on partial yield from either AM or PM milking. Component percentage for fat (DFP) and protein (DPP), on a 24-hour basis is calculated by dividing estimated fat or protein yield by estimated daily milk yield:[[File:Imagefinal.png|center|thumb|339x339px]]

===== Calculation example with method of Liu et al. (2019) =====
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" align = "left" |'''''Table 14. Data from an evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="6" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="6" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="6" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow'''

'''ID'''
|'''Calving date'''
|'''Lactation number'''
| colspan="2" |'''Milk yield (kg)'''
|'''Fat content (%)'''
|'''Protein content (%)'''
|'''Fat yield (kg)'''
|'''Protein yield (kg)'''
|'''Index1'''
|-
|A
|01.01.2020
|1
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1132
|-
|B
|01.01.2020
|2
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1232
|-
|C
|27.03.2020
|1
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1131
|-
|D
|27.03.2020
|2
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1231
|-
|
|
|
|
|
|
|
|
|
|
|}
'''1''' Index is marked in the Appendix table.
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 15. Calculation of 24-hour daily yield and components for evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="3" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="3" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="3" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow ID'''
|'''DMY (kg)'''
|'''DFY (kg)'''
| colspan="2" |'''DPY (kg)'''
|'''DFP (%)'''
|'''DPP (%)'''
|-
|A
|3,47396+25,0

<nowiki>*</nowiki> 1,98268 = 53,0401 ≈ '''53,0'''
|0,2135+0,995

<nowiki>*</nowiki> 1,68050 = 1,8855975
| colspan="2" |0,10471+0,8325* 1,99092 = 1,7621509
|1,8855975 / 53,04096*100

≈ '''3,55'''
|1,7621509 / 53,04096*100

≈ '''3,32'''
|-
|B
|4,15080+25,0* 1,98520 = 53,7808 ≈ '''53,8'''
|0,3635+0,995

<nowiki>*</nowiki> 1,47515 = 1,8312743
| colspan="2" |0,13952+0,8325* 1,97074 = 1,7801611
|1,8312743 / 53,7808*100

≈ '''3,41'''
|1,7801611 / 53,7808*100

≈ '''3,31'''
|-
|C
|2,80244+33,1

<nowiki>*</nowiki> 2,02183 = 69,72501 ≈ '''69,7'''
|0,17663+1,3339 * 1,72438 = 2,4767805
| colspan="2" |0,11078+1,1122 * 1,96422 = 2,2953855
|2,4767805 / 69,725013*100

≈ '''3,55'''
|2,2953855 / 69,725013*100

≈ '''3,29'''
|-
|D
|3,85525+33,1 * 2,00429 = 70,19725 ≈ '''70,2'''
|0,27991+1,3339 * 1,62403 = 2,4462036
| colspan="2" |0,12863+1,1122* 1,98973 = 2,3416077
|2,4462036 / 70,7197249*100 ≈ '''3,48'''
|2,3416077 / 70,7197249*100 ≈ '''''3,34'''''
|-
|
|
|
|
|
|
|
|}
</center>
'''Note''' that intercepts and slopes of the applied regression formulae are underscored.

===== Fat correction for equal measure sampling =====
With Equal measure sampling, it is advisable to use Equation 8 (or the like) to correct fat contents:

Equation 8. Fat correction for equal measure sampling.

Fat, % = Analysed fat, % + 0.69 – 1.3 x (morning milk/ 24-hour milk)

The relation of morning milk to 24-hour milk is to be calculated to at least four decimals.

==== 1.1 Method of Kyntäjä & Nokka (2021)<ref name=":3" />: 24-hour correction factors for fat percentage ====
This method can be applied to calculate 24-hour correction factors for fat percentage, in case the milk recording is based on two milkings, with at least one known milk yield and one sample. A 24-hour recording day is assumed.

The conventional way to calculate correction factors is based on a data set where all milkings have been recorded and analysed separately. This approach requires a lot of effort and extra analysis, and is not cheap to organise. Organisations that have access to a large number of records may be able to use those data to calculate correction factors even if they have no extra analysis.

Requirements for the data set:

# The data set has to be large enough. Every single factor needs to be based on at least 10,000 or, even better, 100,000 observations.
# Each individual data set must contain at least one preceding milking interval, milk weight, and analysed sample. If it contains more milk weights, intervals etc. that is even better. It is also good to include breed, lactation number, days in milk and other data that may have an effect on the factors.

===== Calculation example of the method of Kyntäjä & Nokka (2021)<ref>Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. ICAR Technical Series no. 25: 171-175.</ref> =====

====== The accumulated data set ======
Since 2003, Finland had accumulated a data set of 7.5 million recordings with data on the time of the sampled and preceding milking as reported by the farmer, the lab analysis results, and the 24-hour milk yield. Grouped according to the preceding interval, the analysed fat content gives a nice sigmoid curve with the highest fat content found after a 540 to 630 minutes’ interval (9 to 10.5 hours) and the lowest at 810 to 930 minutes (13.5 to 15.5 hours).
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 16. Average analysed milk fat percentage by preceding interval class, 2003 – 2020.'''''
|- style="background-color:#efefef;"
|'''Interval before'''

'''Sampling (minutes)'''
|'''Number of samples'''
|'''Median interval in the class'''
|'''Average fat content analysed (%)'''
|-
|<510
|93,577
|495
|4.20
|-
|510-539
|19,523
|525
|4.70
|-
|540-569
|111,268
|555
|4.79
|-
|570-599
|253,807
|585
|4.83
|-
|600-629
|1,461,587
|615
|4.75
|-
|630-659
|919,968
|645
|4.66
|-
|660-689
|1,168,683
|675
|4.56
|-
|690-719
|223,877
|705
|4.42
|-
|720-749
|517,447
|735
|4.28
|-
|750-779
|212,428
|765
|4.16
|-
|780-809
|924,014
|795
|4.12
|-
|810-839
|698,463
|825
|4.09
|-
|840-869
|1,104,778
|855
|4.07
|-
|870-899
|154,561
|885
|4.05
|-
|900-929
|77,024
|915
|4.07
|-
|>929
|26,977
|945
|4.13
|}
</center>

The results were also divided into subgroups according to lactation number, phase of lactation, and breed. The effect of the preceding milk interval on milk fat seems to be bigger with older cows and in the beginning of lactation. It was also bigger with Ayrshire cows as compared with Holsteins. At this point, however, the decision was made not to take these factors into account when calculating new correction factors.

====== Calculation of new factors ======
The results above were turned into a simple set of correction factors, dependent solely on the preceding interval. In order to do this, two assumptions were made:

# A 24-hour recording day was assumed. This way, we can deduce the second milking interval from the one we know and mirror the fat percent for that milking.
# Milk secretion rate was assumed to be constant around the 24-hour period. This allows us to deduce the share of the 24-hour yield produced at each milking.

These assumptions allow us to create the new correction factors by mirroring the milk yield and milk fat content in the milking whose actual data we have not got. This way, we get the following formula:

Equation 9. Correction factor.
[[File:Equation9.png|none|thumb|545x545px]]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left" |'''''Table 17. Calculation of the mirrored milking and the correction factors'''''
|- style="background-color:#efefef;"
|'''Interval before sampling (minutes)'''
|'''Average fat in the sampled milking (%)'''
|'''Share of 24-hour milk in the sampled milking'''
|'''Mirrored interval (minutes)'''
|'''Average fat in the mirrored milking (%)'''
|'''Calculated 24-hour average fat(%)'''
|'''Correction factor'''
|-
|<510
|4.21
|0.34
|>929
|4.14
|4.16
|0.989
|-
|510-539
|4.77
|0.36
|900-929
|4.08
|4.33
|0.907
|-
|540-569
|4.82
|0.39
|870-899
|4.05
|4.35
|0.903
|-
|570-599
|4.84
|0.41
|840-869
|4.07
|4.38
|0.906
|-
|600-629
|4.76
|0.43
|810-839
|4.09
|4.37
|0.919
|-
|630-659
|4.66
|0.45
|780-809
|4.12
|4.36
|0.936
|-
|660-689
|4.56
|0.47
|750-779
|4.16
|4.35
|0.953
|-
|690-719
|4.43
|0.49
|720-749
|4.29
|4.36
|0.984
|-
|720-749
|4.29
|0.51
|690-719
|4.43
|4.36
|1.016
|-
|750-779
|4.16
|0.53
|660-689
|4.56
|4.35
|1.046
|-
|780-809
|4.12
|0.55
|630-659
|4.66
|4.36
|1.059
|-
|810-839
|4.09
|0.57
|600-629
|4.76
|4.37
|1.070
|-
|840-869
|4.07
|0.59
|570-599
|4.84
|4.38
|1.076
|-
|870-899
|4.05
|0.61
|540-569
|4.82
|4.35
|1.073
|-
|900-929
|4.08
|0.64
|510-539
|4.77
|4.33
|1.062
|-
|>929
|4.14
|0.66
|<510
|4.21
|4.16
|1.006
|}
</center>

=== Methods to calculate 24-hour yields in Automatic Milking Systems ===

==== General remarks about calculation of 24-hour milk yield ====
It is characteristic for AMS systems that individual cows set their own milking rhythm, thus making it largely irrelevant to use the traditional model of measuring milk yields and sampling at all milkings in the herd during the recording day. In order to determine how much an individual cow’s real 24-hour milk, fat and protein yield is, more complex calculations are required, especially with milk fat that varies considerably from milking to milking. For protein content and cell counts, no correction is needed for a one-milking sample.

The basic idea with calculating a 24-hour milk yield from AMS data is that milk yields per milking are converted into milk yield per time unit (minute or hour) during the preceding interval. This milk yield per time unit is then converted into milk yield in 24 hours. In order to do this, the data set must also contain time stamps for each milking.

How many milkings or how long a measurement period is used for creating 24-hour yields depends on the milk recording organisation. The fewer milkings are used the more random variance there will be in the individual cow milk yields. The absolute minimum is two milkings with preceding intervals, while a measuring period of 96 hours is recommended.

The sampled milking must always be inside the milk yield measurement period. For the calculation of fat and protein yields, it is recommended to use only those milk yields that are from the same period or day. With Z sampling, the 24-hour fat and protein yields may be calculated based on a shorter measurement period than what is used for calculating the 24-hour milk yields.

==== Calculation of milk yield using data of several days (Lazenby ''et al''., 2002<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Automatic Milking Systems (AMS). The average of most recent milk weights can be calculated using a number of preceding milkings or a number of preceding days. If number of milkings is used, the optimal estimate of the milking rate is obtained using an average of current milking together with the 12 most recent milkings back in time. The optimal estimate is the maximum value of the difference curve at which the correlation with the ‘true’ 24-hour milk yield is greatest and the variance across milkings is minimized. If number of days is used, the optimal estimate of the milking rate is obtained using an average of all milkings occurred in the last 96 hours (4 most recent days). In Table 18 the percent of maximum difference for various number of milkings and days is reported. The optimal estimate is independent from stage of lactation and parity.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 18. Percent maximum for different number of days and milkings.'''''
|- style="background-color:#efefef;"
|'''Days'''
|'''Percent Max.'''
|'''Current milking'''

'''+ most recent milkings'''
|'''Percent max.'''
|-
|1
|49.38
|10
|97.85
|-
|2
|77.26
|11
|99.08
|-
|3
|92.34
|12
|99.70
|-
|4
|98.91
|13
|99.81
|-
|5
|98.50
|14
|99.40
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table19.png|center|thumb|911x911px]]
Therefore, 24-hour yield estimation using most recent milkings (1+12) is computed using Equation 10.

''Equation 10. 24-hour yield estimation using 12 previous milkings from AMS.''
[[File:Equation10.png|none|thumb|527x527px]]
and, 24-hour yield estimation using all milkings occurred in the last 96 hours (most recent 4 days), all milking in the last 4 days are included is computed using Equation 11.

''Equation 11. 24 hours yield estimation using milkings from the last 96 hours from AMS''
[[File:Equation11.png|none|thumb|534x534px]]

===== Advantages and disadvantages of this method =====
In terms of Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between milk weights and contents may arise if contents are recorded on one day only. Moreover, some cows may begin or finish their lactation during the period of recording. In this case the computation of milk yield must be adapted. The number of data that need to be validated is higher (for instance, contents have short interval between two milkings).

==== Calculation of milk yield using data on 1 day (Bouloc ''et al''., 2002<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
When the number of milkings is reduced to milkings obtained during one day only, the accuracy of the estimation of the true performance is the same as classical milk recording methods with the same interval between two test days. For instance, Milk Yield estimated from all the milkings recorded during 24 hours, and with an interval between two test days of four weeks has the same accuracy as A4.

==== Calculation of fat and protein yield (Galesloot & Peeters, 2000<ref name=":1" />) ====
Calculation of fat and protein percent must be based on milk weights at time of sampling. The 24-hour protein percentage can be predicted by the protein percentage of the sample without adjustment. However, the 24-hour fat percentage is more difficult to predict, as levels of fat percent are inversely proportional to the amount of milk yield. It is important then to have a close connection between time of samples and actual milk yields.

The Peeters and Galesloot method is a multiple linear regression model for estimating 24-hour fat percent and yields from one-sampled milking during the AMS sampling period. Six different statistical models were tested. This method takes into account fat percent, protein percent, milk weight and milking interval of the sampled milking, milking interval and milk weight of the previous milking (simple model). Another model, based on six different classification of variables (Ca - Cf) such as, time of sampled milking, interval preceding the sampled milking, ratio of fat to protein percent, parity, lactation stage, can be applied (complex model).

===== Simple model =====
24-hour Fat% = b0 + b1* Fat%(n) + b2* Prot%(n) + b3* Int(n) + b4* Int(n-1) + b5* Milk(n) + b6* Milk (n-1) + e

b0= Intercept, b1 to b6 = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, e = Residual effect.

===== Complex model =====
24-hour Fat%i = b0i + b1i* Fat%(n) + b2i* Prot%(n) + b3i* Int(n) + b4i* Int(n-1) + b5i* Milk(n) + b6i* Milk(n-1) + ei

b0i = Intercept, b1i to b6i = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, ei = Residual effect

i = subclass of classification for class variables Cx for x = a, b, c, d, e, f

Ca = Day Time of sampled milking (h) 0-5.59, 6.00-11.59, 12.00-17.59, 18.00-23.59

Cb = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440

Cc = Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

Cd = Parity 1, 2, ≥ 3

Ce = Lactation stage 1-99, 100-199, ≥200

Cf = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440 and Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

The best prediction of 24-hour fat percent and 24-hour fat yields from this method, includes fat percent, protein percent, milk weight and milking interval of the sampled milking, milk weight and milking interval of the preceding milking and the interaction between milking interval, the ratio of fat to protein percent of the sampled milking (complex model corresponding to Cf classification).

The Peeters and Galesloot method has been updated by Roelofs et al. (2006)<ref>Peeters, R. and P. J. B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. J Dairy Sci. 85:682-688.</ref>. The Roelofs method is described in [[Section 02 – Cattle Milk Recording#Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme|Appendix 2]] of this Section.

N.B. This method has been developed by CRV. CRV has available a set of parameters, estimated with this method. For more information about costs and advice on application of this method, please contact CRV. ICAR has no benefit from the application of this method or any other method described in these guidelines.

==== Calculation example of 24-hour fat and protein yields with sampling scheme M ====
With this method, all milkings in a 24-hour recording period must be sampled. The obtained separate analysis results are then used to compute a 24-hour yield of milk solids, and a weighted average of their content.

Individual milkings (last 96 hours) and recording day contents:
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left" |'''''Table 20. Calculation of 24-hour fat and protein contents with sampling scheme M.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY/MM/DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat%'''
|'''Protein%'''
|-
|1
|2021/09/09
|20:45
|525
|13.7
|26.1
|
|
|-
|2
|2021/09/10
|5:30
|617
|16.0
|25.9
|
|
|-
|3
|2021/09/10
|15:47
|720
|18.7
|26.0
|
|
|-
|4
|2021/09/11
|3:25
|645
|16.8
|26.0
|
|
|-
|5
|2021/09/11
|14:10
|899
|18.3
|20.3
|
|
|-
|6
|2021/09/11
|23:27
|557
|14.6
|26.2
|
|
|-
|7
|2021/09/12
|10:51
|684
|17.4
|25.4
|4.53
|3.17
|-
|8
|2021/09/12
|19:44
|533
|14.1
|26.5
|4.92
|3.18
|-
|9
|2021/09/13
|1:35
|351
|9.9
|28.2
|5.92
|3.07
|}
</center>

For example, calculation of fat% on recording day:

24-hour Fat% = (9.9 kg milk x 5.92% fat + 14.1 kg milk x 4.92 % fat + 17.4 kg milk x 4.53 % fat) / (9.9 + 14.1 + 17.4) kg milk = 5.00 %

To calculate the 24-hour fat yield, the calculated 24-hour milk yield is multiplied by the fat content thus obtained (5.00 %).

The same method is used for protein, somatic cell count, urea, lactose and other milk constituents.

Estimation of milk contents: It is recommended to set the robot not to take samples if the preceding milking of the individual cow is not more than 4 hours earlier. If such milkings occur the milk sampled from them is not suitable for 24-hour fat calculation.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left"|'''''Table 21. Calculation of 24-hour fat and protein contents with sampling scheme M where one milking interval was shorter than 4 hours.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY-MM-DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat %'''
|'''Protein%'''
|-
|1
|2021/11/12
|20:05
|590
|15.4
|26.4
|
|
|-
|2
|2021/11/13
|6:31
|626
|16.3
|26.0
|
|
|-
|3
|2021/11/13
|17:12
|641
|17.1
|26.7
|
|
|-
|4
|2021/11/14
|4:40
|688
|17.5
|25.4
|
|
|-
|5
|2021/11/14
|15:11
|631
|16.4
|26.0
|
|
|-
|6
|2021/11/15
|2:25
|674
|16.5
|24.5
|
|
|-
|7
|2021/11/15
|9:47
|452
|10.8
|23.9
|
|
|-
|8
|2021/11/15
|18:30
|523
|13.6
|26.0
|4.71
|3.36
|-
|9
|2021/11/15
|21:15
|165
|3.1
|18.8
|5.161
|3.481
|-
|10
|2021/11/16
|7:49
|634
|16.5
|26.0
|4.47
|3.21
|}
1 Time between two consecutive milkings shorter than 4 hours, data not taken into account for calculation of milk contents.
</center>

Calculation of the fat content of milk during the recording day:

24-hour Fat% = (16.5 kg milk x 4.47 % fat + 13.6 kg milk x 4.71 % fat) / (16.5 kg + 13.6 kg) = 4.57 %

The same method is used for protein, somatic cells, urea, lactose and other milk constituents.

=== Methods to calculate 24-hour yields from electronic milk meters ===

==== Using data on more than one day (Hand ''et al''., 2006<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. J. Dairy Sci. 89:1723–1726.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Electronic Milk Meters. The average of most recent milk weights can be calculated using a number of preceding days. Table 22 reports the concordance correlations for a range of multiple-day averages. As soon as at least the 3 preceding days are used in the calculation, the concordance correlation reaches a high value of at least 0.981. There are no significant differences between 3, 4, 5, 6 and 7-day averages. The correlations are independent from stage of lactation and parity. Thus, 24-hour yields can be the average of from 3 to 7 daily milkings previous to the test day when fat and protein samples were taken.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 22. Concordance correlations for different multiple-day averages.'''''
|- style="background-color:#efefef;"
|'''Multiple-day average'''
|'''Concordance correlation'''
|-
|1
|0.957
|-
|2
|0.975
|-
|3
|0.981
|-
|4
|0.981
|-
|5
|0.982
|-
|6
|0.981
|-
|7
|0.981
|-
|10
|0.979
|-
|14
|0.977
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table20.png|center|thumb|923x923px]]

Therefore, 24-hour yield estimation averaging over 5 days is given by Equation 12.

''Equation 12. 24-hour yield estimation averaging over 5 days.''
[[File:Equation12.png|center|thumb|601x601px]]

===== Advantages and disadvantages of this method =====
Concerning Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between Milk weights and contents have been shown. The estimation bias increases proportionally to the number of days use to compute the 24-hour average. Thus, this method is recommended only if milk weight is the only variable of interest. If milk contents are of interest then the milk weight should be calculated using the milkings from the same day of sampling.

==== Estimation of 24-hour fat and protein yield ====
Fat and protein yields should be determined from the 24-hour yield on the day of sampling, and not the averaged value.

=== Calculation of daily fat percentage from single samples by Gerke et al., 2025 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Gerke.xlsx here]

Constant access to the automatic milking system (AMS) leads to varying milking frequency of cows and subsequently varying milking interval lengths (MI) and milk yield (MY) of single milkings. This influences milk production and can result in variable milk composition in individual milkings during the day. Therefore, the fat percentage from one sampled milking must be adjusted before it can be used as a daily value. The method described specifies the data required and the calculation procedure for deriving a corrected 24 h milk fat percentage from a single sample on test day (TD) in AMS herds.

==== Model specification ====
The multiple linear regression includes transformation, interaction, and polynomial parameters to model non-linearity and thereby improve prediction accuracy. Beside F% of a single milking (''m'') on TD, the model focused on lactation characteristics and milk recording data of up to 4 preceding milkings. With milking intervals ranging between 4 and 20 hours, the method can be applied to milk recording samples from cows with 2 or 3 milkings whose milking intervals lengths (MI) before sampling accumulate to less than 24 h.

The functional form of the model described below specifies the data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample:[[File:Image A.png|center|thumb|636x636px|'''Data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample''']]
</div>where:

DF% = estimated 24 h fat percentage on TD

''m'' = sampled milking on TD

''m-x'' = x milkings before the milking where the sample was taken (x: 1-3)

F% = fat percentage of the sampled milking ''m''

MY(''m'') = milk yield (kg) of ''m''

MI(''m'') = length of time interval (min) preceding the sampled milking ''m''

MY(''m''-x) = milk yields of the 1-3 preceding milkings of ''m''

MI(''m''-x) = milking interval length corresponding to MY(''m''-x)

DIM = days in milk on TD ranging between 5 and 330 d

Parity = parity class (e.g primiparous = 1 and multiparous = 0)

Daytime = time-of-day group of ''m'' (e.g. morning/noon/evening)

e = residual error

The method and its implementation are described in detail by Gerke et al. (2025).

==== Calculation and examples ====
The mathematical notation, with the corresponding regression coefficients in Table 1 for calculating the daily fat percentage (DF%):[[File:Calculating the daily fat percentage (DF%).jpg|center|Calculating the daily fat percentage (DF%)|thumb|511x511px]][[File:Calculating the daily fat percentage (DF%) 2.jpg|center|frame|'''Table 1. Coefficients for regression formula.''']]
</div>
[[File:Example data required for estimating 24 h fat percentage (DF%).jpg|alt=Example data required for estimating 24 h fat percentage (DF%)|center|frame|'''Table 2.''' '''Example data required for estimating 24 h fat percentage (DF%)''']]
Based on the data assembled on TD (Table 2), the corrected 24 h fat percentage (DF%) can be calculated using the mathematical formula und its corresponding coefficients listed in Table 1 as shown in the following examples:
[[File:Corrected 24 h fat percentage.jpg|alt=Corrected 24 h fat percentage|center|thumb|661x661px|'''Corrected 24 h fat percentage''']]

=== Reference ===
Gerke, J. S., Kammer, M., Werner, A., Köstler, R., Piepenburg, J., Mayerhofer, M., … Duda, J. (2025). Estimating daily fat percentage from single samples in herds with automatic milking system using a regression model. ''Livestock Science'', ''293'', 105649. doi: 10.1016/j.livsci.2025.105649

=== Calculation example ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Jenko.xlsx here]

This method estimates daily milk yield (DMY), daily fat yield (DFY), and daily protein yield (DPY) in the alternate one-milking recording (T) scheme. Daily fat percentage (DFP) and daily protein percentage (DPP) are then derived from the daily yield (DY) estimates. Utilizing this method allows us to remove the risk of underestimating high and overestimating low DY and contents.

The following formula is used to estimate the DY from the partial yield (PY) and the estimated PY/DY ratio (y):

DY=PYi/yi

where the subscript i is either morning (a.m.) or evening (p.m.).

The value of y is calculated based on the milking interval in minutes (MI), estimated intercept (µ) and regression coefficients (b1 and b2) for yield traits in a.m. or p.m. milking using the following equations for DMY and DPY:

'''Equation 1. Model for milk yield and protein yield.'''

yi = µ + b1 × MI

and for DFY

'''Equation 2. Model for fat yield.'''

yi = µ + b1 × MI + b2 × MI2

The intercept and regression coefficients can be either estimated from the data with records from both a.m. and p.m. milking or the estimates from Table 1 can be applied.

'''Table 1. Intercept and regression coefficients for calculation of daily yield.'''
{| class="wikitable"
|'''Daily yield'''
|'''Milking'''
|'''µ'''
|'''b1'''
|'''b2'''
|-
|DMY
|a.m.
|0,1081000000
|0,0005503000
|
|-
|
|p.m.
|0,0884200000
|0,0005683000
|
|-
|DPY
|a.m.
|0,1124000000
|0,0005419000
|
|-
|
|p.m.
|0,0966400000
|0,0005593000
|
|-
|DFY .
|a.m.
|0,5903000000
|<nowiki>-0,0005093000</nowiki>
|0,0000005377
|-
|
|p.m.
|0,1574000000
|0,0006705000
|<nowiki>-0,0000002744</nowiki>
|}
Finally, daily fat percentage (DFP) and daily protein percentage (DPP) are calculated from the estimated DY:

DFP=DFY/DMY × 100

DPP=DPY/DMY × 100

==== Calulation example with method of Jenko et al. (2008, 2010) ====
Example of the calculations of daily yields from morning milking and evening milking is presented in tables 3 and 4. Data from the Delorenzo and Wiggans method is used in the calculations (Table 2).

'''Table 2. Data for morning and evening milking.'''
{| class="wikitable"
|'''Milking'''
|'''a.m.'''
|'''p.m.'''
|-
|Beginning of recording
|06:15
|20:22
|-
|Start of preceding milking
|17:25
|06:35
|-
|Milking interval (min)
|770
|827
|-
|'''Milking results'''
|
|
|-
|Milk (kg)
|12,00
|14,00
|-
|Protein (%)
|3,45
|3,40
|-
|Fat (%)
|4,12
|4,00
|}

'''Table 3. Calculation of partial yield (PY) and calculation of y value.'''
{| class="wikitable"
|Trait
|Milking
|PY (%)
|PY (kg)
|y
|-
|Milk
|a.m.
|
|12,00
|0,1081000000 + 0,0005503000 x 770 = 0,531831
|-
|
|p.m.
|
|14,00
|0,0884200000 + 0,0005683000 x 827 = 0,558404
|-
|Protein
|a.m.
|3,45
|12,00 / 3,45 = 0,41
|0,1124000000 + 0,0005419000 x 770 = 0,529663
|-
|
|p.m.
|3,40
|14,00 / 3,40 = 0,48
|0,0966400000 + 0,0005593000 x 827 = 0,559181
|-
|Fat
|a.m.
|

4,12
|12,00 / 4,12 = 0,49
|0,5903000000 -0,0005093000 x 770 + 0,0000005377 x 7702 = 0,516941
|-
|
|p.m.
|

4,00
|12,00 / 4,00 = 0,56
|0,1574000000 +0,0006705000 x 827 - 0,0000002744 x 8272 = 0,524233
|}

'''Table 4. Calculation of daily yield (DY, kg) and daily components (DY, %).'''
{| class="wikitable"
|Trait
|DY
|Milking
|DY (kg)
|DY (%)
|-
|Milk
|DMY
|a.m.
|12,00 / 0,531831 = 22,56356
|
|-
|
|
|p.m.
|14,00 / 0,531831 = 25,07145
|
|-
|Protein
|DPY
|a.m.
|0,41 / 0,529663 = 0,781629
|(0,781629 / 22,56356) x 100 = 3,46
|-
|
|
|p.m.
|0,48 / 0,559181 = 0,851245
|(0,851245 / 25,07145) x 100 = 3,40
|-
|Fat
|DFY
|a.m.
|0,49 / 0,516941 = 0,956395
|(0,956395 / 22,56356) x 100 = 4,24
|-
|
|
|p.m.
|0,56 / 0,524233 = 1,068227
|(1,068227 / 25,07145) x 100 = 4,26
|}

==== References ====

* Jenko, J., Perpar, T., Logar, B., Sadar, M., Ivanovič, B., Jeretina, J., Verbič, J., Podgoršek, P. 2008. Comparison of different models for estimating daily yields from a.m./p.m. milkings in Slovenian dairy scheme. Presented at the 36th ICAR Session, Niagara Falls, New York, United States, June 16-20, 2008.
* Jenko, J., Perpar, T., Gorjanc G., Babnik, D. 2010. Evaluation of different approaches for the estimation of daily yield from single milk testing scheme in cattle, J. Dairy Res., 77 (2010), pp. 137-143; DOI: 10.1017/S0022029909990586

</div>
</div>

== Procedure 2 – Computing of Accumulated Lactation Yield ==
<div class="mw-collapsible mw-collapsed">
<div>
=== The Test Interval Method (TIM) (Sargent, 1968<ref>Sargent, F. D., V. H. Lyton, and 0. G. Wall, J r . 1968. Test interval method of calculating Dairy Herd Improvement Association records. J. Dairy Sci. 51:170.</ref>) ===
Test Interval Method is the reference method for calculating accumulated yields. Another adaptation of the method is the Centering Date Method where the yields from the preceding recording are used until the mid point of the recording interval and then substituted by the yields from the following recording.

The following equations are used to compute the lactation record for milk yield (MY), for fat (and protein) yield (FY), and for fat (and protein) percent (FP).
[[File:Equation1111.png|none|thumb|653x653px]]
Where:
M1, M2, Mn are the weights in kilograms, given to one decimal place, of the milk yielded in the 24 hours of the recording day.

F1, F2, Fn are the fat yields estimated by multiplying the milk yield and the fat percent (given to at least two decimal places) collected on the recording day.

I1, I2, In-1 are the intervals, in days, between recording dates.

I0 is the interval, in days, between the lactation period start date and the first recording date.

In is the interval, in days, between the last recording date and the end of the lactation period.

The equation applied for fat yield and percentage must be applied for any other milk components such as protein and lactose.

Details of how to apply the formulae are shown in Table 3 using the example data in Table 1, below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" align = "left" |'''''Table 1. Raw data used in example (TIM).'''''
|- style="background-color:#efefef;"
| colspan="6" align = "left"|'''Data:'''

'''Calving March 25'''
|- style="background-color:#efefef;"
|
|'''Date of'''

'''recording'''
|'''Number'''

'''of days'''
|'''Quantity of milk'''

'''weighed in kg'''
|'''Fat'''

'''percentage'''
|'''Fat'''

'''in grams'''
|-
|April
|8
|14
|28.2
|3.65
|1 029
|-
|May
|6
|28
|24.8
|3.45
|856
|-
|June
|5
|30
|26.6
|3.40
|904
|-
|July
|7
|32
|23.2
|3.55
|824
|-
|August
|2
|26
|20.2
|3.85
|778
|-
|August
|30
|28
|17.8
|4.05
|721
|-
|September
|25
|26
|13.2
|4.45
|587
|-
|October
|27
|32
|9.6
|4.65
|446
|-
|November
|22
|26
|5.8
|4.95
|287
|-
|December
|20
|28
|4.4
|5.25
|231
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left"|'''''Table 2. Lactation period summary (TIM).'''''
|-
|Beginning of lactation:
|March 26
|-
|End of lactation:
|January 3
|-
|Duration of lactation period:
|284 days
|-
|Number of testings (weighings):
|10
|}
</center>
<center>
{| class="wikitable"
| colspan="8" |'''''Table 3. Computations using Test Interval Method.'''''
|- style="background-color:#efefef;"
| colspan="3" rowspan="2" |'''Interval'''

'''both days included'''
|
| colspan="2" |'''Daily production'''
| colspan="2" |'''Sum'''
|- style="background-color:#efefef;"
|'''Days'''
|'''Kg milk'''
|'''Grams of fat'''
|'''Kg milk'''
|'''Kg fat'''
|-
|Mar 26
|<nowiki>-</nowiki>
|Apr 8
|14
|28.2
|1 029
|395
|14.410
|-
|Apr 9
|<nowiki>-</nowiki>
|May 6
|28
|(28.2+24.8)/2
|(1 029+856) /2
|742
|26.389
|-
|May 7
|<nowiki>-</nowiki>
|June 5
|30
|(24.8+26.6) /2
|(856+904) /2
|771
|26.400
|-
|June 6
|<nowiki>-</nowiki>
|July 7
|32
|(26.6+23.2) /2
|(904+824) /2
|797
|27.648
|-
|July 8
|<nowiki>-</nowiki>
|Aug. 2
|26
|(23.2+20.2) /2
|(824+778) /2
|564
|20.817
|-
|Aug. 3
|<nowiki>-</nowiki>
|Aug 30
|28
|(20.2+17.8) /2
|(778+721) /2
|532
|20.980
|-
|Aug 31
|<nowiki>-</nowiki>
|Sept. 25
|26
|(17.8+13.2) /2
|(721+587) /2
|403
|17.008
|-
|Sept. 26
|<nowiki>-</nowiki>
|Oct. 27
|32
|(13.2+9.6) /2
|(587+446) /2
|365
|16.541
|-
|Oct. 28
|<nowiki>-</nowiki>
|Nov. 22
|26
|(9.6+5.8) /2
|(446+287) /2
|200
|9.536
|-
|Nov. 23
|<nowiki>-</nowiki>
|Dec. 20
|28
|(5.8+4.4) /2
|(287+231) /2
|143
|7.253
|-
|Dec. 21
|<nowiki>-</nowiki>
|Jan. 3
|14
|4.4
|231
|62
|3.234
|-
|
|
|
|284
|
|
|4973
|190.216
|-
| colspan="8" |
|-
| colspan="8" |Total quantity of milk: 4 973. kg
|-
| colspan="8" |Total quantity of fat: 190 kg
|-
| colspan="8" |Average fat percentage (190.216 / 4973) x 100 = 3.82%
|}
</center>

=== Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. Livest. Prod. Sci. 17:l.</ref>) ===
With the method 'Interpolation using Standard Lactation Curves' missing test day yields and 305 day projections are predicted. The method makes use of separate standard lactation curves representing the expected course of the lactation, for a certain herd production level, age at calving and season of calving and yield trait. By interpolation using standard lactation curves, the fact that after calving milk yield generally increases and subsequently decreases is taken into account. The daily yields are predicted for fixed days of the lactation: day 0, 10, 30, 50 etc.

The cumulative yield is calculated as follows in :
[[File:Equation2222222.png|none|thumb|474x474px]]
where:

yi = the i-th daily yield;

INTi = the interval in days between the daily yields yi and yi+1;

''n'' = total number of daily yields (measured daily yields and predicted daily yields).

The next example illustrates the calculation of a record in progress. The cow was tested at day 35 and day 65 of the lactation. To determine the lactation yield, daily milk yields are determined for day 0, 10, 30 and 50 of the lactation, by means of the standard lactation curves. The daily yields are in Table 4.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Measured and derived daily yields, used to calculate the record in progress in the example (ISLC).'''''
|- style="background-color:#efefef;"
|'''Day of lactation'''
|'''Milk (kg)'''
|'''Note'''
|-
|0
|25.9
|Predicted
|-
|10
|27.8
|Predicted
|-
|30
|31.7
|Predicted
|-
|35
|31.8
|Measured
|-
|50
|32.9
|Interpolated using standard lactation curve
|-
|65
|33.0
|Measured
|}
</center>

Next, the record in progress can be calculated by means of the formula for a cumulative yield as follows:

[(10 - 1) * 25.9 + (10+1) * 27.8] / 2 +

[(20 - 1) * 27.8 + (20+1) * 31.7] / 2 +

[(5 - 1) * 31.7 + (5+1) * 31.8] / 2 +

[(15 - 1) * 31.8 + (15+1) * 32.9] / 2 +

[(15 - 1) * 32.9 + (15+1) * 33.0] / 2 = 2005.3 kg.

This corresponds to the surface below the line through the predicted and measured daily yields (see Figure 1).
[[File:Figure1.png|center|thumb|621x621px|''Figure 1. Example of calculation of record in progress.'']]

=== Best prediction (BP) (VanRaden, 1997<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. J. Dairy Sci. 80:3015-3022.</ref>) ===
Recorded milk weights are combined into a lactation record using standard selection index methods. Let vector y contain M1, M2, to Mn and let E('''y''') contain corresponding the expected values for each recorded day. The E(y) are obtained from standard lactation curves for the population or for the herd and should account for the cow's age and other environmental factors such as season, milking frequency, etc. The yields in '''y''' covary as a function of the recording interval between them (I). Diagonal elements in Var(y) are the population or herd variance for that recording day and off diagonals are obtained from autoregressive or similar functions such as Corr(M1, M2)=0.995I for first lactations or 0.992I for later lactations. Covariances of one observation with the lactation yield, for example Cov(M1, MY), are the sum of 305 individual covariances. E(MY) is the sum of 305 daily expected values. Lactation milk yield is then predicted as Equation 3:
[[File:Equation333333.png|none|thumb|640x640px]]
With best prediction, predicted milk yields have less variance than true milk yields. With TIM, estimated yields have more variance than true yields. The reason is that predicted yields are regressed toward the mean unless all 305 daily yields are observed. With best prediction, the predicted MY for a lactation without any observed yields is E(MY) which is the population or herd mean for a cow of that age and season. With TIM, the estimated MY is undefined if no daily yields are recorded.

Milk, fat, and protein yields can be processed separately using single-trait best prediction or jointly using multi-trait best prediction. Replacement of M1, M2, to Mn with F1, F2, to Fn or P1, P2, to Pn gives the single-trait predictions for fat or for protein. Multi-trait predictions require larger vectors and matrices but similar algebra. Products of trait correlations and autoregressive correlations, for example, may provide the needed covariances.

=== Multiple-Trait Procedure (MTP) (Schaeffer & Jamrozik, 1996<ref>Schaeffer, L.R., and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. J. Dairy Sci. 79:2044-2055.</ref>) ===
The Multiple-Trait Procedure predicts 305-d lactation yields for milk, fat, protein and SCS, incorporating information about standard lactation curves and covariances between milk, fat, and protein yields and SCS. Test day yields are weighted by their relative variances, and standard lactation curves of cows of similar breed, region, lactation number, age, and season of calving are used in the estimation of lactation curve parameters for each cow. The multiple-trait procedure can handle long intervals between test days, test days with milk only recorded, and can make 305-d predictions on the basis of just one test day record per cow. The procedure also lends itself to the calculation of peak yield, day of peak yield, yield persistency, and expected test-day yields, which could be useful management tools for a producer on a milk recording program.

The MTP method is based upon Wilmink's model in conjunction with an approach incorporating standard curve parameters for cows with the same production characteristics. Wilmink's function for one trait is given by Equation 4.

Equation 4. Wilmink function for one trait (MTP).

y = A + B''t'' ± C''exp'' (-0.05''t'') + ''e''

where y is yield on day t of lactation, A, B, and C are related to the shape of the lactation curve.

The parameters A, B, and C need to be estimated for each yield trait. The yield traits have high phenotypic correlations, and MTP would incorporate these correlations. Use of MTP would allow for the prediction of yields even if data were not available on each test day for a cow.

The vector of parameters to be estimated for one cow are designated:
[[File:Vectro.png|center|thumb]]
where M, F, and P represent milk, fat, and protein, respectively, and S represents somatic cell score. The vector c is to be estimated from the available test-day records. Let c0 represent the corresponding parameters estimated across all cows with the same production characteristics as the cow in question.

Let
[[File:Vector2.png|center|thumb]]

be the vector of yield traits and somatic cell scores on test ''k'' at day ''t'' of the lactation.

The incidence matrix, ''Xk'', is constructed as follows:
[[File:Vector3.png|center|thumb|558x558px]]

The MTP equations are:
[[File:Equation55555.png|none|thumb|560x560px]]
and ''n'' is the number of tests for that cow. ''Rk'' is a matrix of order 4 that contains the variances and covariances among the yields on ''kth'' test at day ''t'' of lactation. The elements of this matrix were derived from regression formulas based on fitting phenotypic variances and covariances of yields to models with ''t'' and ''t2'' as covariables. Thus, element ''ij'' of ''Rk'' would be determined by

rij(t) = ß0ij + ß1ij (t) + ß2ij (t2)

G is a 12 x 12 matrix containing variances and covariances among the parameters in '''ĉ''' and represents the cow to cow variation in these parameters, which includes genetic and permanent environmental effects, but ignores genetic covariances between cows. The parameters for '''''G''''' and '''''Rk''''' vary depending on the breed, but must be known. Initially, these matrices were allowed to vary by region of Canada in addition to breed, but this meant that there could exist two cows with identical production records on the same days in milk, but because one cow was in one region and the other cow was in another region, then the accuracy of their predictions would be different. This was considered to be too confusing for dairy producers, so that regional differences in variance-covariance matrices were ignored and one set of parameters would be used for all regions for a particular breed. Estimation of G is described later.

If a cow has a test, but only milk yield is reported, then

y’k(Mk 0 0 0)

and
[[File:And.png|center|thumb|540x540px]]

The inverse of '''''Rk''''' is the regular inverse of the nonzero submatrix within '''''Rk''''', ignoring the zero rows and columns. Thus, missing yields can be accommodated in MTP.

Accuracy of predicted 305-d lactation totals depends on the number of test-day records during the lactation and DIM associated with each test. Thus, any prediction procedure will require reliability figures to be reported with all predictions, especially if fewer tests at very irregular intervals are going to be frequent in milk recording. At the moment, an approximate procedure is applied that uses the inverse elements of '''(X’R-1X + G-1) -1.'''

==== 1.1 Example calculations ====
Four test day records on a 25 month old, Holstein cow calving in June from Ontario are given in the Table 5 below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 5. Example test day data for a cow (MTP).'''''
|- style="background-color:#efefef;"
|'''Test no.'''
|'''DIM=''t'''''
|'''Exp(-0.05''t'')'''
|'''Milk (kg)'''
|'''Fat (kg)'''
|'''Protein (kg)'''
|'''SCS'''
|-
|1
|15
|0.47237
|28.8
|
|
|3.130
|-
|2
|54
|0.06721
|29.2
|1.12
|0.87
|2.463
|-
|3
|188
|0.000083
|23.7
|0.97
|0.78
|2.157
|-
|4
|250
|0.0000037
|20.8
|
|
|2.619
|}
</center>

Notice that two tests do not have fat and protein yields, and that intervals between tests are irregular and large. The vector of standard curve parameters based on all available comparable cow, is
[[File:Vector4.png|center|thumb]]
The R^(-1)_k matrices for each test day need to be constructed. These matrices are derived from regression equations. The equations for Holsteins were:
<center>
{| class="wikitable" style="text-align: center;"
|''rMM(t) =''
|71.0752 - 0.281201''t'' + 0.0004977''t2''
|-
|''rMF(t) =''
|2.4365 - 0.013274''t'' + 0.0000302''t2''
|-
|''rMP(t) =''
|2.0504 - 0.008286''t'' + 0.0000163''t2''
|-
|''rMS(t) =''
|<nowiki>-1.7993 + 0.013209</nowiki>''t'' - 0.000056''t2''
|-
|''rFF(t) =''
|0.1312 - 0.000725''t'' + 0.000001586''t2''
|-
|''rFP(t) =''
|0.0739 - 0.000386''t'' + 0.000000926''t2''
|-
|''rFS(t) =''
|<nowiki>- 0.0386 + 0.000292</nowiki>''t'' - 0.000001796''t2''
|-
|''rPP(t) =''
|0.066 - 0.000267''t'' + 0.0000005636''t2''
|-
|''rPS(t) =''
|<nowiki>- 0.0404 + 0.000369</nowiki>''t'' - 0.000001743''t2''
|-
|''rSS(t) =''
|3.0404 - 0.000083''t'' - 0.000006105''t2''
|}
</center>

The inverses of the residual variance-covariance matrices for yields for the four test days are as follows:
<center>
{| class="wikitable" style="text-align: center;"
|
|0.0151259
|0
|0
|0.0080354
|-
|'''R^(-1)_1''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0080354
|0
|0
|0.3334553
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.1685584
|0.345947
|<nowiki>-4.851935</nowiki>
|0.0254775
|-
|'''R^(-1)_2''' = =
|<nowiki>-0.345947</nowiki>
|26.830915
|<nowiki>-17.40281</nowiki>
|<nowiki>-0.041445</nowiki>
|-
|
|<nowiki>-4.851935</nowiki>
|<nowiki>-17.40281</nowiki>
|187.18579
|<nowiki>-0.584885</nowiki>
|-
|
|0.0254775
|<nowiki>-0.041445</nowiki>
|<nowiki>-0.584885</nowiki>
|0.3365425
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.2620161
|0.1479068
|<nowiki>-7.943903</nowiki>
|0.0316069
|-
|'''R^(-1)_3''' = =
|0.1479068
|54.446977
|<nowiki>-56.01333</nowiki>
|0.3306741
|-
|
|<nowiki>-7.943903</nowiki>
|<nowiki>-56.01333</nowiki>
|317.9609
|<nowiki>-0.92601</nowiki>
|-
|
|0.0316069
|0.3306741
|<nowiki>-0.92601</nowiki>
|0.3654369
|}
{| class="wikitable" style="text-align: center;"
|

|0.0329465
|0
|0
|0.0251039
|-
|'''R^(-1)_4''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0251039
|0
|0
|0.3981981
|}

Inverse matrix G^(-1) of order 12 is the same for all cows of the same breed:

[[File:Left 6x6.jpg|center|thumb|600x600px|Inverse matrix G^(-1) of order 12]]

</center>
Note that many covariances between different parameters of the lactation curves have been set to zero. When all covariances were included, the prediction errors for individual cows were very large, possibly because the covariances were highly correlated to each other within and between traits. Including only covariances between the same parameter among traits gave much smaller prediction errors.

The elements of the MTP equations of order 12 for this cow are shown in partitioned format also:

'''X’R-1X ='''
<center>[[File:Elements of the MTP equations of order 12.jpg|center|thumb|600x600px|Elements of the MTP equations of order 12]]
</center>
[[File:Equation7.png|center|thumb|632x632px]]

The solution vector for this cow is
[[File:Equation6666.png|center|thumb]]

To predict 305-day yields, Y305
[[File:Equation7777.png|none|thumb|551x551px]]
Equation 6 is used separately for each trait (milk, fat, protein, and SCS). The results for this cow were 7456 kg milk, 301 kg fat, and 239 kg protein. The result for SCS is divided by 305 to give an average daily SCS of 2.477.
</div>
</div>

= Appendices =
== Appendix 1 - Adjustment factors to calculate 24-hour yields using the Liu method ==
<div class="mw-collapsible mw-collapsed">
<div>
In Table 6 the adjustment factors to calculate 24-hour yields, using the Liu method, can be found. The description of the Liu method can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2.]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" |'''''Table 1. Adjustment factors to calculate 24-hour yields using the Liu method. Milking time (MT) is either 1 (PM) or 2 (AM), i = parity class, j= milking interval class and k = stage of lactation class.'''''
|- style="background-color:#efefef;"
|'''MT'''
|'''i'''
|'''j'''
|'''k'''
| colspan="2" |'''Milk yield (DMY)'''
| colspan="2" |'''Fat yield (DFY)'''
| colspan="2" |'''Protein yield (DPY)'''
|-
| colspan="4" |
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|-
|1
|1
|1
|1
|5.29333
|1.83283
|0.30911
|1.43518
|0.18984
|1.77461
|-
|1
|1
|1
|2
|4.17676
|1.97447
|0.2803
|1.56914
|0.12246
|2.00568
|-
|1
|1
|1
|3
|4.26476
|1.95945
|0.18826
|1.82468
|0.12624
|2.0137
|-
|1
|1
|1
|4
|3.41282
|2.01814
|0.25025
|1.64707
|0.12519
|1.99629
|-
|1
|1
|1
|5
|1.79548
|2.22665
|0.06578
|2.09515
|0.05249
|2.24065
|-
|1
|1
|1
|6
|3.7751
|1.95508
|0.12854
|1.93892
|0.11936
|2.00979
|-
|1
|1
|1
|7
|1.544
|2.1478
|0.06425
|2.06779
|0.0569
|2.13851
|-
|1
|1
|2
|1
|5.8584
|1.79409
|0.33193
|1.42953
|0.20756
|1.7288
|-
|1
|1
|2
|2
|5.45524
|1.84258
|0.32877
|1.43235
|0.21332
|1.74001
|-
|1
|1
|2
|3
|4.64052
|1.86706
|0.27155
|1.57017
|0.16439
|1.84539
|-
|1
|1
|2
|4
|2.86835
|2.06209
|0.18647
|1.79403
|0.10803
|2.0193
|-
|1
|1
|2
|5
|2.11336
|2.12055
|0.10435
|1.97206
|0.07193
|2.10651
|-
|1
|1
|2
|6
|2.00673
|2.0636
|0.1386
|1.83336
|0.06892
|2.06532
|-
|1
|1
|2
|7
|1.71752
|2.11269
|0.06501
|2.0379
|0.05569
|2.12881
|-
|1
|1
|3
|1
|2.80244
|2.02183
|0.17663
|1.72438
|0.11078
|1.96422
|-
|1
|1
|3
|2
|3.47396
|1.98268
|0.2135
|1.6805
|0.10471
|1.99092
|-
|1
|1
|3
|3
|2.81702
|2.04348
|0.20754
|1.71868
|0.1127
|1.98403
|-
|1
|1
|3
|4
|3.1989
|1.998
|0.21578
|1.6991
|0.10802
|1.99517
|-
|1
|1
|3
|5
|2.47055
|2.04826
|0.15418
|1.83151
|0.07492
|2.07547
|-
|1
|1
|3
|6
|1.923
|2.07728
|0.11783
|1.89678
|0.06457
|2.08391
|-
|1
|1
|3
|7
|1.85264
|2.0873
|0.13047
|1.86711
|0.071
|2.06917
|-
|1
|1
|4
|1
|2.75042
|1.96631
|0.24794
|1.61741
|0.09248
|1.95376
|-
|1
|1
|4
|2
|2.97505
|1.96711
|0.20029
|1.71842
|0.09381
|1.97081
|-
|1
|1
|4
|3
|2.33365
|2.02986
|0.17021
|1.79996
|0.07631
|2.03167
|-
|1
|1
|4
|4
|3.41505
|1.94107
|0.1845
|1.76799
|0.10989
|1.95456
|-
|1
|1
|4
|5
|2.67488
|1.97797
|0.13433
|1.85893
|0.09432
|1.97755
|-
|1
|1
|4
|6
|1.89907
|2.04841
|0.08715
|1.96251
|0.07132
|2.04225
|-
|1
|1
|4
|7
|1.80326
|2.03554
|0.1251
|1.86477
|0.06072
|2.04747
|-
|1
|1
|5
|1
|2.76763
|1.92863
|0.15754
|1.72474
|0.10187
|1.88749
|-
|1
|1
|5
|2
|3.36896
|1.92048
|0.2236
|1.64149
|0.12369
|1.8823
|-
|1
|1
|5
|3
|2.22763
|2.00452
|0.17614
|1.7474
|0.08019
|1.9782
|-
|1
|1
|5
|4
|2.44625
|1.97049
|0.17217
|1.74753
|0.0889
|1.94647
|-
|1
|1
|5
|5
|2.379
|1.97307
|0.15965
|1.76134
|0.0896
|1.94575
|-
|1
|1
|5
|6
|1.62948
|2.02491
|0.11021
|1.85546
|0.0852
|1.94593
|-
|1
|1
|5
|7
|1.45651
|2.0254
|0.07479
|1.92789
|0.05846
|2.00196
|-
|1
|1
|6
|1
|2.01088
|1.9497
|0.16548
|1.68143
|0.101
|1.85846
|-
|1
|1
|6
|2
|2.96605
|1.93064
|0.25841
|1.52566
|0.12097
|1.86061
|-
|1
|1
|6
|3
|2.2281
|1.96085
|0.19036
|1.69013
|0.08032
|1.9375
|-
|1
|1
|6
|4
|2.39473
|1.952
|0.17854
|1.72423
|0.06863
|1.97582
|-
|1
|1
|6
|5
|2.37955
|1.94127
|0.19579
|1.66419
|0.08447
|1.93156
|-
|1
|1
|6
|6
|0.36203
|2.12393
|0.14291
|1.75822
|0.03845
|2.04562
|-
|1
|1
|6
|7
|1.5702
|1.96794
|0.1336
|1.76796
|0.06449
|1.94829
|-
|1
|1
|7
|1
|3.93654
|1.82772
|0.2359
|1.61894
|0.15032
|1.76054
|-
|1
|1
|7
|2
|4.39662
|1.81581
|0.24969
|1.5881
|0.16909
|1.74794
|-
|1
|1
|7
|3
|3.78325
|1.82778
|0.19228
|1.71802
|0.12368
|1.8268
|-
|1
|1
|7
|4
|3.39116
|1.86302
|0.1969
|1.71838
|0.12282
|1.848
|-
|1
|1
|7
|5
|3.20111
|1.83255
|0.09893
|1.86309
|0.1044
|1.84257
|-
|1
|1
|7
|6
|3.75639
|1.78665
|0.25205
|1.56174
|0.14105
|1.76802
|-
|1
|1
|7
|7
|1.42153
|1.95649
|0.09226
|1.85882
|0.04636
|1.96245
|-
|1
|1
|8
|1
|2.3454
|1.90436
|0.14321
|1.77423
|0.10703
|1.82306
|-
|1
|1
|8
|2
|3.97557
|1.82746
|0.26651
|1.58374
|0.15298
|1.76385
|-
|1
|1
|8
|3
|4.26939
|1.80503
|0.22918
|1.64925
|0.12924
|1.81061
|-
|1
|1
|8
|4
|2.90779
|1.89861
|0.18578
|1.73968
|0.13948
|1.79679
|-
|1
|1
|8
|5
|2.8265
|1.87632
|0.19374
|1.67929
|0.12377
|1.80944
|-
|1
|1
|8
|6
|2.26312
|1.87397
|0.09917
|1.82528
|0.08819
|1.84453
|-
|1
|1
|8
|7
|0.31382
|2.04402
|0.05049
|1.95773
|0.02612
|1.99012
|-
|1
|2
|1
|1
|4.63752
|1.99615
|0.31102
|1.58962
|0.16637
|1.96686
|-
|1
|2
|1
|2
|5.56226
|1.91521
|0.26761
|1.64342
|0.16973
|1.94145
|-
|1
|2
|1
|3
|4.51983
|1.96962
|0.26221
|1.65088
|0.12245
|2.03857
|-
|1
|2
|1
|4
|4.51563
|1.93033
|0.18468
|1.80715
|0.15252
|1.94807
|-
|1
|2
|1
|5
|2.60334
|2.07338
|0.16011
|1.81257
|0.09892
|2.05493
|-
|1
|2
|1
|6
|2.86068
|1.98457
|0.15381
|1.79197
|0.08619
|2.04046
|-
|1
|2
|1
|7
|1.6596
|2.11753
|0.13089
|1.83687
|0.09908
|1.96479
|-
|1
|2
|2
|1
|3.94656
|2.03607
|0.23716
|1.6988
|0.19559
|1.88765
|-
|1
|2
|2
|2
|4.20525
|1.98621
|0.3553
|1.46663
|0.1657
|1.92175
|-
|1
|2
|2
|3
|3.31729
|2.04589
|0.29682
|1.57761
|0.12491
|2.00945
|-
|1
|2
|2
|4
|1.95977
|2.13926
|0.16059
|1.79846
|0.06713
|2.12835
|-
|1
|2
|2
|5
|1.49014
|2.14889
|0.10057
|1.90772
|0.05279
|2.14047
|-
|1
|2
|2
|6
|0.82235
|2.22517
|0.07573
|1.94963
|0.04014
|2.17549
|-
|1
|2
|2
|7
|1.53608
|2.08972
|0.11472
|1.81148
|0.0676
|2.03957
|-
|1
|2
|3
|1
|3.85525
|2.00429
|0.27991
|1.62403
|0.12863
|1.98973
|-
|1
|2
|3
|2
|4.1508
|1.9852
|0.3635
|1.47515
|0.13952
|1.97074
|-
|1
|2
|3
|3
|3.31493
|2.02332
|0.31131
|1.55183
|0.11703
|2.00696
|-
|1
|2
|3
|4
|2.47354
|2.0652
|0.20828
|1.71637
|0.09402
|2.04147
|-
|1
|2
|3
|5
|1.68517
|2.08809
|0.14418
|1.80246
|0.06917
|2.05808
|-
|1
|2
|3
|6
|1.316
|2.12714
|0.11206
|1.87179
|0.04723
|2.12486
|-
|1
|2
|3
|7
|0.4841
|2.20538
|0.04633
|2.02915
|0.02369
|2.18113
|-
|1
|2
|4
|1
|2.82623
|2.01819
|0.25826
|1.69268
|0.11251
|1.97665
|-
|1
|2
|4
|2
|3.24039
|1.9811
|0.36283
|1.50648
|0.11719
|1.96246
|-
|1
|2
|4
|3
|2.4545
|2.03386
|0.19627
|1.75339
|0.09698
|2.00807
|-
|1
|2
|4
|4
|2.46446
|2.01626
|0.17827
|1.76414
|0.08026
|2.02912
|-
|1
|2
|4
|5
|2.11339
|2.00724
|0.14884
|1.77964
|0.07749
|2.00585
|-
|1
|2
|4
|6
|1.51141
|2.04563
|0.11559
|1.82474
|0.06194
|2.02586
|-
|1
|2
|4
|7
|0.95936
|2.09963
|0.07044
|1.95281
|0.03645
|2.0993
|-
|1
|2
|5
|1
|3.36561
|1.97323
|0.2649
|1.65361
|0.13019
|1.92402
|-
|1
|2
|5
|2
|3.66222
|1.95479
|0.35065
|1.51028
|0.14652
|1.89882
|-
|1
|2
|5
|3
|3.20442
|1.96165
|0.28676
|1.58823
|0.12031
|1.93028
|-
|1
|2
|5
|4
|1.78673
|2.0426
|0.17183
|1.75198
|0.0678
|2.02025
|-
|1
|2
|5
|5
|1.61868
|2.01988
|0.11914
|1.80878
|0.06624
|1.99283
|-
|1
|2
|5
|6
|1.30123
|2.02218
|0.10515
|1.80653
|0.05345
|2.00292
|-
|1
|2
|5
|7
|0.65695
|2.08269
|0.06835
|1.89102
|0.0332
|2.0525
|-
|1
|2
|6
|1
|2.3773
|1.9669
|0.24867
|1.6336
|0.08319
|1.94741
|-
|1
|2
|6
|2
|2.82556
|1.95506
|0.31731
|1.51798
|0.12008
|1.89324
|-
|1
|2
|6
|3
|2.7235
|1.94883
|0.30621
|1.5177
|0.09365
|1.93764
|-
|1
|2
|6
|4
|1.77727
|1.98273
|0.17989
|1.69341
|0.07314
|1.95161
|-
|1
|2
|6
|5
|0.81041
|2.05295
|0.13961
|1.74391
|0.04468
|2.01091
|-
|1
|2
|6
|6
|0.72188
|2.0465
|0.09874
|1.79927
|0.03137
|2.03309
|-
|1
|2
|6
|7
|1.21598
|1.97942
|0.07065
|1.87211
|0.04484
|1.98491
|-
|1
|2
|7
|1
|3.55054
|1.89128
|0.27402
|1.61031
|0.10827
|1.89085
|-
|1
|2
|7
|2
|5.0062
|1.81574
|0.3119
|1.54857
|0.18009
|1.76865
|-
|1
|2
|7
|3
|3.95204
|1.84947
|0.30465
|1.53907
|0.16048
|1.789
|-
|1
|2
|7
|4
|2.36233
|1.9168
|0.18751
|1.70412
|0.09531
|1.88355
|-
|1
|2
|7
|5
|1.48851
|1.94443
|0.09973
|1.81041
|0.05904
|1.92497
|-
|1
|2
|7
|6
|1.22525
|1.94454
|0.06617
|1.87082
|0.05516
|1.91259
|-
|1
|2
|7
|7
|1.13847
|1.93756
|0.08109
|1.83388
|0.04706
|1.93165
|-
|1
|2
|8
|1
|4.09874
|1.87708
|0.20312
|1.73434
|0.15506
|1.83083
|-
|1
|2
|8
|2
|4.66403
|1.84302
|0.31808
|1.56093
|0.18049
|1.78288
|-
|1
|2
|8
|3
|3.24375
|1.89351
|0.2827
|1.59546
|0.13583
|1.83427
|-
|1
|2
|8
|4
|2.24175
|1.92084
|0.17795
|1.72611
|0.09636
|1.87438
|-
|1
|2
|8
|5
|1.63783
|1.93625
|0.1225
|1.78642
|0.0659
|1.90934
|-
|1
|2
|8
|6
|2.01753
|1.89095
|0.13742
|1.74752
|0.08289
|1.86553
|-
|1
|2
|8
|7
|0.97568
|1.97215
|0.05926
|1.88807
|0.04057
|1.95672
|-
|2
|1
|1
|1
|3.44076
|1.73133
|0.27759
|1.55037
|0.13323
|1.68913
|-
|2
|1
|1
|2
|4.99596
|1.64527
|0.2322
|1.58033
|0.17533
|1.62422
|-
|2
|1
|1
|3
|3.83372
|1.68144
|0.25087
|1.52033
|0.14525
|1.66706
|-
|2
|1
|1
|4
|3.87034
|1.68102
|0.20979
|1.60153
|0.13627
|1.68885
|-
|2
|1
|1
|5
|1.76134
|1.80424
|0.15241
|1.70485
|0.06231
|1.81524
|-
|2
|1
|1
|6
|0.79304
|1.89072
|0.09906
|1.80312
|0.03277
|1.89435
|-
|2
|1
|1
|7
|1.43535
|1.80614
|0.0593
|1.81589
|0.0407
|1.85002
|-
|2
|1
|2
|1
|3.72284
|1.68499
|0.19226
|1.66567
|0.1237
|1.66453
|-
|2
|1
|2
|2
|4.42667
|1.66508
|0.24314
|1.55652
|0.14361
|1.66251
|-
|2
|1
|2
|3
|2.7019
|1.75871
|0.32717
|1.38452
|0.11056
|1.72312
|-
|2
|1
|2
|4
|2.41538
|1.75937
|0.14575
|1.68355
|0.09038
|1.74138
|-
|2
|1
|2
|5
|1.65412
|1.81649
|0.13926
|1.70623
|0.0597
|1.81378
|-
|2
|1
|2
|6
|2.0843
|1.7735
|0.21052
|1.57508
|0.07244
|1.78566
|-
|2
|1
|2
|7
|1.43238
|1.80651
|0.08031
|1.78712
|0.05269
|1.81727
|-
|2
|1
|3
|1
|2.45314
|1.77068
|0.18152
|1.73443
|0.07657
|1.78025
|-
|2
|1
|3
|2
|3.01217
|1.70966
|0.19388
|1.66175
|0.05624
|1.80606
|-
|2
|1
|3
|3
|2.09997
|1.74945
|0.14493
|1.68277
|0.05446
|1.7922
|-
|2
|1
|3
|4
|2.36683
|1.71741
|0.12244
|1.71407
|0.06775
|1.75721
|-
|2
|1
|3
|5
|1.56776
|1.75755
|0.08776
|1.76946
|0.04244
|1.79675
|-
|2
|1
|3
|6
|1.63824
|1.75452
|0.09422
|1.76794
|0.04181
|1.80604
|-
|2
|1
|3
|7
|0.74114
|1.83421
|0.08039
|1.78306
|0.02347
|1.85596
|-
|2
|1
|4
|1
|1.47047
|1.78588
|0.17271
|1.69379
|0.06511
|1.74985
|-
|2
|1
|4
|2
|2.22168
|1.72985
|0.20701
|1.59429
|0.08178
|1.71455
|-
|2
|1
|4
|3
|2.50108
|1.69618
|0.16828
|1.61962
|0.08598
|1.70516
|-
|2
|1
|4
|4
|1.97141
|1.7202
|0.1446
|1.66357
|0.06856
|1.73201
|-
|2
|1
|4
|5
|1.17054
|1.75879
|0.1172
|1.69234
|0.04624
|1.75806
|-
|2
|1
|4
|6
|1.74755
|1.70968
|0.12562
|1.67603
|0.0629
|1.72333
|-
|2
|1
|4
|7
|0.52482
|1.80155
|0.07345
|1.75615
|0.02671
|1.79288
|-
|2
|1
|5
|1
|1.76464
|1.76219
|0.24301
|1.59094
|0.07156
|1.73136
|-
|2
|1
|5
|2
|1.99594
|1.73438
|0.1984
|1.5954
|0.06489
|1.73449
|-
|2
|1
|5
|3
|1.8804
|1.72362
|0.13019
|1.67977
|0.06783
|1.71916
|-
|2
|1
|5
|4
|1.83337
|1.71477
|0.11197
|1.70244
|0.05764
|1.73194
|-
|2
|1
|5
|5
|1.49752
|1.72615
|0.13128
|1.65461
|0.04656
|1.7433
|-
|2
|1
|5
|6
|1.3042
|1.7305
|0.07173
|1.75315
|0.04482
|1.7399
|-
|2
|1
|5
|7
|2.00868
|1.67669
|0.12298
|1.64761
|0.09175
|1.64669
|-
|2
|1
|6
|1
|0.84993
|1.75972
|0.12918
|1.74026
|0.0328
|1.74802
|-
|2
|1
|6
|2
|1.93666
|1.67406
|0.16606
|1.59943
|0.04535
|1.7106
|-
|2
|1
|6
|3
|2.12115
|1.64964
|0.19988
|1.50821
|0.05229
|1.68986
|-
|2
|1
|6
|4
|0.68831
|1.73901
|0.09674
|1.6838
|0.01696
|1.75787
|-
|2
|1
|6
|5
|1.13081
|1.69479
|0.06413
|1.72559
|0.04936
|1.67757
|-
|2
|1
|6
|6
|0.5893
|1.72537
|0.02598
|1.80138
|0.01591
|1.74082
|-
|2
|1
|6
|7
|0.72519
|1.71955
|0.03157
|1.78405
|0.02889
|1.71972
|-
|2
|1
|7
|1
|1.85937
|1.66064
|0.2416
|1.49676
|0.06807
|1.63599
|-
|2
|1
|7
|2
|1.8527
|1.64892
|0.2374
|1.43845
|0.06336
|1.6431
|-
|2
|1
|7
|3
|1.56905
|1.66084
|0.15434
|1.55598
|0.04336
|1.68109
|-
|2
|1
|7
|4
|0.74968
|1.69857
|0.13496
|1.56636
|0.02871
|1.6933
|-
|2
|1
|7
|5
|1.08222
|1.65925
|0.10847
|1.613
|0.03305
|1.67829
|-
|2
|1
|7
|6
|1.1124
|1.68059
|0.14267
|1.57525
|0.04416
|1.6776
|-
|2
|1
|7
|7
|0.88031
|1.6751
|0.10534
|1.60483
|0.04216
|1.66444
|-
|2
|1
|8
|1
|0.62802
|1.72402
|0.19225
|1.54631
|0.03247
|1.69368
|-
|2
|1
|8
|2
|0.83902
|1.68303
|0.15492
|1.53421
|0.05922
|1.61411
|-
|2
|1
|8
|3
|1.33727
|1.63407
|0.19835
|1.43309
|0.05874
|1.61141
|-
|2
|1
|8
|4
|1.06381
|1.64762
|0.11026
|1.58762
|0.04019
|1.64574
|-
|2
|1
|8
|5
|1.13714
|1.61716
|0.13322
|1.53166
|0.05648
|1.59149
|-
|2
|1
|8
|6
|1.19134
|1.60463
|0.11089
|1.54864
|0.06258
|1.56912
|-
|2
|1
|8
|7
|1.58872
|1.60204
|0.066
|1.64659
|0.04748
|1.63282
|-
|2
|2
|1
|1
|3.46775
|1.78609
|0.28956
|1.68515
|0.15003
|1.72171
|-
|2
|2
|1
|2
|5.69879
|1.67614
|0.3725
|1.5045
|0.19774
|1.64659
|-
|2
|2
|1
|3
|5.18985
|1.66571
|0.40124
|1.40574
|0.17828
|1.65793
|-
|2
|2
|1
|4
|3.43435
|1.74182
|0.20332
|1.66994
|0.11075
|1.76221
|-
|2
|2
|1
|5
|2.48643
|1.76219
|0.13714
|1.7396
|0.09636
|1.75624
|-
|2
|2
|1
|6
|1.41151
|1.82292
|0.15415
|1.6725
|0.06549
|1.80013
|-
|2
|2
|1
|7
|0.9096
|1.8409
|0.08811
|1.7823
|0.03467
|1.85275
|-
|2
|2
|2
|1
|1.85358
|1.83615
|0.28355
|1.64765
|0.06055
|1.83138
|-
|2
|2
|2
|2
|3.81188
|1.74978
|0.25972
|1.62799
|0.11238
|1.7646
|-
|2
|2
|2
|3
|3.16717
|1.76679
|0.29832
|1.53409
|0.09407
|1.78959
|-
|2
|2
|2
|4
|2.33664
|1.78934
|0.22694
|1.60101
|0.07273
|1.80371
|-
|2
|2
|2
|5
|2.01675
|1.79303
|0.10664
|1.79792
|0.06062
|1.8184
|-
|2
|2
|2
|6
|1.80809
|1.80081
|0.13659
|1.70935
|0.07335
|1.79213
|-
|2
|2
|2
|7
|1.01661
|1.8295
|0.0548
|1.84688
|0.03414
|1.84213
|-
|2
|2
|3
|1
|2.01474
|1.8142
|0.21867
|1.74325
|0.05359
|1.83088
|-
|2
|2
|3
|2
|3.53989
|1.71985
|0.28196
|1.60868
|0.10823
|1.73763
|-
|2
|2
|3
|3
|3.38412
|1.69907
|0.27409
|1.56164
|0.11042
|1.71397
|-
|2
|2
|3
|4
|2.2171
|1.74622
|0.16076
|1.70107
|0.07372
|1.75906
|-
|2
|2
|3
|5
|1.11799
|1.80944
|0.11087
|1.75678
|0.03792
|1.81891
|-
|2
|2
|3
|6
|1.40464
|1.76033
|0.10048
|1.72933
|0.05342
|1.75745
|-
|2
|2
|3
|7
|0.11328
|1.8972
|0.04052
|1.87101
|0.00787
|1.88753
|-
|2
|2
|4
|1
|2.59777
|1.74476
|0.28154
|1.66509
|0.10763
|1.71072
|-
|2
|2
|4
|2
|3.53853
|1.69511
|0.38311
|1.46839
|0.13243
|1.66523
|-
|2
|2
|4
|3
|2.80538
|1.70587
|0.26686
|1.55787
|0.1126
|1.68024
|-
|2
|2
|4
|4
|2.18191
|1.72068
|0.18333
|1.65612
|0.085
|1.71029
|-
|2
|2
|4
|5
|1.23383
|1.7716
|0.12824
|1.71179
|0.04845
|1.76628
|-
|2
|2
|4
|6
|0.85652
|1.79279
|0.0763
|1.79314
|0.03563
|1.78528
|-
|2
|2
|4
|7
|0.97995
|1.77178
|0.0797
|1.7577
|0.03846
|1.77043
|-
|2
|2
|5
|1
|2.47016
|1.74985
|0.32061
|1.60073
|0.10455
|1.71058
|-
|2
|2
|5
|2
|3.76194
|1.68979
|0.32787
|1.54675
|0.11781
|1.69109
|-
|2
|2
|5
|3
|2.61421
|1.70766
|0.20307
|1.64866
|0.08315
|1.71378
|-
|2
|2
|5
|4
|1.6809
|1.74028
|0.16795
|1.66491
|0.06202
|1.73305
|-
|2
|2
|5
|5
|1.31241
|1.75722
|0.14383
|1.68302
|0.05338
|1.74562
|-
|2
|2
|5
|6
|1.66563
|1.71781
|0.12721
|1.69231
|0.06147
|1.72101
|-
|2
|2
|5
|7
|0.87471
|1.74991
|0.07882
|1.71706
|0.04173
|1.73246
|-
|2
|2
|6
|1
|1.70055
|1.72832
|0.20839
|1.67759
|0.06001
|1.71779
|-
|2
|2
|6
|2
|3.20558
|1.65143
|0.33676
|1.47797
|0.09642
|1.6546
|-
|2
|2
|6
|3
|1.5827
|1.71538
|0.19719
|1.62038
|0.05324
|1.71254
|-
|2
|2
|6
|4
|1.7692
|1.69473
|0.14854
|1.66225
|0.05758
|1.69946
|-
|2
|2
|6
|5
|1.33003
|1.70542
|0.10726
|1.69398
|0.04565
|1.7096
|-
|2
|2
|6
|6
|1.01266
|1.71155
|0.09376
|1.70285
|0.04005
|1.70822
|-
|2
|2
|6
|7
|0.9856
|1.70091
|0.06454
|1.73063
|0.0394
|1.69796
|-
|2
|2
|7
|1
|2.02441
|1.67788
|0.30435
|1.5407
|0.08673
|1.63673
|-
|2
|2
|7
|2
|1.43949
|1.71143
|0.30098
|1.47963
|0.06527
|1.67295
|-
|2
|2
|7
|3
|1.68946
|1.66442
|0.24777
|1.47116
|0.06594
|1.64834
|-
|2
|2
|7
|4
|1.10967
|1.68591
|0.15663
|1.60109
|0.04949
|1.67069
|-
|2
|2
|7
|5
|0.77866
|1.70882
|0.11248
|1.64389
|0.03402
|1.70215
|-
|2
|2
|7
|6
|0.67502
|1.69719
|0.10289
|1.62419
|0.03507
|1.67744
|-
|2
|2
|7
|7
|0.65216
|1.70336
|0.05545
|1.73388
|0.02233
|1.72102
|-
|2
|2
|8
|1
|1.33877
|1.67358
|0.18369
|1.64385
|0.06055
|1.63818
|-
|2
|2
|8
|2
|0.71697
|1.71038
|0.25461
|1.49037
|0.04798
|1.66397
|-
|2
|2
|8
|3
|2.13197
|1.62429
|0.2393
|1.47673
|0.08136
|1.6065
|-
|2
|2
|8
|4
|1.16932
|1.66188
|0.13759
|1.60108
|0.0463
|1.64856
|-
|2
|2
|8
|5
|1.48369
|1.62387
|0.12547
|1.58988
|0.06919
|1.5925
|-
|2
|2
|8
|6
|1.18879
|1.65442
|0.10031
|1.62813
|0.07392
|1.58846
|-
|2
|2
|8
|7
|0.58052
|1.68546
|0.02696
|1.7382
|0.01982
|1.70519
|}
</center>
</div>
</div>

== Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme ==
<div class="mw-collapsible mw-collapsed">
<div>
=== Abstract ===
Based on comments on imprecision of the estimation method for 24-hour fat % in AM/PM milk recording schemes the regression formula was extended and re-estimated. Non-linearity for the existing effects of protein % of the milk sample, interval before sampling, milk amount of sample, milk amount of previous milking and interval before the previous milking was incorporated by using polynomials. Extensions were made by adding the effects of time of sampling, parity and month of sampling as class variables and lactation stage as polynomial. In total a reduction of the standard deviation of the difference between true and estimated 24-hour fat % of 2.4% was reached (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

'''''Keywords''''': estimation, fat %, AM/PM.

=== Introduction ===
The AM/PM milk recording routine is based on only one morning (a.m.) or evening (p.m.) milk sample which are collected in an alternating way. A condition to take part in this AM/PM milk recording in The Netherlands is that on farm electronic milk measurements (EMM) are available. EMM-data consists of time of milking and milk quantity of every milking. Based on one milk sample and the EMM-data the 24-hour fat % is estimated (Peeters & Galesloot, 2002<ref name=":2">Peeters, R. and P. Galesloot, 2002.Estimating daily fat yield from a single milking on test day for herds with a robotic milking system. J. Dairy Sci. 85, 682-688.</ref>). Also for farms with an automatic milking system (AMS) this estimation is used when only one milk sample is available for analysis on milk composition.

Based on comments from farmers on fluctuations in 24-hour fat % preliminary research was conducted. This showed that the current estimation caused an underestimation of 24-hour fat % based on an a.m.-sample of 0.09% while the estimate based on a p.m.-sample was overestimated by 0.05%. Possible causes for this fluctuation are differences in milk-fat synthesis between day- and night-time as was shown by Gilbert et al. (1972) <ref>Gilbert, G.R., G.L. Hargrove and M. Kroger, 1972. Diurnal variations in milk yield, fat yield, milk fat % and milk protein % by the test interval method. J. Dairy Sci. 56, 409-410.</ref>and Lee & Wardorp (1984)<ref>Lee, A.J. and Wardorp, 1984. Predicting daily milk yield, fat percent, and protein percent from morning or afternoon tests. J. Dairy Sci. 67, 351-360.</ref>. Other factors of imprecision in the current estimation can be caused by lactation stage and parity, two factors that are accounted for in the method of Liu et al. (2000)<ref>Liu, Z., R. Reents, F. Reinhardt and K Kuwan, 2000. Approaches to estimating daily yield from single milk testing schemes and use of a.m.-p.m. records in test-day model genetic evaluation in dairy cattle. J. Dairy Sci. 83, 2672-2682.</ref>.

The objective of this research is to re-estimate the regression formula which is used to estimate the 24-hour fat %s in AM/PM milk recording and AMS recordings with only one sample. By testing for non-linearity of current effects and introducing new explanatory variables the aim is to increase the accuracy of the estimated 24-hour fat %.

=== Material and Methods ===
The data needed for the objective had to meet a number of criteria. The most important criteria were that the data comprised:

* differences in interval between milking times;
* different milking times;
* multiple samples per cow per herd test date;
* milking time and quantity of all milkings;

Only data of farms that use an AMS met all of these criteria. Therefore the research was conducted on data of all farms that used an AMS from January 20th 2001 until July 1st 2004. Records with only one sample per herd test date were excluded from the analysis.

In order to estimate as well as validate the new regression formula the each herd test date was assigned at random into two separate datasets. Dataset 1 was used for estimation and contained 371.528 samplings on 50.591 cows on 537 farms. Dataset 2 was used for validation and contained 371.885 milkings on 50.643 cows on 538 farms. Some characteristics of variables of both datasets are presented in Table 1.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" |'''''Table 1. Characteristics of variables in dataset 1 (estimation) and dataset 2 (validation).'''''
|-
| rowspan="2" |'''Variable'''
| colspan="2" |'''Dataset 1 (estimation)'''
| colspan="2" |'''Dataset 2 (validation)'''
|-
|'''Mean'''
|'''Std'''
|'''Mean'''
|'''Std'''
|-
|Sample milk amount (kg)
|10.1
|3.1
|10.1
|3.1
|-
|Sample fat (%)
|4.40
|0.76
|4.41
|0.76
|-
|Sample protein (%)
|3.49
|0.35
|3.49
|0.35
|-
|Time at sampling
|12.29
|7.24
|12.31
|7.24
|-
|Interval before sample (min)
|520
|154
|521
|155
|-
|Interval before prev. milking (min)
|526
|158
|527
|159
|}
</center>

=== Methods ===
The analysis started with the currently used regression formula which uses the effects: fat %, protein %, milk amount of sampling, interval before sampling, milk amount of the previous milking and interval before the previous milking (Peeters & Galesloot, 2002<ref name=":2" />). All these effects are considered to be linear. As an extra check of the data this regression formula was re-estimated and compared to the currently used regression formula. In order to estimate the regression formula first of all the 24-hour fat % was determined by using a weighted average of all milk samples for that cow on that herd test date.

Subsequently, a number of changes to the regression formula were tested for their effect on the accuracy of the 24-hour fat %. The changes that are tested are:

# non-linearity of the current effects;
# effect of time at sampling;
# effect of lactation stage;
# effect of parity;
# month of milk recording;

The effects were all tested in a similar way by plotting the residuals of the regression formula without the effect that is tested to the tested effect. Based on this plot a possible relation between residual and effect becomes clear and the best way of incorporating the effect is shown. The conclusion if an effect had a positive effect on the accuracy of the regression formula was based on the standard deviation of the difference between estimated and true 24-hour fat %. Also the correlation between the two fat %s and the b-factor (regression coefficient) of the linear regression between the two fat %s were considered.

=== Results ===
The regression coefficients of the re-estimated regression formula differed slightly from the estimates by Peeters & Galesloot (2002)<ref name=":1" />, probably due to the different dataset.

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %.
[[File:Imagefig1.png|center|thumb|''Figure 1a: Average residual per class for the variables sample fat %'']]
[[File:Imagefig1b.png|center|thumb|''Figure 1b: Sample protein %'' ]]
[[File:Imagefig1c.png|center|thumb|''Figure 1c : Interval before sampling'']]
[[File:Imagefig1d.png|center|thumb|''Figure 1d : Interval before previous milking'']]
[[File:Imagefig1e.png|center|thumb|''Figure 1e : Sample milk amount'']]
[[File:Imagefig1f.png|center|thumb|''Figure 1f: Milk amount before sampling'']]

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %. Of all variables, only fat % of the milk sample (Figure 1a) seemed to be linear. A 2nd order polynomial fitted the interval before the previous milking. The other variables, i.e. protein % of the milk sample, interval before sampling, milk amount of sample and milk amount of the previous milking were described by a 3rd order polynomial. For all variables except fat % of the sample higher order polynomials were found significant. This however was caused by the large amount of data and no longer a possible biological effect since it also had no effect on the accuracy of the estimation.

The effect of time of sampling showed a large amount of variability over time. Using a polynomial to fit the data was therefore difficult. Estimation of the effect by hourly intervals was a good alternative as is shown in Figure 2. Lactation stage had mainly an effect in the first 50 days of lactation as is shown by Figure 3. A 3rd order polynomial fitted the data properly.
[[File:Imagefig2.png|center|thumb|''Figure 2. Average residual per class for time of sampling (minutes after midnight).'']]
[[File:Imagefig33.png|center|thumb|''Figure 3. Average residual per class for lactation stage (days).'']]

The effects of parity and month of milk sampling were both considered as class variables. For parity the effects of parity 1 to 6 and 7 or higher were considered. Table 2 shows that mainly for the lower parities the estimated 24-hour fat % was overestimated. Also the months May to October, usually the pasture period, showed an overestimation of 24-hour fat %.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" |'''''Table 2. Effect of parity and month of sampling on estimated 24-hour fat % (*100).'''''
|-
|'''Parity'''
|'''Estimate'''
|'''Month of sampling'''
|'''Estimate'''
|-
|1
|<nowiki>-6.58</nowiki>
|January
|<nowiki>-0.24</nowiki>
|-
|2
|<nowiki>-3.56</nowiki>
|February
|<nowiki>-0.28</nowiki>
|-
|3
|<nowiki>-1.42</nowiki>
|June
|<nowiki>-0.54</nowiki>
|-
|4
|<nowiki>-0.48</nowiki>
|April
|<nowiki>-0.27</nowiki>
|-
|5
|<nowiki>-0.35</nowiki>
|May
|<nowiki>-2.07</nowiki>
|-
|6
|<nowiki>-0.35</nowiki>
|June
|<nowiki>-3.36</nowiki>
|-
|7+
|<nowiki>-0.00</nowiki>
|July
|<nowiki>-4.32</nowiki>
|-
|
|
|August
|<nowiki>-5.52</nowiki>
|-
|
|
|September
|<nowiki>-4.74</nowiki>
|-
|
|
|October
|<nowiki>-2.24</nowiki>
|-
|
|
|November
|<nowiki>-0.97</nowiki>
|-
|
|
|December
|<nowiki>-0.00</nowiki>
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" |'''''Table 3. Statistics of the difference between true and estimated 24-hour fat % for six regression formulas (current, re-estimated + five steps), each also including preceding steps.'''''
|-
|style="text-align: left;"|'''Regression'''
|'''Std.'''
|'''Min'''
|'''Max'''
|'''Cor'''
|'''b-factor'''
|-
|style="text-align: left;"|Current, re-estimated
|0.2856
|<nowiki>-1.840</nowiki>
|2.224
|0.898
|0.807
|-
|style="text-align: left;"|Non-linearity
|0.2820
|<nowiki>-1.890 </nowiki>
|2.198
|0.901
|0.812
|-
|style="text-align: left;"|Time of sampling
|0.2817
|<nowiki>-1.877 </nowiki>
|2.211
|0.901
|0.813
|-
|style="text-align: left;"|Lactation stage
|0.2803
|<nowiki>-1.883 </nowiki>
|2.196
|0.902
|0.814
|-
|style="text-align: left;"|Parity
|0.2794
|<nowiki>-1.887 </nowiki>
|2.179
|0.903
|0.816
|-
|style="text-align: left;"|Month of sampling
|0.2788
|<nowiki>-1.868 </nowiki>
|2.175
|0.903
|0.817
|}
</center>

Table 3 shows some statistics of the difference between the true and estimated 24-hour fat % based on dataset 2 (validation) of the different regression formulas. Each of the five changes to the regression formula had a (minor) positive effect on either the standard deviation of the difference between the true and estimated 24-hour fat % (Std.), the correlation (Cor) between the two fat %s, the b-factor of the linear regression between the two fat %s or a combination of the these. All changes together reduced the standard deviation with 2.4% from 0.2856 to 0.2788, increased the correlation from 0.898 to 0.903 and increased the b-factor from 0.807 to 0.817.

=== Conclusions ===
The regression formula to estimate the 24-hour fat % based on one milk sample was improved. Improvements were first of all considering non-linearity of the variables by using polynomials for protein % of the milk sample (3rd order), interval before sampling (3rd order), milk amount of sample (3rd order), milk amount of previous milking (3rd order) and interval before the previous milking (2nd order). Secondly, adding the effects of time of sampling (class variable), lactation stage (3rd order polynomial), parity (class variable) and month of sampling (class variable) gave a further reduction of the difference between true and estimated 24-hour fat %. The total reduction in standard deviation of the difference between true and estimated 24-hour fat % is 2.4% (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

</div>
</div>

== Appendix 3 - A unified Python implementation of standardized 305 day yield calculation methods ==
<div class="mw-collapsible mw-collapsed">
<div>
The ICAR guideline is translated into an open-source Python package that can serve as a reference implementation for 305-day yield calculation. In addition to implementing the methods described in the original guideline (with the exception of the multi-trait method, which will be added in future work), the package incorporates 14 lactation-curve models, including traditional parametric models, Bayesian fitting approaches, and an AI-based model. The package also provides tools to derive biologically relevant lactation characteristics such as time to peak, peak yield, cumulative yield, and persistency. The package is publicly available through PyPI and can be installed directly using pip install lactationcurve (van Leerdam et al., 2026). Extensive documentation was developed alongside the package to improve transparency and reproducibility [https://bovi-analytics.github.io/bovi/lactationcurve.html https://bovi-analytics.github.io/bovi/lactationcurve.html.]

Through a companioning website (https://tools.bovi-analytics.org<nowiki/>/), users can upload milk-recording data in CSV format, fit and visualize the implemented lactation-curve models, and compare different cumulative milk-yield methodologies on both test-day and fully daily-recorded lactations using metrics such as RMSE, Pearson correlation, MAPE, and MAE. Reference datasets are provided to allow organizations to benchmark their own calculations against alternative methodologies. In addition, downloadable PDF reports summarize the results through detailed statistics and scatterplots, both overall and stratified by parity.
</div>
</div>

Section 02 – Cattle Milk Recording

2026-07-22T18:12:04Z

Cmosconi:

= Overview =
<div class="mw-collapsible mw-collapsed">
<div>
== Introduction ==
Information about milk production traits is very important for managing and breeding dairy herds. The milk recording process starts with the collection of animal identification, a calving date of milking cows, the amount of milk given and the date with time or time frame of a day. A milk sample may be taken. The obtained milk sample is analysed for milk constituents. The results of the analysis plus the data about milk yield and time of milking are stored in a database. Subsequently a number of parameters, cumulative yields and indices are calculated and stored in the database and, finally, reported to the farmer

This Section 2 of the ICAR Guidelines focuses on the milk recording process for dairy cattle.

== Scope ==
Figure 1 gives a pictorial summary of the main elements of this guideline.

In summary, this section of the ICAR Guidelines covers the milk recording process from the enrolment of a herd for milk recording, through to the delivery of information which a herd owner can use to assist in a range of decisions.
[[File:Scope of Section 2 - Dairy cattle milk recording..png|thumb|Figure 1. Scope of Section 2 -Dairy cattle milk recording.|center|524x524px]]

Not covered in this section are:
# Standards and guidelines for ICAR approval of milk recording devices. Please consult [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices|Section 11]] for this subject.
# Standards and guidelines for ICAR approval of ID devices. Please consult [[Section 10 – Identification Device Certification|Section 10]] for this subject.
# Standards and guidelines for preparation of milk samples and for quality assurance of milk analysis. Please consult [[Section 12 – Milk Analysis|Section 12]] for this subject.
# Standards and guidelines for in-line milk analysis on the farm. Please consult [[Section 13 – On-farm Milk Analysis|Section 13]] for this subject.

== Enrolment ==

Enrolment of new herds in the recording process should involve an agreement between the farmer and the recording organisation regarding technical and financial questions such as:

# General information about the recording programme itself, i.e.
#* Herd and cow identification.
#* Scope of recorded data, including database setup as required by the user.
#* Scheduling recording.
#* Data capture and processing.
#* Recording methods and intervals.
#* Milk measuring and meters.
#* Sampling and sample transport.
#* Reports (outcomes) and supporting decisions.
# Definition of supervision scheme and other quality assurance and plausibility checking steps.
# Fee structure and invoicing.
# Approval of technicians by milk recording organisations (MROs) so as to give them free access to farms for all recording and supervision actions.

In cases where the owner of the recorded cows or his employees carry out the recording itself, it is up to the organisation to decide upon, and provide for, any necessary training.

== Standard and Guidelines for Milk Recording ==
These standards and guidelines for milk recording are valid for all milking systems, including AMS where applicable.
====General Standards and Guidelines for milk recording====
#ICAR-approved (electronic) milk meters and sampling devices must be used on the recording day (see [https://wiki.icar.org/index.php/Section_11_%E2%80%93_Testing,_Approval_and_Checking_of_Measuring,_Recording_and_Sampling_Devices#Procedure_1:_Procedure_for_Application_for_Testing_of_Measuring,_Recording_and_Sampling_Devices_or_Sensor_Systems Procedure 1 of Section 11 - Guidelines for Testing, Approval and Checking of Milk Recording Devices]). The list of approved milk meters, jars and AMS and automatic milk sampler/tray combinations sampling devices can be found on the [https://www.icar.org/index.php/certifications/icar-certifications-for-milk-meters-for-cow-sheep-goats/ ICAR web page].
#Milk weights are recorded for each milking of the recording period. The measurement may be done using any of the ICAR approved recording devices, or by weighing. The minimum accuracy of the measurement is 0.2 kg.
#Where milk constituents are analysed, the equipment used must meet ICAR standards for accuracy. Please consult [[Section 12 – Milk Analysis|Sections 12]] and [[Section 13 – On-farm Milk Analysis|Section 13]] of the Guidelines for details.
#The accuracy of the equipment used for milk recording and sampling must be checked by an agency approved by the member organisations, on a regular and systematic basis using methods approved by ICAR. The list of methods is given in [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices#Procedure 6: Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices|Procedure 6 of Section 11]] - Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices.
#All analyses of the constituents of a milk sample must be carried out on the same milk sample.
#These samples should ideally represent the 24-hour milking period.
#If milk samples do not represent a 24-hour period, the results of milk analyses must be corrected to a 24-hour period by a method approved by ICAR (see [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]).
#In cases where the duration of recording deviates from 24 hours, the results must be converted into 24-hour yields. Only approved 24-hour yield calculation methods can be used. The appropriate methodology is described in [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]
#As date of recording, we recommend to use the date on which the last sample was taken. As alternative, the date of the first sample can be used.
#Calculation methods
##The quantities of milk and milk constituents shall be calculated according to one of the methods outlined in this section of the ICAR Guidelines (see [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Standard methods for calculating 24 hour yields]).
##Member organisations should keep the ICAR Secretariat informed about the calculation methods being used by the records processing operations in their organisation or country and shall be responsible for ensuring that the records are corrected and calculated as specified in this section of the ICAR Guidelines.
====Standards and Guidelines for milk recording using AMS====
This subsection covers systems where milk weights, milk quality or other traits of the cows are monitored constantly and automatically. This can be done in both automatic and manually operated milking systems.

Requirements:
*Animal identification is automatic and reliable. Farm transponders can also be used for automatic identification if they are linked to the cow’s official identification in farm software.
*All individual milkings must be recorded from all AMSs in the farm and transmitted to the recording database for calculation, interrupted milkings included.
*For official milk recording purposes, the data file obtained from electronic milk meters must contain the following: 1) Cow ID, 2) Milking time stamp, 3) Milk weight and 4) Sampling stamp to mark the milking where the sample comes from.
*All milkings within the recording period may be sampled, and in this case the samples should be analysed separately. Alternatively, a one-milking sample can be taken for each cow, followed by fat correction calculation.
*All cows in milk on the recording day have to be sampled. The sampling device must remain in operation until all cows are sampled. When the number of available sampling devices is smaller than the number of AMS units, sampling may need to be prolonged beyond one day to allow complete sampling of all cows. In that case, the sampling device has to be moved between AMS units.
*During sampling, the automatic sampler must be monitored to make sure there are vials left for the next cows.
*24-hour yield calculations must be carried out by a MRO, independently of the AMS manufacturer. This is done in order to guarantee harmonisation of calculation methods between the different brands of equipment and software.
*Data of all milkings over a given time period must be collected for the 24-hour milk yield calculation. A 96-hour data collection period is recommended.
Recommendations:
#Ideally, data of all milkings should be collected and used to compute lactation yield.
#Description of formats to exchange data recorded by an AMS can be requested from the manufacturer or the ICAR ADE data exchange standard for milking data can be used.
#In the case of milk recording method B (see [[Section 02 – Cattle Milk Recording#Recording|chapter 1.4 "Recording]]") with AMS, the milk recording organization should make sure that the farmer knows how to load or transfer data.
#Data can be extracted by: 1) manual operation by MRO Technician’s or Farmer (file extraction), 2) automated system and data transfer through an Application Programming Interface (API), 3) another data transfer and exchange system.
#Raw milk recording data from the AMS must be easily accessible for MRO data processing.
#For official milk recording purposes, the data file obtained from electronic milk meters may also contain the following: 1) Vial ID (this is obligatory with M sampling scheme), 2) Milking duration, 3) Milking speed, 4) Incomplete milking in automatic milking systems and 5) Other relevant data measured or reported by the equipment.
#Individual milkings should be tested for milk secretion rate in order to detect interrupted and unrecorded milkings, which in turn have an effect on the calculated 24-hour yields. If there is an interrupted milking or a milking that follows an interrupted milking at the beginning of the recording period, these two milkings must be excluded from the calculations. During the recording period they can be excluded but do not need to be.
#It is recommended to individually sample all milkings within the 24-hour recording period for 24-hour fat content calculation due to the high variability of milking frequency and milk fat content. In cases where sampling all milkings is not possible, please consult Chapter 2 of [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 - Computing 24-hour Yields] (for approved correction calculation methods).
#It is recommended to sample only milkings with a preceding interval longer than 4 hours.
====Authorisation to record====
It is recommended that professional milk recording technicians are trained and certified before they carry out recordings on their own. Ideally, such training includes a period of supervised work with a certified technician. Where such a certification system is in place, it is not allowed to record without an authorisation.

It is also recommended that frequent training is given to milk recording technicians on new technologies and equipment, safety instructions and data quality issues.

In B and C recording, farmers or their employees doing the practical recording need to be capable of operating the recording equipment correctly (e.g. milk meters, data capture tools) and are familiar with recording techniques.

It is recommended to have a conformation test from a certified recording agency and that frequent training take place.
====Cows to be recorded====
In a recorded herd, all milk-producing cows must be recorded. If a herd is divided into groups, all animals in the group have to be recorded on the same recording scheme. If different recording schemes are practiced on the farm all cows must be recorded according to the standards for recording and sampling intervals in table 3.

Acceptable reasons for missing data are discussed below, in 5.5. Missing results and/or abnormal intervals are reported [[Section 02 – Cattle Milk Recording#Missing results|here]].

===Identification (ID)===
====Herd ID====
Each herd in milk recording must be allocated a unique permanent identification number.
====Animal ID====
An official milk recording system must be based on a clearly identifiable and unique animal ID. It is recommended that one identification scheme for the whole country is used. Animal identification must also be in accordance with national and international regulation (e.g. EU member countries with EU legislation - 1760/2000 for cattle), and with relevant parts of currently valid ICAR Guidelines. The animal must be marked with an ICAR approved identification device or system. If the ID of imported animals is changed, the connection to the original ID must be maintained. Management numbers for cows can be used aside the official ID.
====Identification of the sample vial====
The sample, the milk weight and the cow ID must be linked at the milking.

Vials can be identified according to:
#Vial placement in the sampling unit.
#Cow or sample ID written on the vials.
#Barcoded vial with printed cow ID.
#Barcoded vial with cow ID registered at the milking.
#RFID vial with cow ID registered at the milking.
=====Sample identification without electronic equipment=====
Samples are identified according to their placement in the sampling unit. Additionally, sample or cow numbers can be written on the vials with a waterproof marker. If this marking is not done, there must be a sure and efficient way to identify sample No. 1 (e.g. different colour) and the sequence of other samples.

Each sampling unit must be connected to a list of samples where cow ID is given for each sample. Each transportation box also has to carry the relevant herd ID’s and, preferably, the sampling dates.
=====Barcoded vials=====
Samples are identified according to the barcode on the vial label.

If the label contains cow and/or herd ID, no electronic equipment is needed at the recording. The samples can be sent to the laboratory without accompanying sample lists or herd ID markings on the box.

If the label contains a random sample ID number, the cow ID must be connected with it on the farm. This is done with a barcode reader and computer programmes making the connection possible.
=====Vials with RFID=====
Samples are identified according to the RFID chip in the vial. This system requires the use of RFID readers and specific computer programmes creating a file where the cow and vial ID’s are connected.
=====Automatic sampling systems=====
In automatic milking systems (AMS), ICAR approved automatic samplers have to be used. Sample identification in these systems can be based on vial placement, barcode or RFID. The file with corresponding cow ID is in the management programme of the milking system. Data transfer is carried out with specific software and via a specific interface from the AMS to the MRO.
=====Sample ID in the laboratory=====
For impartiality and better quality, it is recommended that the samples are identified without cow ID and sent to the laboratory anonymously and the analysis results are merged afterwards in the data processing centre.
====Connection of the sample to milking and 24 h yield====
=====Sample and milk weight from the same milking=====
The ideal situation is that the sample and milk weight represent the same milking.
=====Sample from one milking, milk weight from two=====
A corrected analysis is routinely attached to the 24-hour yield.
=====Sample from one milking, milk weight from two or more, corrected by intervals=====
In this case, a 24-hour-yield is also combined with a one-milking sample, but the 24‑hour yield is obtained by correcting the recorded milkings according to the length of the preceding milking intervals. For example, if a cow has produced 20 kg milk in two milkings and the preceding intervals total 20 hours, her 24-hour yield is calculated as 20 kg * (24 h/20 h) = 24 kg. A corrected analysis is attached to this 24‑hour yield.
=====Sample from one milking or day, milk weight from several days=====
With electronic milk meters, it is possible to use the milk production from several days. This gives better accuracy of milk yield estimation; the highest accuracy with uncorrected milk weights is reached using a 4-day average. The problem is that the sample results become disconnected from the milk yield and a loss in fat and protein yield accuracy will occur. Ideally, fat and protein production should be connected to the recording day even in AMS.

In this case, there are three options to connect samples to the 24-hour yield:
#Milk weight is estimated from a longer measurement period but for fat and protein yield estimation only the milk yield on sampling day is used.
#Information only from the recording day for constituents in milk and milk yield estimation.
#Combination of multiple day milk yield with constituents from sampling. See ICAR procedures for using data from more than one day (Lazenby ''et al''., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>, estimation of fat and protein yield (Galesloot and Peeters , 2000)<ref name=":1">Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>.
The analysis data are merged with milk weights in the laboratory or data processing centre and the date of the analysis must be known.

=== Traits to be recorded ===

==== Definition of milking speed and box time ====

===== Introduction =====
Automated Milking Systems (AMS) do measure many traits. The definition of these traits might be different per brand of AMS. Data of these traits is often used by e.g. milk recording organisations, herdbooks or management software providers. When organisations store these data in their databases and use for certain services, it is important to know how these traits are defined.

These definitions could be used by milk recording organisations etc. to take into account differences between traits measured by different brands of AMS. These definitions could also be used by manufacturers of AMS to take into account for product development, to get more alignment in trait definitions between different brands of AMS.

Aim of this document is to propose a harmonized definition of some traits measured by AMS.

At this stage, the traits milking speed and box time are taken into account. Traits related to teat coordinates are described in Section 5 (Conformatoin Recording) of the ICAR guidelines.

==== Average milking speed ====
Definition = AverageMilkingSpeed (gr/min) = {TotalMilkYield / TotalMilkingTime}

* Total milk yield (kg) = Sum of all quarter level milk yields (kg)
* Total milking time = Last Take-off time (of any teat) - Begin of milk flow (of any teat)

Recommendations for manufacturers:

* Exclude any pre-treatment time from milking time.
* Provide take-off settings (threshold in gr/min at take-off, user-defined or default) and settings for the beginning of the measurement period, as milking time will be influenced by take-off settings and by the definition of the beginning of the milk flow.

Recommendations for data users:

* Don't report milking sessions with kick-off´s, interrupted and re-attached milkings because milking time will vary for these milkings.

==== Box time ====
Different types of box time:

* Milking
* Feed-only
* Pass-through
* Selection
* Training

Definition = {End box time - Begin box time} (HH:MM:SS)

* Begin box time = datetime of recognition of animal
* End box time = datetime when cow has exited the box (which might be different from opening of the gate), best to detect when cow has actually left the box

Additional data is needed to understand the status and completeness of the milking visit (Wethal and Heringstad, 2019). Registered issues during the milking are e.g.

* ff: at least 1 teat cup kicked off
* TeatNotFound: unable to find at least 1 of the teats for milking
* IncompleteMilking/FailedMilking: Minimum of 1 teat was registered as incompletely milked.
* The expected milk yield for a milking session depends on previous milkings. Settings like yield less than 80% of expectation for a teat, the milking session would be recorded as having an incompletely milked teat.
* Manual interaction like teat manually attached or milking finished manually.

Recommendations for manufacturers:

* Make the codes available that express if a milking was successful and the cause if the milking was not successful.
* Uniform names and definitions for interrupted, incomplete or failed milkings as well.

Recommendations for data users:

* Check the availability of a code that expresses if a milking was successful and the cause if the milking was not successful. The meaning of the code can be used to consider if the box time record has to be used for the intended purpose or not.
* To check if there is any extra box time due to feeding concentrates, e.g. through user specific settings such as 'PriorityFeeding'.

=== Traits to be recorded ===
In official milk recording, the following data have to be recorded, wherever available:

# Identification of each cow in the herd, even if they remain in the herd for a very short time.
# Birth date, sex, breed and parents of each animal when known.
# All services and embryo flushings and transfers: date, recipient, sire, dam of the embryo.
# All animal deaths and movements between farms and owners.
# Recording dates and locations.
# Milk yields for each cow and recording date.
# Fat content in milk for each cow and sampling date.

It is recommended to record also the following:

# Protein content in milk for each cow and sampling date.
# Milk somatic cell count for each cow and sampling date.
# Other results obtained from milk analysis.
# Milking duration and milking speed where possible.
# Milking times during recording.
# Recording methods and respective symbols used in records.
# Information about cow during the rearing period.

=== Recording method ===
The recording method for the herd consists of using five different symbols for:

# Responsibility for the practical recording.
# Sampling scheme.
# Recording interval.
# Sampling interval (if different from the above).
# Number of milkings per day (especially any deviation from 2x milking).

The symbols in Table 2 should be used:<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Symbols for milk recording schemes.''
|- style="background-color:#efefef; text-align:center;"

|'''Responsibility for recording'''
|'''Sampling scheme'''
|'''Recording interval (weeks)'''
|'''Sampling interval (weeks)'''
|'''Number of milkings per day'''
|-
| style="text-align:center;" | A
| style="text-align:center;" | P
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | B
| style="text-align:center;" | E
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | C
| style="text-align:center;" | Z
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" |
| style="text-align:center;" | T
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" |
| style="text-align:center;" | M
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:center;" | R x
|-
| style="text-align:center;" |
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | S x
|}
</center>

As an example: Recording method is CP36, 2x means that this is a recording where records/ samples are taken partly by the owner (farmer), and partly by a technician from the MRO, where the recording frequency is every 3 weeks, where the sampling frequency is every 6 weeks, and where the number of milkings per day is 2. If a national nomenclature system is used, it should be possible to transfer this system into ICAR nomenclature.

The reference milk recording method is by a representative of the recording organisation, measuring and sampling every four weeks, with proportional sampling and two milkings per day (AP44, 2x).

Recording other than by the reference method must be indicated using the appropriate symbols.

It is recommended that a limit is set for changing the recording method e.g. so that normally it is only possible to change the method twice per year.

It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

In the next sections the symbols are explained:
====Responsibility for the recording====
This symbol indicates who is responsible for measuring the milk yields and taking samples in the herd.
#Representative of the MRO (Method A; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Farmer or his/her representative (Method B; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Mixed responsibility (Method C; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
====ICAR Standards for sampling schemes====
=====Proportional sampling (P)=====
Samples and milk weights are taken at each milking during the recording day. The sampled amount corresponds to the milk yield of each milking. This is achieved by the use of a pipette in equal number of pipetting at each milking or of a specially designed tool which ensures proportional sampling to create one mixed sample. This is the default sampling scheme with no necessary correction to the analysis results, all other schemes must be reported.
=====Equal measure sampling (E)=====
Samples and milk weights are taken at each milking during the recording day. The amount of the sample is measured to be equal at each milking and mixed into one sample. The analysis results for fat should be corrected if one of the milking intervals is shorter than 10 or longer than 14 hours.
=====Multiple sampling (M)=====
Samples are taken at more than one milking during the recording day while milk weights are taken at each milking or over several days. Samples from different milkings are not mixed but they are kept in distinct vials so that each cow has at least two samples. The analysis results must be corrected to correspond to the 24-hour fat and protein yields. For example: a cow is milked 3x during 24 hours and 2 or 3 separate samples are taken, kept and analysed in different vials. This is the gold standard for AMS. It produces the most accurate results but is more expensive.
=====One-milking sampling with milk weights from more than one milking (Z)=====
Samples are taken from one milking during the recording day while milk weights are taken at each milking or over several days. The analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Alternated one-milking recording (T)=====
Samples and milk weights are taken during one milking, alternating between morning and evening milkings. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Constant one-milking recording (C)=====
Samples and milk weights are taken during one milking, constantly during morning or evening milking. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====In-line analysis recording (I)=====
Milk is not sampled but its constituents are continuously analysed by a stationary analyser.
====ICAR Standards for recording and sampling intervals====

<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Standards for recording and sampling intervals.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| rowspan="2" style="text-align:center;" |'''Recording or sampling interval (weeks)'''
| rowspan="2" style="text-align:center;" |'''Minimum number of recordings or samplings per year'''
| colspan="2" style="text-align:center;" |'''Interval between recordings or samplings (days)'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| rowspan="10" style="text-align:center;" |Reference method
| style="text-align:center;" |1
| style="text-align:center;" |44
| style="text-align:center;" |4
| style="text-align:center;" |10
|-
| style="text-align:center;" |2
| style="text-align:center;" |22
| style="text-align:center;" |10
| style="text-align:center;" |18
|-
| style="text-align:center;" |3
| style="text-align:center;" |15
| style="text-align:center;" |16
| style="text-align:center;" |26
|-
| style="text-align:center;" |4
| style="text-align:center;" |11
| style="text-align:center;" |22
| style="text-align:center;" |37
|-
| style="text-align:center;" |5
| style="text-align:center;" |9
| style="text-align:center;" |32
| style="text-align:center;" |46
|-
| style="text-align:center;" |6
| style="text-align:center;" |8
| style="text-align:center;" |38
| style="text-align:center;" |53
|-
| style="text-align:center;" |7
| style="text-align:center;" |7
| style="text-align:center;" |44
| style="text-align:center;" |60
|-
| style="text-align:center;" |8
| style="text-align:center;" |6
| style="text-align:center;" |50
| style="text-align:center;" |70
|-
| style="text-align:center;" |9
| style="text-align:center;" |5
| style="text-align:center;" |55
| style="text-align:center;" |75
|-
| style="text-align:center;" |Daily
| style="text-align:center;" |310
| style="text-align:center;" |1
| style="text-align:center;" |3
|}
</center>

====ICAR standards for number of milkings per day====

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 3. Symbols for number of milkings per day.''
|- style="background-color:#efefef; text-align:center;"
|'''Number of milkings per day'''
|'''Symbol'''
|-
| style="text-align:center;" | Once per day milking
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | Two milkings
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | Three milkings
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" | Four milkings
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" | Continuous milking (e.g. AMS)
| style="text-align:center;" | R x
|-
| style="text-align:center;" | Regular milkings not at the same times on each day (e.g. 10 milkings per week)
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" | Shown as the average number of milkings per day.
| style="text-align:center;" |
|-
| style="text-align:center;" | Animals that are both milked and suckled. (Number of times milked to prefix the S)
| style="text-align:center;" | S x
|}
</center>

Where a herd is dry for a period of the year, the minimum number of recordings should be adjusted proportionately to the production period.

Minimum number of herd recordings should be at least 85% of the normal number of recordings.

=== Missing results and/or abnormal intervals ===
{{anchor|Missing_results}}A recorded 24-hour yield is the best estimate of the yield and the constituents of the milk, weighed, sampled and recorded within 24 hours on the day of recording.
#When herds are normally milked at intervals such that the recording day is other than 24 hours, the yields shall be adjusted to a 24-hour interval using the following procedure (or other procedures approved by the ICAR):
#*Divide 24 by the interval, then multiply by the yield. For example:
#**For a 25 hour interval (24/25) x 35 kg = 33.6 kg
#**For a 20 hour interval (24/20) x 35 kg = 42.0 kg
#A recording is a set of daily test values for a given animal on a given day of recording, one or some or all of them can be missed (missing values)
#Missing values can be due to:
#*Out of range.
#*Sickness.
#*Disaster.
#*No sample analysis results.
#The number of the official and complete (milk, fat and protein) recordings in the lactation or other accumulated yield should be reported.
#Permitted range of the daily recorded values is given in Table 5. Outside of these ranges, the daily recorded<ref>'''Note:''' High fat breeds have breed average higher than 5.0 for fat %.</ref> value will be considered as a missing value.

<center>
{| class="wikitable"
! colspan="7" style="text-align:left;" | ''Table 5. Permitted range of the daily recorded values.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| colspan="2" style="text-align:center;" |'''Milk (kg)'''
| colspan="2" style="text-align:center;" |'''Fat %'''
| colspan="2" style="text-align:center;" |'''Protein %'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| style="text-align:center;" | Main Dairy Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 1.5
| style="text-align:center;" | 9.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 7.0
|-
| style="text-align:center;" | High Fat1 Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 2.0
| style="text-align:center;" | 12.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 9.0
|}
</center>1Note: High fat breeds have breed average higher than 5.0 for fat %The true daily recorded values collected from animals labelled by the farmer as sick, injured or under treatment must be used in the computation of the lactation record unless the milk yield is less than 50% of the previous milk yield or less than 60% of the predicted yield. In such a case, the whole set of daily recorded values may be considered as missing.

Estimates of the missing values of a daily recording can be computed by using interpolation procedures or by more sophisticated procedures approved by ICAR

== Samples ==

=== Representative sample ===
The milk sample has to represent the complete milking linked to it. This is achieved by mixing the milk thoroughly or pouring it into another vessel right before sampling.

Sampling scheme P requires using a pipette for making the sample proportional between different milkings.

With sampling scheme E, it is advisable to use a measuring cup to make sure the sample parts actually are equal.

Immediately after sampling, the vials have to be preserved, capped, shaken and marked. Samples should be stored cool and dark.

=== Transport ===
Samples should be transported for analysis to a laboratory as soon as possible after sampling.

The samples need to be packed for transport and handled during transport in a manner that guarantees that sample IDs are not compromised or mixed. It is also recommended to protect the packages from external interference.

The packing material must be clean and disposable or easy to clean.

During transportation, it is recommended that the temperature of the samples stays below +10°C.

== Database ==
Storing the recorded data in a milk recording database is an indispensable part of the recording. It is recommended to use the quickest possible means to store the data in the database in order to ensure up-to-date breeding values and management applications. Where computerised data capture is possible, it should not take more than five days after the recording to have the complete recording data set in the database.

The application of the Guidelines in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield], together with other parts of the Guidelines, ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

The guidelines on storage of data collected by the milk recording process are:

# For every recording, cow identification (ID), 24-hour milk yield or individual milk yields with a minimum of 0.2 kg (or the equivalent thereof) milk accuracy and recording date have to be stored.
# Where possible, it is advisable to store each milking separately. The data stored can include milk yield, time and date of milking, and milking scheme.
# Analysed results of the milk sample are stored, namely: sample ID, fat content (or percentage), sample status, sample type. Optional data can be stored on protein and/or lactose content, somatic cell count and additional analyses.
# Analysis results can be linked to one or more milkings of the cow.
# In case of storage or performance problems it might be necessary to remove old data of individual cow milkings from the database.
# Recording day information is the yield over 24 hours and should at least be kept in the database for the current lactation and the previous lactation.
# If recording day information is changed after batch processing it should be marked with a user-ID and time stamp.
# Yields are stored in kg or lbs or, in the case of fat and protein contents, in percent units.

The necessary additional information about how the results have been obtained include:

# Who did the recording (certified technician, farmer etc.).
# Herd and/or cow milking frequency.
# How many milkings were measured.
# How many milkings were sampled.
# Sampling scheme when sampling.
# Daily yield calculation method used.
# Recording and sampling intervals.
# It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

Basic checks for recording data:

# Farm (herd) ID: identified by a unique key.
# Animal ID: has to be unique in database.
# Format of animal ID: compliant to international standards of identification and registration.
# Recording date: less than or equal to today, greater than last recording date.
# Milk yield: stored with one decimal.
# 24 hour milk yield within range ( Table 5).
# Fat and protein content: e.g. within a range of +/- 3 standard deviation of population average (Table 5).
# Calving date: greater than birthday of cow (e.g. greater than birthday of cow + 20 months).
# Calving date: less than or equal to today.
# Sample analysis

This section of the ICAR Guidelines examines how observations are performed on farms and how data are collected, analysed and reported back to farmers. It forms an integral part with other sections of the ICAR Guidelines. It ensures that samples are analysed to the relevant degree of accuracy for the purposes of milk recording, breeding value prediction and other areas of usage. ICAR members operate in a range of situations, ranging from places with almost fully automated recording systems to areas with no roads and electricity. Therefore, the guidelines only demand standards that can be followed, irrespective of production situations and recommend more advanced options, where possible or required. Under the guidelines some practices might not be permitted while other practices are tolerated but not recommended.

== Yield calculations ==
This section covers 24-hour yields and accumulated yields for milk, fat, protein and somatic cells. It also describes the procedure for acceptance of new methods not previously mentioned in the guidelines.

The basic requirements for all calculation methods are that rounding shall only take place at the last step of the computation.

=== Lactation period ===

==== Commencement of the lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, is considered to commence is:

# The day that the cow calves (calving date), or
# In the absence of a calving date, the best estimate of the day that the cow commenced milk production.

A (valid) calving is defined as a parturition taking place:

# After the mid-point of the gestation period if a service has been recorded, or,
# After at least 75% of the normal gestation period has elapsed since the previous calving recorded if no service event has been recorded.

Any parturition falling outside the above definition shall be recorded as an abortion and shall not start a new lactation period.

For cows of dairy breeds the normal gestation length shall be deemed to be 280 days unless more specific breed information is available for use.

If the first recording is done on the calving date or within the first 4 days after calving, the milk yield and constituents at the first recording should not form part of the official lactation record, especially for automated milking systems (AMS) with multiple recorded days.

==== Completion of lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, has been completed is or:

# The day that the cow ceases to give milk (goes dry) or
# The day the cow gives less than 3.0 kg/day or 1.0 kg/milking in a recording (unless recorded sick) or
# When it is common practice not to record the dry-off date, the day of the midpoint between the last recording with the cow in milk and the first recording day with the animal dry may be assumed to be the dry-off date.

The lactation period ends on whichever date above occurs first.

Cows may be recorded as absent or sick on the recording day, without the lactation period being defined as terminated.

=== Production period ===
In the case where yield records are calculated on the basis of a period of production, usually a year, the record should be expressed as a ‘production period record‘ (symbol PP).

The production period begins the day after the end of the previous production period and ends as defined by the length (in days) of the production period.

=== Additional notes ===
For any ICAR method the interval between two consecutive recordings must routinely fulfil the value for the acceptable range on the herd level.

If the first recording occurs within 14 days from calving, then no adjustment is required to the first recorded value when computing the accumulated record. If the first recording occurs 15 to 95 days from calving, then an adjustment procedure may be applied.

If the 305th day of a lactation falls before the last recording, the interpolation method should be used also for the last period to compute the yields.

=== Standard methods for calculating 24 hour yields ===
The ICAR approved methods are presented in '''[https://www.icar.org/Guidelines/02-Procedure-1-Computing-24-Hour-Yield.pdf Procedure 1 of Section 2]'''. They include:

1. Methods for calculating daily yields from AM/PM milkings:

# Method of Delorenzo and Wiggans (1986)<ref>Delorenzo, M.A., and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. [https://www.journalofdairyscience.org/article/S0022-0302(86)80678-6/pdf J Dairy Sci 69; 2386]</ref>
# Method of Liu et al. (2019). Please note that in 2022 the method of Liu et al. (2000)<ref name=":0">Liu, Z., R. Reents, F. Reinhardt and K. Kuwan. 2000. Approaches to Estimating Daily Yield from Single Milk Testing Schemes and Use of a.m.-p.m. Records in Test-Day Model Genetic Evaluation in Dairy Cattle. [https://www.journalofdairyscience.org/article/S0022-0302(00)75161-7/pdf J. Dairy Sci. 83:2672-2682].</ref> has been updated to the method of Liu et al. (2019). We recommend to organisations that currently have implemented the method of Liu et al. (2000)<ref name=":0" /> to update to method of Liu et al. (2019).
# Method of Kyntäjä et al. (2021)<ref name=":3">1. Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. [https://www.icar.org/Documents/technical_series/ICAR-Technical-Series-no-25-Virtual-Meeting/Kyntaja.pdf ICAR Technical Series no. 25: 171-175.]</ref>

2. Methods to estimate 24h yield from Automatic Milking Systems:

# Using data on more than one day (Lazenby et al., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Using data on 1 day (Bouloc et al., 2002)<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Estimation of fat and protein yield (Galesloot and Peeters, 2000)<ref>Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>
# Sampling period (Hand et al., 2004<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D.F. 2004. Comparison of Protocols to Estimate 24 Hour Percent Fat and Protein. Presented at 34th ICAR session, Sousse, Tunisia, June, 2004. Proceedings of the 34th ICAR Meeting EAAP Publication No. 113:219-224</ref>; Bouloc et al., 2004)

3. Standard methods to estimate 24h yield from electronic milk meters:

# Estimation of 24-hour milk yield
# Using data on more than one day (Hand et al., 2006)<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. [https://doi.org/10.3168/jds.S0022-0302(06)72240-8 J. Dairy Sci. 89:1723-1726]</ref>
# Estimation of 24-hour fat and protein yield

=== Standard methods for calculating accumulated yields ===
The ICAR approved methods are presented in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_2_%E2%80%93_Computing_of_Accumulated_Lactation_Yield Procedure 2 of Section 2]. They include:

# Test Interval Method (TIM) (Sargent, 1968)<ref>Sargent, F.D., V.H. Lyton, and O.G. Wall, Jr . 1968. Test interval method of calculating Dairy Herd Improvement Association records. [https://doi.org/10.3168/jds.S0022-0302(68)86943-7 J. Dairy Sci. 51:170].</ref>
# Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987)<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. [https://doi.org/10.1016/0301-6226(87)90049-2 Livest. Prod. Sci. 17:l].</ref>
# Best prediction (VanRaden, 1997)<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. [https://doi.org/10.3168/jds.S0022-0302(97)76268-4 J. Dairy Sci. 80:3015-3022].</ref>
# Multiple-Trait Procedure (MTP) (Schaeffer and Jamrozik, 1996)<ref>Schaeffer, L.R. and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. [https://doi.org/10.3168/jds.S0022-0302(96)76578-5 J. Dairy Sci. 79:2044-2055.]</ref>

=== Procedure to approve new methods ===

# All parties interested in seeking approval for any new accumulated yield calculation method will notify the ICAR Secretariat and provide a description of the proposed method.
# These parties will provide a detailed report including statistical details, scientific references and other relevant data to the ICAR Dairy Cattle Milk Recording Working Group.
# The ICAR Dairy Cattle Milk Recording Working Group will then consider the proposal and recommend that it be conditionally approved, approved or rejected.
# The final steps will consist of approval by the General Assembly and publication in the guidelines. .

== Reporting ==
This subsection covers reports, data files, statistics and calculated key figures provided to farmers for breeding and management purposes.

It is recommended that farmers are given reports after each recording and at the end of the recording year or another longer recording period. These reports should contain data on both cow and herd level. In bigger herds, it is also advisable to present results by management groups or otherwise chosen cow groups within the herd. The reporting may be done on paper, through web pages and/or in the form of data files or electronic reports.

Where data files are distributed or direct access given to the results in the database, care must be taken that data ownership is clearly defined. This also includes defining who has access to data and how this access can be authorised.

ICAR members are advised to prepare annual statistics in a reasonable timeframe after closing the recording year. The minimum data requirements are what is needed for the ICAR [https://my.icar.org/stats/list Dairy Cattle Yearly Enquiry on-line database].

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 5. Examples of key figures for herd to be used by farmers and other users.''
|- style="background-color:#efefef; text-align:center;"
|style="text-align:left |'''Key figure'''
|style="text-align:left |'''Explanation'''
|-
| style="text-align:left;" | 12-month rolling average yield
| style="text-align:center;" | Total milk, fat and protein produced during the 365 (366) days preceding the recording divided by the average number of cows for the same period.
|-
| style="text-align:left;" | Average 305-day yield
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations finished during the reporting period divided with the number of finished 305-day lactations.
|-
| style="text-align:left;" | Average 305-day yield within a period
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations during the reporting period divided with the average number of cows on a 305-day lactation within the reporting period.
|-
| style="text-align:left;" | Average annual yield
| style="text-align:center;" | Total milk, fat and protein produced during the recording year divided by the average number of cows for the same recording year.
|-
| style="text-align:left;" | Average calving interval
| style="text-align:center;" | The average preceding intervals of all calvings second and more during the reporting period.
|-
| style="text-align:left;" | Average fat, protein or lactose contents in milk
| style="text-align:center;" | Total fat, protein and lactose yields divided by the total milk yield, usually expressed with two decimals.
|-
| style="text-align:left;" | Average lactation yield
| style="text-align:center;" | Total milk, fat and protein produced within lactations of any length finished during the reporting period divided with the number of finished lactations.
|-
| style="text-align:left;" | Average lactation yield within a period
| style="text-align:center;" | Total milk, fat and protein produced during the reporting period divided with the average number of cows in milk within the reporting period.
|-
| style="text-align:left;" | Average number of cows
| style="text-align:center;" | Average number of cows in the herd (or group) on a given day during the reporting period. Usually expressed with one decimal.
|-
| style="text-align:left;" | Average somatic cell count
| style="text-align:center;" | The average of all individual cow somatic cell counts weighted for individual milk yields.
|-
| style="text-align:left;" | Daily milk, fat and protein yields
| style="text-align:center;" | 1) Total daily milk, fat and protein yields divided by number of cows, or 2) Total daily milk, fat and protein yields divided by number of cows in milk.
|-
| style="text-align:left;" | Energy Corrected Milk (ECM)
| style="text-align:center;" | Calculated according to a national standard.
Example from the Nordic countries:

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + milk yield, kg * 0.7832)/3.14

or, if lactose has been analysed

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + lactose yield * 16.54 + milk yield, kg * 0.0207)/3.14.

From solids expressed as %:

ECM = [(fat content, % * 383 + protein content, % * 242 + 783.2)/3140]* milk yield, kg

or, if lactose has been analysed

ECM = [(fat content, % * 383 + protein content, % * 242 + lactose content, % * 165.4 + 20.7)/3140]* milk yield, kg.
|-
| style="text-align:left;" | Number of lactations
| style="text-align:center;" | Total number of finished lactations in the herd (or group) during the reporting period.
|-
| style="text-align:left;" | Reporting period
| style="text-align:center;" | The period presented in the given report. The most usual options are: one day, one recording interval, lactation, rolling 365 days, recording or calendar year, and the cow’s lifetime.
|}
</center>

== Decisions ==

As a result of the recording process and reports prepared on the basis of its results, decisions can be made on one or more of the following:

=== Short term impact: day-to-day management decisions taken on farms ===

# Decisions about bulk milk quality.
# Feeding decisions - daily diet based on group or individual performance.
# Pasture management decisions.
# Grouping decisions - placing cows in different management or feeding groups.
# Culling decisions - decisions on the sale or slaughter of cattle.
# Mating decisions.
# Decisions regarding programmes of certification for milk and milk products.
# Decisions based on data flow from MRO’s to farms and vice versa.

=== Medium-term impact ===

# Farmers’ decisions based on advisory services, veterinarians, independent experts and other services.
# Decisions about production planning on farms (herd development).

=== Long-term impact ===
# Breeding programme and selection decisions - breeding partners informed by genetic evaluation ([[Section 09 – Dairy Cattle Genetic Evaluation|Section 9)]] based on milk recording results.
# Decisions based on herd book and breeder association activities and deciding on business actions related to breeding animals, i.e. in some countries animal recording data are required for international trade with breeding animals.

=== Strategic decisions ===
# Research programmes concerning management, recording and breeding.
# Political decisions about possible subsidies in dairy cattle breeding at the governmental level and implementing measurements according to agriculture policy.

== Quality control ==
This Section together with other parts of the Guidelines ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

=== Bulk tank data comparison ===
It is a recommended practice to compare milk recording data with dairy deliveries and bulk tank milk contents. This can be done on the recording day or over a longer period of time. The calculation is done as follows:

# Comparison ratio = Total recorded milk yield, kg /Total milk produced, kg. This comparison is used where there is a reliable estimate of the farm use of milk.
# Quick comparison ratio = Total recorded milk yield, kg/ Total milk delivered, kg. This comparison is used where farm use of milk is not estimated.
# Content comparison = Recorded average fat / Bulk tank average fat
# Comparison ratio for fat = Total recorded fat yield, kg/ Total fat produced, kg
# Total recorded milk yield, kg = Ʃ (Individual milk yield, kg)
# Total milk delivered, kg = Total milk delivered, litres * milk density kg/litre
# Total milk produced, kg = (Total milk delivered, litres + Milk used or discarded on the farm, litres) * milk density kg/litre
# Total fat produced, kg = Total milk produced, kg x (Bulk tank fat percent/100)
# Recorded average fat = Ʃ [Individual milk yield kg x (Individual fat percent/100)]/Ʃ (Individual milk yield, kg)

The recommended acceptable range for comparison ratios is 0.95 - 1.05, and for quick comparison ratios 0.90 - 1.00, with due regard to herd size.

=== One day bulk tank data comparison ===
Milk yields and fat yields or contents are compared on the recording day. Comparing the contents is routinely possible where every delivery is sampled or by taking a bulk tank sample (see point [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Bulk_tank_data_comparison 1.10] above for how the comparison is done.)

=== Bulk tank data comparison over a longer period ===
Milk yields and fat yields or contents are compared over a longer period of time, e.g. 4 months or 12 months. This option requires a routine to obtain the applicable data from the dairies or milk buyers. Farm use of milk may be taken into account where applicable.

=== Bulk tank sample ===
Bulk tank samples can be used to verify the milk contents analysis obtained in milk recording. A sample is taken from a well-mixed bulk tank on the recording day. It must represent the milk of the whole 24-hour period. Bulk tank fat and protein contents are then compared to the weighted averages of the fat and protein percent obtained from milk recording. Normally, the difference between the values should not be more than 5%.

=== Supervised or repeated recording ===
Supervised recording is a tool designed to verify that individual cow records are reliable. It is based on repeating the herd recording as soon as possible after the original recording, and the obtained results are compared with the original recording. It is obligatory for ICAR Certificate of Quality (CoQ) holders to practice regular supervision, irrespective of recording methods used.

It is recommended that the supervised recording will follow immediately after the original recording, but for a good reason it can be postponed for up to 7 days.

The farmer and any other staff doing the original recording must not know that a supervised recording will follow. The technician who performs the supervised recording should not be the same person who did the original recording.

Usually supervised recording is done by recording the whole herd again, using the same sampling scheme and recording method (or a reference method) as in the previous recording. When herd size exceeds 200 cows, it is also allowed to do a supervised recording to selected, or randomised groups of animals in the herd.

Choosing the herds for supervised recording may be random or based on preselection. Traits for this preselection may include high yield, great increase in yield, presence of bull dams in the herd, and general suspicions about the correctness of herd results.

The traits compared in supervised recording must include milk and fat. Comparing protein is also recommended.

=== Supervision - example of comparison calculations ===

# Milk, fat and protein yields per cow are calculated for both the original and the supervised milking.
# Individual cow records where results between supervised recording and the original recording differ outside the norms might be excused where a good explanation can be given for exclusion (illness, heat, missed milking)
# Deviations (%) are calculated for each cow and yield constituent according to the formula: deviation = (supervised yield/unsupervised yield)*100-100
# Herd averages of the absolute values for each yield constituent are calculated.
# If the supervised recording occurs within 2 days of the original recording, the acceptable difference in herd averages are 7% for milk and protein and 9% for fat.
# If the supervised recording occurs between 3 and 7 days after the original recording, the acceptable difference of the aforementioned herd averages are 9% for milk and protein and 12% for fat.

The limits mentioned in these examples are typically applied by some of the member organisations, and are not meant to be understood as exact norms. Such norms should be laid down by each member organisation.

=== Evaluation of recording data ===
It is recommended that data quality is evaluated for each herd recording day. When such an evaluation is applied, the following features of the data have to be included:

# Person responsible for the recording.
# ICAR approval and calibration status of the recording equipment if owned by the farmer.
# Number of herd recordings per time period and/or recording interval.
# Number of herd samplings per time period and/or sampling interval.

The following features are also recommended to be included if possible:

# Deviation of milk and fat yields from dairy deliveries.
# Deviation of milk and fat yields from previous or predicted yields.
# Standard deviation of individual cow records.
# Number of recorded and/or sampled milkings within the recording day.
# Number of cows missed or not recorded in the recording.
</div>
</div>
= Procedures =
== Procedure 1: Computing 24-hour Yields ==

<div class="mw-collapsible mw-collapsed">
<div>

=== Methods to calculate 24-hour yield for milk yield and fat percentage from a single milking ===

==== Method of Delorenzo & Wiggans (1986)<ref>Delorenzo, M.A. and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. J. Dairy Sci. 69: 2386-2394.</ref> ====
Daily milk (DMY) and fat yield (DFY) estimates are based on measured yield and milking frequency. An adjustment factor accounts for differences in the average milking interval (expressed in decimal hours) between the preceding milking and the measured milking, and the time of day of the measured milking (started in a.m. or p.m.). For 2X milking, an additional adjustment is applied to milk yield for the interaction between milking interval and stage of lactation, with mid lactation (158 DIM) set to zero. Milking interval does not affect protein and solids non fat (SNF) percentages and so the percentages for the sampled milking are used for test-day estimates. Protein yield is calculated from the measured percentage and the adjusted milk yield.

The prediction of DMY and DFY from single milking on morning or evening in herds milked twice a day requires factors, that are the reciprocal of the proportion of total yield expected from single milkings in relation to the milking interval.

We propose to derive these coefficients (intercept, slope, etc.) for each country separately.

===== Adjustment of milking interval =====
The milking interval is the interval between milking time for the observed milking and the milking time preceding the observed milking. The milking interval is divided into 15-minutes classes. Factors for milk and fat yields may be calculated to each class using Equation 1:

''Equation 1. Factors for milk and fat yields.''
[[File:Equation 1.png|none|thumb|397x397px]]

===== Adjustment of lactation stage =====
Because the lactation stage of the cow has an influence on the effect of different milking intervals on milk production a second adjustment is made for every interval class through a covariate of days in milk as addition:

Covariate x (days in milk - 158)

===== Estimating sample day yields =====
Formulas for prediction sample day yields and percentages in herds with two milkings are:

''Equation 2. Equation for predicting 24-hour milk yield.''
[[File:Equation2.png|none|thumb|428x428px]]

''Equation 3. Equation for predicting 24-hour fat percentage.''
[[File:Equation3.png|none|thumb|431x431px]]

''Equation 4. Equation for predicting 24-hour fat yield.''
[[File:Equation4.png|none|thumb]]

''Equation 5. Equation for predicting 24-hour protein yield.''
[[File:Equation5.png|none|thumb|316x316px]]

===== Calculation examples =====

====== Practical Application ======
Two sets of factors are available for estimating DMY from a single milking, each for morning or evening milking sampling. The factors are calculated from the formula as described above and given in Table 1.
<center>
{| class="wikitable"
| colspan="5" align="left" |'''''Table 1. Factor of milk yield and covariate for herds milked twice a day.'''''
|- style="background-color:#efefef;"
| rowspan="2" align="center" |'''Length of milking interval in hours (minutes in decimal)'''
| colspan="2" align="center" |'''Morning milking'''
| colspan="2" align="center" |'''Evening milking'''
|- style="background-color:#efefef;"
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
|-
| align="center" |< 9.00
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.594
| align="center" |0.00378
|-
| align="center" |9.00-9.24
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.534
| align="center" |0.00485
|-
| align="center" |9.25-9.49
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.477
| align="center" |0.00486
|-
| align="center" |9.50-9.74
| align="center" |2.411
| align="center" |0.00716
| align="center" |2.423
| align="center" |0.00511
|-
| align="center" |9.75-9.99
| align="center" |2.359
| align="center" |0.00726
| align="center" |2.370
| align="center" |0.00473
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |10.00-10.24
| align="center" |2.310
| align="center" |0.00458
| align="center" |2.321
| align="center" |0.00337
|-
| align="center" |10.25-10.49
| align="center" |2.262
| align="center" |0.00399
| align="center" |2.273
| align="center" |0.00214
|-
| align="center" |10.50-10.74
| align="center" |2.217
| align="center" |0.00294
| align="center" |2.227
| align="center" |0.00000
|-
| align="center" |10.75-10.99
| align="center" |2.173
| align="center" |0.00223
| align="center" |2.183
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |11.00-11.24
| align="center" |2.131
| align="center" |0.00000
| align="center" |2.140
| align="center" |0.00000
|-
| align="center" |11.25-11.49
| align="center" |2.091
| align="center" |0.00000
| align="center" |2.099
| align="center" |0.00000
|-
| align="center" |11.50-11.74
| align="center" |2.052
| align="center" |0.00000
| align="center" |2.060
| align="center" |0.00000
|-
| align="center" |11.75-11.99
| align="center" |2.014
| align="center" |0.00000
| align="center" |2.022
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |12.00
| align="center" |2.000
| align="center" |0.00000
| align="center" |2.000
| align="center" |0.00000
|-
| align="center" |12.01-12.24
| align="center" |1.978
| align="center" |0.00000
| align="center" |1.986
| align="center" |0.00000
|-
| align="center" |12.25-12.49
| align="center" |1.943
| align="center" |0.00000
| align="center" |1.951
| align="center" |0.00000
|-
| align="center" |12.50-12.74
| align="center" |1.910
| align="center" |0.00000
| align="center" |1.917
| align="center" |0.00000
|-
| align="center" |12.75-12.99
| align="center" |1.877
| align="center" |0.00000
| align="center" |1.884
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |13.00-13.24
| align="center" |1.846
| align="center" |0.00000
| align="center" |1.852
| align="center" |-0.00190
|-
| align="center" |13.25-13.49
| align="center" |1.815
| align="center" |0.00000
| align="center" |1.822
| align="center" |-0.00231
|-
| align="center" |13.50-13.74
| align="center" |1.786
| align="center" |-0.00167
| align="center" |1.792
| align="center" |-0.00308
|-
| align="center" |13.75-13.99
| align="center" |1.757
| align="center" |-0.00258
| align="center" |1.763
| align="center" |-0.00339
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |14.00-14.24
| align="center" |1.730
| align="center" |-0.00347
| align="center" |1.736
| align="center" |-0.00509
|-
| align="center" |14.25-14.49
| align="center" |1.703
| align="center" |-0.00363
| align="center" |1.709
| align="center" |-0.00471
|-
| align="center" |14.50-14.74
| align="center" |1.677
| align="center" |-0.00332
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |14.75-14.99
| align="center" |1.652
| align="center" |-0.00316
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |≥ 15.00
| align="center" |1.628
| align="center" |-0.00235
| align="center" |1.683
| align="center" |-0.00454
|}
</center>

For estimating daily fat percentage there is only one table independent of morning or evening sampling – refer to Table 2.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" |'''''Table 2. Factor of fat percentage for herds milked twice a day.'''''
|- style="background-color:#efefef;"
|'''Length of milking'''

'''interval in hours'''
|'''Fat (percentage'''

'''factor)'''
|-
|< 9.00
|0.919
|-
|9.00-9.24
|0.927
|-
|9.25-9.49
|0.934
|-
|9.50-9.74
|0.941
|-
|9.75-9.99
|0.948
|-
|
|
|-
|10.00-10.24
|0.955
|-
|10.25-10.49
|0.961
|-
|10.50-10.74
|0.968
|-
|10.75-10.99
|0.974
|-
|
|
|-
|11.00-11.24
|0.980
|-
|11.25-11.49
|0.986
|-
|11.50-11.74
|0.992
|-
|11.75-11.99
|0.997
|-
|
|
|-
|12.00
|1.000
|-
|12.01-12.24
|1.003
|-
|12.25-12.49
|1.008
|-
|12.50-12.74
|1.013
|-
|12.75-12.99
|1.018
|-
|
|
|-
|13.00-13.24
|1.023
|-
|13.25-13.49
|1.028
|-
|13.50-13.74
|1.033
|-
|13.75-13.99
|1.037
|-
|
|
|-
|14.00-14.24
|1.042
|-
|14.25-14.49
|1.046
|-
|14.50-14.74
|1.050
|-
|14.75-14.99
|1.054
|-
|≥ 15.00
|1.058
|}
</center>

Milking-interval factors are calculated using Equation 1, where the intercept and slope are as in Table 3.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 3. Slope and intercept for milk yield and fat yield.'''''
|- style="background-color:#efefef;"
| rowspan="2" |'''Trait'''
| colspan="2" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started in a.m.'''
|'''For measured milking started in p.m.'''
|-
|Milk yield
|0.0654
|0.0634
|0.0363
|-
|Fat yield
|0.1965
|0.1939
|0.0254
|}
</center>
The milking interval has no significant influence on protein percentage. Therefore, the protein percentage of the sampled milking is used as the daily protein percentage.

====== Calculation of daily yields from morning milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Data for a cow from morning milking.'''''
|-
|Begin of recording:
|6:15
|(Morning milking)
|-
|Start of preceding milking:
|17:25
|
|-
|Length of milking interval:
|12 hours 50 minutes
|(Expressed as decimal 12.83)
|-
|Milk results at morning:
|12,0
|Milk-kg
|-
|
|4,12
|Fat-percentage
|-
|
|3,45
|Protein-percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 5. Factors for morning milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.877
|-
|The covariate is
|0
|-
|The factor for fat percentage from Table 2 is
|1.018
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 6. Example calculations for morning milking.'''''
|-
|The sample-day milk yield:
|1.877 x 12,0 kg + 0 x (120 - 158) = 22,5 kg
|-
|The sample-day fat percentage:
|1.018 x 4,12 = 4,19
|-
|The sample-day fat yield:
|22,5 kg x 0,0419 = 0,94 kg
|-
|The sample-day protein yield:
|22,5 kg x 0,0345 = 0,78 kg
|}
</center>

====== Calculation of daily yields from evening milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 7. Data for a cow from evening milking.'''''
|-
|Begin of recording:
|16:48
|Evening milking
|-
|Start of preceding milking:
|6:35
|
|-
|Length of milking interval:
|13 hours 47 minutes
|Expressed as decimal 13.78
|-
|Milk results at evening:
|14,0
|Milk kg
|-
|
|4,00
|Fat percentage
|-
|
|3,40
|Protein percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 8. Factors for evening milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.763
|-
|The covariate is
|<nowiki>-0,00339</nowiki>
|-
|The factor for fat percentage from Table 2 is
|1.037
|}
{| class="wikitable"
| colspan="2" |'''''Table 9. Example calculations for evening milking.'''''
|-
|The sample-day milk yield:
|1.763 x 14,0 kg - 0,00339 x (120 - 158) = 24,8 kg
|-
|The sample-day fat percentage:
|1.037 x 4,00 = 4,15
|-
|The sample-day fat yield:
|24,8 kg x 0,0415 = 1,03 kg
|-
|The sample-day protein yield:
|24,8 kg x 0,0340 = 0,84 kg
|}
</center>

====== Alternate recording of components and milk yield at both milkings ======
For this plan only the sample-day fat yield has to be calculated with regard to milking interval. The milk yield is the sum of evening and morning milk results.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 10. Example data for a cow from both milkings.'''''
|-
|Begin of recording evening:
|17:25
|
|-
|Milk results at evening:
|10:00
|Milk kg (only milking-yield)
|-
|Begin of recording morning:
|6:15
|
|-
|Milk results at morning:
|12:00
|Milk kg
|-
|
|4:20
|Fat percentage
|-
|
|3:50
|Protein percentage
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 11. Factor for fat percentage.'''''
|-
|Length of milking interval:
|12 hours 50 minutes (expressed

as decimal 12.83)
|-
|The factor for fat percentage from Table 2 is
|1.018.
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 12. Example calculation of daily yields.'''''
|-
|The sample-day milk yield:
|10,0 kg + 12,0 kg = 22,0 kg
|-
|The sample-day fat percentage:
|1.018 x 4,20 = 4,28
|-
|The sample-day fat yield:
|22,0 kg x 0,0428 = 0,94 kg
|-
|The sample-day protein yield:
|22,0 kg x 0,0350 = 0,77 kg
|}
</center>

====== Calculation for 3X Milking ======
For 3X herds, a single milking or two consecutive milkings may be weighed. The sample may be collected at one or both of these milkings. Stage of lactation × milking interval adjustments are not used for greater than 2× milking. These AM/PM factors for estimating daily yields in 3X herds should not be confused with factors that adjust 3X records to a 2X basis. Milking-interval factors are calculated using the same formula with the intercept and slope as in Table 13.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" align = "left" |'''''Table 13. Slope and intercept factors for 3X milking.'''''
|- style="background-color:#efefef;"
| rowspan="2" | '''Trait'''
| colspan="3" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started between 2 a.m. and 9:59 a.m.'''
|'''For measured milking started between 10 a.m. and 5:59 p.m.'''
|'''For measured milking started between 6:00 p.m. and 1:59 a.m.'''
|-
|Milk yield
|0.077
|0.068
|0.066
|0.0329
|-
|Fat yield
|0.186
|0.186
|0.182
|0.0186
|}
</center>
When two milkings are included for sampling, the intercepts and intervals for both milkings are included in determining a factor for calculated estimated milk yield that is applied to the total yield from both milkings as in Equation 6.

''Equation 6. Milking interval factor for 3X milking.''
[[File:Equation6.png|none|thumb|536x536px]]
Milk and fat percent factors are calculated separately based on the number of milkings weighed or sampled.

====== Calculation for 4X - 6X Milking ======
The intercept terms for calculating 3X factors (0.077, 0.068, and 0.066) are multiplied by the factor [3 / (milkings per day)] for use in calculating factors for milking frequencies greater than 3X.

==== Method of Liu et al. (2019) ====
A multiple regression method (MRM) is used for estimating 24-hour daily milk yield (DMY), daily fat yield (DFY) and daily protein yield (DPY) based on partial yields from either morning (AM) or evening (PM) milking. Fat percentage (DFP) or protein percentage (DPP) on a 24-hour daily basis are then derived using the estimated 24-hour daily yields. The MRM can be used as a reference method for estimating daily yields and component percentages.

The method of Liu et al. (2019) is an updated version of the method of Liu et al. (2000). The model is only used for farms with 2 time milkings during 24 hours.

The following formula is used to estimate DMY, DFY, DPY based on partial yields (PMY, PFY,PPY) from either morning (AM) or evening (PM) milking:

''Equation 7. Model for predicting 24-hour yield.''

''yijk = a + bijk * xijk''

where:

yijk is the estimated 24-hour daily yield (DMY, DFY or DPY);

xijk is AM or PM partial daily yield on a test day (PMY, PFY, or PPY).

Subscript '''''i''''' represents class of parity effect with 2 levels: first and higher parities.

Subscript '''''j''''' represents class of length of preceding milking interval with 8 levels for AM milking: < 720 minutes, < 740 minutes, < 760 minutes, < 780 minutes, < 800 minutes, < 820 minutes, < 840 minutes, >= 840 minutes and 8 levels for PM milking: < 600 minutes, < 620 minutes, < 640 minutes, < 660 minutes, < 680 minutes, < 700 minutes, < 720 minutes, >= 720 minutes.

Subscript '''''k''''' represents class of lactation stage with 7 classes: < 60 days, < 120 days, < 180 days, < 240 days, < 300 days, < 360 days, >= 360 days.

'''''a''''' is the estimated intercept for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

'''''b'''''ijk is the estimated slope for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

The factors for '''''a''''' and '''''b'''''ijk can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Appendix_1_-_Adjustment_factors_to_calculate_24-hour_yields_using_the_Liu_method Appendix 1].

For a given yield trait a total number of 112 formulae are to be estimated for calculating 24-hour daily yield based on partial yield from either AM or PM milking. Component percentage for fat (DFP) and protein (DPP), on a 24-hour basis is calculated by dividing estimated fat or protein yield by estimated daily milk yield:[[File:Imagefinal.png|center|thumb|339x339px]]

===== Calculation example with method of Liu et al. (2019) =====
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" align = "left" |'''''Table 14. Data from an evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="6" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="6" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="6" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow'''

'''ID'''
|'''Calving date'''
|'''Lactation number'''
| colspan="2" |'''Milk yield (kg)'''
|'''Fat content (%)'''
|'''Protein content (%)'''
|'''Fat yield (kg)'''
|'''Protein yield (kg)'''
|'''Index1'''
|-
|A
|01.01.2020
|1
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1132
|-
|B
|01.01.2020
|2
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1232
|-
|C
|27.03.2020
|1
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1131
|-
|D
|27.03.2020
|2
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1231
|-
|
|
|
|
|
|
|
|
|
|
|}
'''1''' Index is marked in the Appendix table.
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 15. Calculation of 24-hour daily yield and components for evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="3" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="3" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="3" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow ID'''
|'''DMY (kg)'''
|'''DFY (kg)'''
| colspan="2" |'''DPY (kg)'''
|'''DFP (%)'''
|'''DPP (%)'''
|-
|A
|3,47396+25,0

<nowiki>*</nowiki> 1,98268 = 53,0401 ≈ '''53,0'''
|0,2135+0,995

<nowiki>*</nowiki> 1,68050 = 1,8855975
| colspan="2" |0,10471+0,8325* 1,99092 = 1,7621509
|1,8855975 / 53,04096*100

≈ '''3,55'''
|1,7621509 / 53,04096*100

≈ '''3,32'''
|-
|B
|4,15080+25,0* 1,98520 = 53,7808 ≈ '''53,8'''
|0,3635+0,995

<nowiki>*</nowiki> 1,47515 = 1,8312743
| colspan="2" |0,13952+0,8325* 1,97074 = 1,7801611
|1,8312743 / 53,7808*100

≈ '''3,41'''
|1,7801611 / 53,7808*100

≈ '''3,31'''
|-
|C
|2,80244+33,1

<nowiki>*</nowiki> 2,02183 = 69,72501 ≈ '''69,7'''
|0,17663+1,3339 * 1,72438 = 2,4767805
| colspan="2" |0,11078+1,1122 * 1,96422 = 2,2953855
|2,4767805 / 69,725013*100

≈ '''3,55'''
|2,2953855 / 69,725013*100

≈ '''3,29'''
|-
|D
|3,85525+33,1 * 2,00429 = 70,19725 ≈ '''70,2'''
|0,27991+1,3339 * 1,62403 = 2,4462036
| colspan="2" |0,12863+1,1122* 1,98973 = 2,3416077
|2,4462036 / 70,7197249*100 ≈ '''3,48'''
|2,3416077 / 70,7197249*100 ≈ '''''3,34'''''
|-
|
|
|
|
|
|
|
|}
</center>
'''Note''' that intercepts and slopes of the applied regression formulae are underscored.

===== Fat correction for equal measure sampling =====
With Equal measure sampling, it is advisable to use Equation 8 (or the like) to correct fat contents:

Equation 8. Fat correction for equal measure sampling.

Fat, % = Analysed fat, % + 0.69 – 1.3 x (morning milk/ 24-hour milk)

The relation of morning milk to 24-hour milk is to be calculated to at least four decimals.

==== 1.1 Method of Kyntäjä & Nokka (2021)<ref name=":3" />: 24-hour correction factors for fat percentage ====
This method can be applied to calculate 24-hour correction factors for fat percentage, in case the milk recording is based on two milkings, with at least one known milk yield and one sample. A 24-hour recording day is assumed.

The conventional way to calculate correction factors is based on a data set where all milkings have been recorded and analysed separately. This approach requires a lot of effort and extra analysis, and is not cheap to organise. Organisations that have access to a large number of records may be able to use those data to calculate correction factors even if they have no extra analysis.

Requirements for the data set:

# The data set has to be large enough. Every single factor needs to be based on at least 10,000 or, even better, 100,000 observations.
# Each individual data set must contain at least one preceding milking interval, milk weight, and analysed sample. If it contains more milk weights, intervals etc. that is even better. It is also good to include breed, lactation number, days in milk and other data that may have an effect on the factors.

===== Calculation example of the method of Kyntäjä & Nokka (2021)<ref>Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. ICAR Technical Series no. 25: 171-175.</ref> =====

====== The accumulated data set ======
Since 2003, Finland had accumulated a data set of 7.5 million recordings with data on the time of the sampled and preceding milking as reported by the farmer, the lab analysis results, and the 24-hour milk yield. Grouped according to the preceding interval, the analysed fat content gives a nice sigmoid curve with the highest fat content found after a 540 to 630 minutes’ interval (9 to 10.5 hours) and the lowest at 810 to 930 minutes (13.5 to 15.5 hours).
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 16. Average analysed milk fat percentage by preceding interval class, 2003 – 2020.'''''
|- style="background-color:#efefef;"
|'''Interval before'''

'''Sampling (minutes)'''
|'''Number of samples'''
|'''Median interval in the class'''
|'''Average fat content analysed (%)'''
|-
|<510
|93,577
|495
|4.20
|-
|510-539
|19,523
|525
|4.70
|-
|540-569
|111,268
|555
|4.79
|-
|570-599
|253,807
|585
|4.83
|-
|600-629
|1,461,587
|615
|4.75
|-
|630-659
|919,968
|645
|4.66
|-
|660-689
|1,168,683
|675
|4.56
|-
|690-719
|223,877
|705
|4.42
|-
|720-749
|517,447
|735
|4.28
|-
|750-779
|212,428
|765
|4.16
|-
|780-809
|924,014
|795
|4.12
|-
|810-839
|698,463
|825
|4.09
|-
|840-869
|1,104,778
|855
|4.07
|-
|870-899
|154,561
|885
|4.05
|-
|900-929
|77,024
|915
|4.07
|-
|>929
|26,977
|945
|4.13
|}
</center>

The results were also divided into subgroups according to lactation number, phase of lactation, and breed. The effect of the preceding milk interval on milk fat seems to be bigger with older cows and in the beginning of lactation. It was also bigger with Ayrshire cows as compared with Holsteins. At this point, however, the decision was made not to take these factors into account when calculating new correction factors.

====== Calculation of new factors ======
The results above were turned into a simple set of correction factors, dependent solely on the preceding interval. In order to do this, two assumptions were made:

# A 24-hour recording day was assumed. This way, we can deduce the second milking interval from the one we know and mirror the fat percent for that milking.
# Milk secretion rate was assumed to be constant around the 24-hour period. This allows us to deduce the share of the 24-hour yield produced at each milking.

These assumptions allow us to create the new correction factors by mirroring the milk yield and milk fat content in the milking whose actual data we have not got. This way, we get the following formula:

Equation 9. Correction factor.
[[File:Equation9.png|none|thumb|545x545px]]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left" |'''''Table 17. Calculation of the mirrored milking and the correction factors'''''
|- style="background-color:#efefef;"
|'''Interval before sampling (minutes)'''
|'''Average fat in the sampled milking (%)'''
|'''Share of 24-hour milk in the sampled milking'''
|'''Mirrored interval (minutes)'''
|'''Average fat in the mirrored milking (%)'''
|'''Calculated 24-hour average fat(%)'''
|'''Correction factor'''
|-
|<510
|4.21
|0.34
|>929
|4.14
|4.16
|0.989
|-
|510-539
|4.77
|0.36
|900-929
|4.08
|4.33
|0.907
|-
|540-569
|4.82
|0.39
|870-899
|4.05
|4.35
|0.903
|-
|570-599
|4.84
|0.41
|840-869
|4.07
|4.38
|0.906
|-
|600-629
|4.76
|0.43
|810-839
|4.09
|4.37
|0.919
|-
|630-659
|4.66
|0.45
|780-809
|4.12
|4.36
|0.936
|-
|660-689
|4.56
|0.47
|750-779
|4.16
|4.35
|0.953
|-
|690-719
|4.43
|0.49
|720-749
|4.29
|4.36
|0.984
|-
|720-749
|4.29
|0.51
|690-719
|4.43
|4.36
|1.016
|-
|750-779
|4.16
|0.53
|660-689
|4.56
|4.35
|1.046
|-
|780-809
|4.12
|0.55
|630-659
|4.66
|4.36
|1.059
|-
|810-839
|4.09
|0.57
|600-629
|4.76
|4.37
|1.070
|-
|840-869
|4.07
|0.59
|570-599
|4.84
|4.38
|1.076
|-
|870-899
|4.05
|0.61
|540-569
|4.82
|4.35
|1.073
|-
|900-929
|4.08
|0.64
|510-539
|4.77
|4.33
|1.062
|-
|>929
|4.14
|0.66
|<510
|4.21
|4.16
|1.006
|}
</center>

=== Methods to calculate 24-hour yields in Automatic Milking Systems ===

==== General remarks about calculation of 24-hour milk yield ====
It is characteristic for AMS systems that individual cows set their own milking rhythm, thus making it largely irrelevant to use the traditional model of measuring milk yields and sampling at all milkings in the herd during the recording day. In order to determine how much an individual cow’s real 24-hour milk, fat and protein yield is, more complex calculations are required, especially with milk fat that varies considerably from milking to milking. For protein content and cell counts, no correction is needed for a one-milking sample.

The basic idea with calculating a 24-hour milk yield from AMS data is that milk yields per milking are converted into milk yield per time unit (minute or hour) during the preceding interval. This milk yield per time unit is then converted into milk yield in 24 hours. In order to do this, the data set must also contain time stamps for each milking.

How many milkings or how long a measurement period is used for creating 24-hour yields depends on the milk recording organisation. The fewer milkings are used the more random variance there will be in the individual cow milk yields. The absolute minimum is two milkings with preceding intervals, while a measuring period of 96 hours is recommended.

The sampled milking must always be inside the milk yield measurement period. For the calculation of fat and protein yields, it is recommended to use only those milk yields that are from the same period or day. With Z sampling, the 24-hour fat and protein yields may be calculated based on a shorter measurement period than what is used for calculating the 24-hour milk yields.

==== Calculation of milk yield using data of several days (Lazenby ''et al''., 2002<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Automatic Milking Systems (AMS). The average of most recent milk weights can be calculated using a number of preceding milkings or a number of preceding days. If number of milkings is used, the optimal estimate of the milking rate is obtained using an average of current milking together with the 12 most recent milkings back in time. The optimal estimate is the maximum value of the difference curve at which the correlation with the ‘true’ 24-hour milk yield is greatest and the variance across milkings is minimized. If number of days is used, the optimal estimate of the milking rate is obtained using an average of all milkings occurred in the last 96 hours (4 most recent days). In Table 18 the percent of maximum difference for various number of milkings and days is reported. The optimal estimate is independent from stage of lactation and parity.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 18. Percent maximum for different number of days and milkings.'''''
|- style="background-color:#efefef;"
|'''Days'''
|'''Percent Max.'''
|'''Current milking'''

'''+ most recent milkings'''
|'''Percent max.'''
|-
|1
|49.38
|10
|97.85
|-
|2
|77.26
|11
|99.08
|-
|3
|92.34
|12
|99.70
|-
|4
|98.91
|13
|99.81
|-
|5
|98.50
|14
|99.40
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table19.png|center|thumb|911x911px]]
Therefore, 24-hour yield estimation using most recent milkings (1+12) is computed using Equation 10.

''Equation 10. 24-hour yield estimation using 12 previous milkings from AMS.''
[[File:Equation10.png|none|thumb|527x527px]]
and, 24-hour yield estimation using all milkings occurred in the last 96 hours (most recent 4 days), all milking in the last 4 days are included is computed using Equation 11.

''Equation 11. 24 hours yield estimation using milkings from the last 96 hours from AMS''
[[File:Equation11.png|none|thumb|534x534px]]

===== Advantages and disadvantages of this method =====
In terms of Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between milk weights and contents may arise if contents are recorded on one day only. Moreover, some cows may begin or finish their lactation during the period of recording. In this case the computation of milk yield must be adapted. The number of data that need to be validated is higher (for instance, contents have short interval between two milkings).

==== Calculation of milk yield using data on 1 day (Bouloc ''et al''., 2002<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
When the number of milkings is reduced to milkings obtained during one day only, the accuracy of the estimation of the true performance is the same as classical milk recording methods with the same interval between two test days. For instance, Milk Yield estimated from all the milkings recorded during 24 hours, and with an interval between two test days of four weeks has the same accuracy as A4.

==== Calculation of fat and protein yield (Galesloot & Peeters, 2000<ref name=":1" />) ====
Calculation of fat and protein percent must be based on milk weights at time of sampling. The 24-hour protein percentage can be predicted by the protein percentage of the sample without adjustment. However, the 24-hour fat percentage is more difficult to predict, as levels of fat percent are inversely proportional to the amount of milk yield. It is important then to have a close connection between time of samples and actual milk yields.

The Peeters and Galesloot method is a multiple linear regression model for estimating 24-hour fat percent and yields from one-sampled milking during the AMS sampling period. Six different statistical models were tested. This method takes into account fat percent, protein percent, milk weight and milking interval of the sampled milking, milking interval and milk weight of the previous milking (simple model). Another model, based on six different classification of variables (Ca - Cf) such as, time of sampled milking, interval preceding the sampled milking, ratio of fat to protein percent, parity, lactation stage, can be applied (complex model).

===== Simple model =====
24-hour Fat% = b0 + b1* Fat%(n) + b2* Prot%(n) + b3* Int(n) + b4* Int(n-1) + b5* Milk(n) + b6* Milk (n-1) + e

b0= Intercept, b1 to b6 = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, e = Residual effect.

===== Complex model =====
24-hour Fat%i = b0i + b1i* Fat%(n) + b2i* Prot%(n) + b3i* Int(n) + b4i* Int(n-1) + b5i* Milk(n) + b6i* Milk(n-1) + ei

b0i = Intercept, b1i to b6i = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, ei = Residual effect

i = subclass of classification for class variables Cx for x = a, b, c, d, e, f

Ca = Day Time of sampled milking (h) 0-5.59, 6.00-11.59, 12.00-17.59, 18.00-23.59

Cb = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440

Cc = Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

Cd = Parity 1, 2, ≥ 3

Ce = Lactation stage 1-99, 100-199, ≥200

Cf = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440 and Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

The best prediction of 24-hour fat percent and 24-hour fat yields from this method, includes fat percent, protein percent, milk weight and milking interval of the sampled milking, milk weight and milking interval of the preceding milking and the interaction between milking interval, the ratio of fat to protein percent of the sampled milking (complex model corresponding to Cf classification).

The Peeters and Galesloot method has been updated by Roelofs et al. (2006)<ref>Peeters, R. and P. J. B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. J Dairy Sci. 85:682-688.</ref>. The Roelofs method is described in [[Section 02 – Cattle Milk Recording#Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme|Appendix 2]] of this Section.

N.B. This method has been developed by CRV. CRV has available a set of parameters, estimated with this method. For more information about costs and advice on application of this method, please contact CRV. ICAR has no benefit from the application of this method or any other method described in these guidelines.

==== Calculation example of 24-hour fat and protein yields with sampling scheme M ====
With this method, all milkings in a 24-hour recording period must be sampled. The obtained separate analysis results are then used to compute a 24-hour yield of milk solids, and a weighted average of their content.

Individual milkings (last 96 hours) and recording day contents:
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left" |'''''Table 20. Calculation of 24-hour fat and protein contents with sampling scheme M.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY/MM/DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat%'''
|'''Protein%'''
|-
|1
|2021/09/09
|20:45
|525
|13.7
|26.1
|
|
|-
|2
|2021/09/10
|5:30
|617
|16.0
|25.9
|
|
|-
|3
|2021/09/10
|15:47
|720
|18.7
|26.0
|
|
|-
|4
|2021/09/11
|3:25
|645
|16.8
|26.0
|
|
|-
|5
|2021/09/11
|14:10
|899
|18.3
|20.3
|
|
|-
|6
|2021/09/11
|23:27
|557
|14.6
|26.2
|
|
|-
|7
|2021/09/12
|10:51
|684
|17.4
|25.4
|4.53
|3.17
|-
|8
|2021/09/12
|19:44
|533
|14.1
|26.5
|4.92
|3.18
|-
|9
|2021/09/13
|1:35
|351
|9.9
|28.2
|5.92
|3.07
|}
</center>

For example, calculation of fat% on recording day:

24-hour Fat% = (9.9 kg milk x 5.92% fat + 14.1 kg milk x 4.92 % fat + 17.4 kg milk x 4.53 % fat) / (9.9 + 14.1 + 17.4) kg milk = 5.00 %

To calculate the 24-hour fat yield, the calculated 24-hour milk yield is multiplied by the fat content thus obtained (5.00 %).

The same method is used for protein, somatic cell count, urea, lactose and other milk constituents.

Estimation of milk contents: It is recommended to set the robot not to take samples if the preceding milking of the individual cow is not more than 4 hours earlier. If such milkings occur the milk sampled from them is not suitable for 24-hour fat calculation.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left"|'''''Table 21. Calculation of 24-hour fat and protein contents with sampling scheme M where one milking interval was shorter than 4 hours.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY-MM-DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat %'''
|'''Protein%'''
|-
|1
|2021/11/12
|20:05
|590
|15.4
|26.4
|
|
|-
|2
|2021/11/13
|6:31
|626
|16.3
|26.0
|
|
|-
|3
|2021/11/13
|17:12
|641
|17.1
|26.7
|
|
|-
|4
|2021/11/14
|4:40
|688
|17.5
|25.4
|
|
|-
|5
|2021/11/14
|15:11
|631
|16.4
|26.0
|
|
|-
|6
|2021/11/15
|2:25
|674
|16.5
|24.5
|
|
|-
|7
|2021/11/15
|9:47
|452
|10.8
|23.9
|
|
|-
|8
|2021/11/15
|18:30
|523
|13.6
|26.0
|4.71
|3.36
|-
|9
|2021/11/15
|21:15
|165
|3.1
|18.8
|5.161
|3.481
|-
|10
|2021/11/16
|7:49
|634
|16.5
|26.0
|4.47
|3.21
|}
1 Time between two consecutive milkings shorter than 4 hours, data not taken into account for calculation of milk contents.
</center>

Calculation of the fat content of milk during the recording day:

24-hour Fat% = (16.5 kg milk x 4.47 % fat + 13.6 kg milk x 4.71 % fat) / (16.5 kg + 13.6 kg) = 4.57 %

The same method is used for protein, somatic cells, urea, lactose and other milk constituents.

=== Methods to calculate 24-hour yields from electronic milk meters ===

==== Using data on more than one day (Hand ''et al''., 2006<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. J. Dairy Sci. 89:1723–1726.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Electronic Milk Meters. The average of most recent milk weights can be calculated using a number of preceding days. Table 22 reports the concordance correlations for a range of multiple-day averages. As soon as at least the 3 preceding days are used in the calculation, the concordance correlation reaches a high value of at least 0.981. There are no significant differences between 3, 4, 5, 6 and 7-day averages. The correlations are independent from stage of lactation and parity. Thus, 24-hour yields can be the average of from 3 to 7 daily milkings previous to the test day when fat and protein samples were taken.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 22. Concordance correlations for different multiple-day averages.'''''
|- style="background-color:#efefef;"
|'''Multiple-day average'''
|'''Concordance correlation'''
|-
|1
|0.957
|-
|2
|0.975
|-
|3
|0.981
|-
|4
|0.981
|-
|5
|0.982
|-
|6
|0.981
|-
|7
|0.981
|-
|10
|0.979
|-
|14
|0.977
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table20.png|center|thumb|923x923px]]

Therefore, 24-hour yield estimation averaging over 5 days is given by Equation 12.

''Equation 12. 24-hour yield estimation averaging over 5 days.''
[[File:Equation12.png|center|thumb|601x601px]]

===== Advantages and disadvantages of this method =====
Concerning Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between Milk weights and contents have been shown. The estimation bias increases proportionally to the number of days use to compute the 24-hour average. Thus, this method is recommended only if milk weight is the only variable of interest. If milk contents are of interest then the milk weight should be calculated using the milkings from the same day of sampling.

==== Estimation of 24-hour fat and protein yield ====
Fat and protein yields should be determined from the 24-hour yield on the day of sampling, and not the averaged value.

=== Calculation of daily fat percentage from single samples by Gerke et al., 2025 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Gerke.xlsx here]

Constant access to the automatic milking system (AMS) leads to varying milking frequency of cows and subsequently varying milking interval lengths (MI) and milk yield (MY) of single milkings. This influences milk production and can result in variable milk composition in individual milkings during the day. Therefore, the fat percentage from one sampled milking must be adjusted before it can be used as a daily value. The method described specifies the data required and the calculation procedure for deriving a corrected 24 h milk fat percentage from a single sample on test day (TD) in AMS herds.

==== Model specification ====
The multiple linear regression includes transformation, interaction, and polynomial parameters to model non-linearity and thereby improve prediction accuracy. Beside F% of a single milking (''m'') on TD, the model focused on lactation characteristics and milk recording data of up to 4 preceding milkings. With milking intervals ranging between 4 and 20 hours, the method can be applied to milk recording samples from cows with 2 or 3 milkings whose milking intervals lengths (MI) before sampling accumulate to less than 24 h.

The functional form of the model described below specifies the data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample:[[File:Image A.png|center|thumb|636x636px|'''Data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample''']]
</div>where:

DF% = estimated 24 h fat percentage on TD

''m'' = sampled milking on TD

''m-x'' = x milkings before the milking where the sample was taken (x: 1-3)

F% = fat percentage of the sampled milking ''m''

MY(''m'') = milk yield (kg) of ''m''

MI(''m'') = length of time interval (min) preceding the sampled milking ''m''

MY(''m''-x) = milk yields of the 1-3 preceding milkings of ''m''

MI(''m''-x) = milking interval length corresponding to MY(''m''-x)

DIM = days in milk on TD ranging between 5 and 330 d

Parity = parity class (e.g primiparous = 1 and multiparous = 0)

Daytime = time-of-day group of ''m'' (e.g. morning/noon/evening)

e = residual error

The method and its implementation are described in detail by Gerke et al. (2025).

==== Calculation and examples ====
The mathematical notation, with the corresponding regression coefficients in Table 1 for calculating the daily fat percentage (DF%):[[File:Calculating the daily fat percentage (DF%).jpg|center|Calculating the daily fat percentage (DF%)|thumb|511x511px]][[File:Calculating the daily fat percentage (DF%) 2.jpg|center|frame|'''Table 1. Coefficients for regression formula.''']]
</div>
[[File:Example data required for estimating 24 h fat percentage (DF%).jpg|alt=Example data required for estimating 24 h fat percentage (DF%)|center|frame|'''Table 2.''' '''Example data required for estimating 24 h fat percentage (DF%)''']]
Based on the data assembled on TD (Table 2), the corrected 24 h fat percentage (DF%) can be calculated using the mathematical formula und its corresponding coefficients listed in Table 1 as shown in the following examples:
[[File:Corrected 24 h fat percentage.jpg|alt=Corrected 24 h fat percentage|center|thumb|661x661px|'''Corrected 24 h fat percentage''']]

=== Reference ===
Gerke, J. S., Kammer, M., Werner, A., Köstler, R., Piepenburg, J., Mayerhofer, M., … Duda, J. (2025). Estimating daily fat percentage from single samples in herds with automatic milking system using a regression model. ''Livestock Science'', ''293'', 105649. doi: 10.1016/j.livsci.2025.105649

=== Calculation of daily fat percentage from single samples by Jenko et al., 2008, 2010 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Jenko.xlsx here]

This method estimates daily milk yield (DMY), daily fat yield (DFY), and daily protein yield (DPY) in the alternate one-milking recording (T) scheme. Daily fat percentage (DFP) and daily protein percentage (DPP) are then derived from the daily yield (DY) estimates. Utilizing this method allows us to remove the risk of underestimating high and overestimating low DY and contents.

The following formula is used to estimate the DY from the partial yield (PY) and the estimated PY/DY ratio (y):

DY=PYi/yi

where the subscript i is either morning (a.m.) or evening (p.m.).

The value of y is calculated based on the milking interval in minutes (MI), estimated intercept (µ) and regression coefficients (b1 and b2) for yield traits in a.m. or p.m. milking using the following equations for DMY and DPY:

'''Equation 1. Model for milk yield and protein yield.'''

yi = µ + b1 × MI

and for DFY

'''Equation 2. Model for fat yield.'''

yi = µ + b1 × MI + b2 × MI2

The intercept and regression coefficients can be either estimated from the data with records from both a.m. and p.m. milking or the estimates from Table 1 can be applied.

'''Table 1. Intercept and regression coefficients for calculation of daily yield.'''
{| class="wikitable"
|'''Daily yield'''
|'''Milking'''
|'''µ'''
|'''b1'''
|'''b2'''
|-
|DMY
|a.m.
|0,1081000000
|0,0005503000
|
|-
|
|p.m.
|0,0884200000
|0,0005683000
|
|-
|DPY
|a.m.
|0,1124000000
|0,0005419000
|
|-
|
|p.m.
|0,0966400000
|0,0005593000
|
|-
|DFY .
|a.m.
|0,5903000000
|<nowiki>-0,0005093000</nowiki>
|0,0000005377
|-
|
|p.m.
|0,1574000000
|0,0006705000
|<nowiki>-0,0000002744</nowiki>
|}
Finally, daily fat percentage (DFP) and daily protein percentage (DPP) are calculated from the estimated DY:

DFP=DFY/DMY × 100

DPP=DPY/DMY × 100

==== Calulation example with method of Jenko et al. (2008, 2010) ====
Example of the calculations of daily yields from morning milking and evening milking is presented in tables 3 and 4. Data from the Delorenzo and Wiggans method is used in the calculations (Table 2).

'''Table 2. Data for morning and evening milking.'''
{| class="wikitable"
|'''Milking'''
|'''a.m.'''
|'''p.m.'''
|-
|Beginning of recording
|06:15
|20:22
|-
|Start of preceding milking
|17:25
|06:35
|-
|Milking interval (min)
|770
|827
|-
|'''Milking results'''
|
|
|-
|Milk (kg)
|12,00
|14,00
|-
|Protein (%)
|3,45
|3,40
|-
|Fat (%)
|4,12
|4,00
|}

'''Table 3. Calculation of partial yield (PY) and calculation of y value.'''
{| class="wikitable"
|Trait
|Milking
|PY (%)
|PY (kg)
|y
|-
|Milk
|a.m.
|
|12,00
|0,1081000000 + 0,0005503000 x 770 = 0,531831
|-
|
|p.m.
|
|14,00
|0,0884200000 + 0,0005683000 x 827 = 0,558404
|-
|Protein
|a.m.
|3,45
|12,00 / 3,45 = 0,41
|0,1124000000 + 0,0005419000 x 770 = 0,529663
|-
|
|p.m.
|3,40
|14,00 / 3,40 = 0,48
|0,0966400000 + 0,0005593000 x 827 = 0,559181
|-
|Fat
|a.m.
|

4,12
|12,00 / 4,12 = 0,49
|0,5903000000 -0,0005093000 x 770 + 0,0000005377 x 7702 = 0,516941
|-
|
|p.m.
|

4,00
|12,00 / 4,00 = 0,56
|0,1574000000 +0,0006705000 x 827 - 0,0000002744 x 8272 = 0,524233
|}

'''Table 4. Calculation of daily yield (DY, kg) and daily components (DY, %).'''
{| class="wikitable"
|Trait
|DY
|Milking
|DY (kg)
|DY (%)
|-
|Milk
|DMY
|a.m.
|12,00 / 0,531831 = 22,56356
|
|-
|
|
|p.m.
|14,00 / 0,531831 = 25,07145
|
|-
|Protein
|DPY
|a.m.
|0,41 / 0,529663 = 0,781629
|(0,781629 / 22,56356) x 100 = 3,46
|-
|
|
|p.m.
|0,48 / 0,559181 = 0,851245
|(0,851245 / 25,07145) x 100 = 3,40
|-
|Fat
|DFY
|a.m.
|0,49 / 0,516941 = 0,956395
|(0,956395 / 22,56356) x 100 = 4,24
|-
|
|
|p.m.
|0,56 / 0,524233 = 1,068227
|(1,068227 / 25,07145) x 100 = 4,26
|}

==== References ====

* Jenko, J., Perpar, T., Logar, B., Sadar, M., Ivanovič, B., Jeretina, J., Verbič, J., Podgoršek, P. 2008. Comparison of different models for estimating daily yields from a.m./p.m. milkings in Slovenian dairy scheme. Presented at the 36th ICAR Session, Niagara Falls, New York, United States, June 16-20, 2008.
* Jenko, J., Perpar, T., Gorjanc G., Babnik, D. 2010. Evaluation of different approaches for the estimation of daily yield from single milk testing scheme in cattle, J. Dairy Res., 77 (2010), pp. 137-143; DOI: 10.1017/S0022029909990586

</div>
</div>

== Procedure 2 – Computing of Accumulated Lactation Yield ==
<div class="mw-collapsible mw-collapsed">
<div>
=== The Test Interval Method (TIM) (Sargent, 1968<ref>Sargent, F. D., V. H. Lyton, and 0. G. Wall, J r . 1968. Test interval method of calculating Dairy Herd Improvement Association records. J. Dairy Sci. 51:170.</ref>) ===
Test Interval Method is the reference method for calculating accumulated yields. Another adaptation of the method is the Centering Date Method where the yields from the preceding recording are used until the mid point of the recording interval and then substituted by the yields from the following recording.

The following equations are used to compute the lactation record for milk yield (MY), for fat (and protein) yield (FY), and for fat (and protein) percent (FP).
[[File:Equation1111.png|none|thumb|653x653px]]
Where:
M1, M2, Mn are the weights in kilograms, given to one decimal place, of the milk yielded in the 24 hours of the recording day.

F1, F2, Fn are the fat yields estimated by multiplying the milk yield and the fat percent (given to at least two decimal places) collected on the recording day.

I1, I2, In-1 are the intervals, in days, between recording dates.

I0 is the interval, in days, between the lactation period start date and the first recording date.

In is the interval, in days, between the last recording date and the end of the lactation period.

The equation applied for fat yield and percentage must be applied for any other milk components such as protein and lactose.

Details of how to apply the formulae are shown in Table 3 using the example data in Table 1, below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" align = "left" |'''''Table 1. Raw data used in example (TIM).'''''
|- style="background-color:#efefef;"
| colspan="6" align = "left"|'''Data:'''

'''Calving March 25'''
|- style="background-color:#efefef;"
|
|'''Date of'''

'''recording'''
|'''Number'''

'''of days'''
|'''Quantity of milk'''

'''weighed in kg'''
|'''Fat'''

'''percentage'''
|'''Fat'''

'''in grams'''
|-
|April
|8
|14
|28.2
|3.65
|1 029
|-
|May
|6
|28
|24.8
|3.45
|856
|-
|June
|5
|30
|26.6
|3.40
|904
|-
|July
|7
|32
|23.2
|3.55
|824
|-
|August
|2
|26
|20.2
|3.85
|778
|-
|August
|30
|28
|17.8
|4.05
|721
|-
|September
|25
|26
|13.2
|4.45
|587
|-
|October
|27
|32
|9.6
|4.65
|446
|-
|November
|22
|26
|5.8
|4.95
|287
|-
|December
|20
|28
|4.4
|5.25
|231
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left"|'''''Table 2. Lactation period summary (TIM).'''''
|-
|Beginning of lactation:
|March 26
|-
|End of lactation:
|January 3
|-
|Duration of lactation period:
|284 days
|-
|Number of testings (weighings):
|10
|}
</center>
<center>
{| class="wikitable"
| colspan="8" |'''''Table 3. Computations using Test Interval Method.'''''
|- style="background-color:#efefef;"
| colspan="3" rowspan="2" |'''Interval'''

'''both days included'''
|
| colspan="2" |'''Daily production'''
| colspan="2" |'''Sum'''
|- style="background-color:#efefef;"
|'''Days'''
|'''Kg milk'''
|'''Grams of fat'''
|'''Kg milk'''
|'''Kg fat'''
|-
|Mar 26
|<nowiki>-</nowiki>
|Apr 8
|14
|28.2
|1 029
|395
|14.410
|-
|Apr 9
|<nowiki>-</nowiki>
|May 6
|28
|(28.2+24.8)/2
|(1 029+856) /2
|742
|26.389
|-
|May 7
|<nowiki>-</nowiki>
|June 5
|30
|(24.8+26.6) /2
|(856+904) /2
|771
|26.400
|-
|June 6
|<nowiki>-</nowiki>
|July 7
|32
|(26.6+23.2) /2
|(904+824) /2
|797
|27.648
|-
|July 8
|<nowiki>-</nowiki>
|Aug. 2
|26
|(23.2+20.2) /2
|(824+778) /2
|564
|20.817
|-
|Aug. 3
|<nowiki>-</nowiki>
|Aug 30
|28
|(20.2+17.8) /2
|(778+721) /2
|532
|20.980
|-
|Aug 31
|<nowiki>-</nowiki>
|Sept. 25
|26
|(17.8+13.2) /2
|(721+587) /2
|403
|17.008
|-
|Sept. 26
|<nowiki>-</nowiki>
|Oct. 27
|32
|(13.2+9.6) /2
|(587+446) /2
|365
|16.541
|-
|Oct. 28
|<nowiki>-</nowiki>
|Nov. 22
|26
|(9.6+5.8) /2
|(446+287) /2
|200
|9.536
|-
|Nov. 23
|<nowiki>-</nowiki>
|Dec. 20
|28
|(5.8+4.4) /2
|(287+231) /2
|143
|7.253
|-
|Dec. 21
|<nowiki>-</nowiki>
|Jan. 3
|14
|4.4
|231
|62
|3.234
|-
|
|
|
|284
|
|
|4973
|190.216
|-
| colspan="8" |
|-
| colspan="8" |Total quantity of milk: 4 973. kg
|-
| colspan="8" |Total quantity of fat: 190 kg
|-
| colspan="8" |Average fat percentage (190.216 / 4973) x 100 = 3.82%
|}
</center>

=== Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. Livest. Prod. Sci. 17:l.</ref>) ===
With the method 'Interpolation using Standard Lactation Curves' missing test day yields and 305 day projections are predicted. The method makes use of separate standard lactation curves representing the expected course of the lactation, for a certain herd production level, age at calving and season of calving and yield trait. By interpolation using standard lactation curves, the fact that after calving milk yield generally increases and subsequently decreases is taken into account. The daily yields are predicted for fixed days of the lactation: day 0, 10, 30, 50 etc.

The cumulative yield is calculated as follows in :
[[File:Equation2222222.png|none|thumb|474x474px]]
where:

yi = the i-th daily yield;

INTi = the interval in days between the daily yields yi and yi+1;

''n'' = total number of daily yields (measured daily yields and predicted daily yields).

The next example illustrates the calculation of a record in progress. The cow was tested at day 35 and day 65 of the lactation. To determine the lactation yield, daily milk yields are determined for day 0, 10, 30 and 50 of the lactation, by means of the standard lactation curves. The daily yields are in Table 4.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Measured and derived daily yields, used to calculate the record in progress in the example (ISLC).'''''
|- style="background-color:#efefef;"
|'''Day of lactation'''
|'''Milk (kg)'''
|'''Note'''
|-
|0
|25.9
|Predicted
|-
|10
|27.8
|Predicted
|-
|30
|31.7
|Predicted
|-
|35
|31.8
|Measured
|-
|50
|32.9
|Interpolated using standard lactation curve
|-
|65
|33.0
|Measured
|}
</center>

Next, the record in progress can be calculated by means of the formula for a cumulative yield as follows:

[(10 - 1) * 25.9 + (10+1) * 27.8] / 2 +

[(20 - 1) * 27.8 + (20+1) * 31.7] / 2 +

[(5 - 1) * 31.7 + (5+1) * 31.8] / 2 +

[(15 - 1) * 31.8 + (15+1) * 32.9] / 2 +

[(15 - 1) * 32.9 + (15+1) * 33.0] / 2 = 2005.3 kg.

This corresponds to the surface below the line through the predicted and measured daily yields (see Figure 1).
[[File:Figure1.png|center|thumb|621x621px|''Figure 1. Example of calculation of record in progress.'']]

=== Best prediction (BP) (VanRaden, 1997<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. J. Dairy Sci. 80:3015-3022.</ref>) ===
Recorded milk weights are combined into a lactation record using standard selection index methods. Let vector y contain M1, M2, to Mn and let E('''y''') contain corresponding the expected values for each recorded day. The E(y) are obtained from standard lactation curves for the population or for the herd and should account for the cow's age and other environmental factors such as season, milking frequency, etc. The yields in '''y''' covary as a function of the recording interval between them (I). Diagonal elements in Var(y) are the population or herd variance for that recording day and off diagonals are obtained from autoregressive or similar functions such as Corr(M1, M2)=0.995I for first lactations or 0.992I for later lactations. Covariances of one observation with the lactation yield, for example Cov(M1, MY), are the sum of 305 individual covariances. E(MY) is the sum of 305 daily expected values. Lactation milk yield is then predicted as Equation 3:
[[File:Equation333333.png|none|thumb|640x640px]]
With best prediction, predicted milk yields have less variance than true milk yields. With TIM, estimated yields have more variance than true yields. The reason is that predicted yields are regressed toward the mean unless all 305 daily yields are observed. With best prediction, the predicted MY for a lactation without any observed yields is E(MY) which is the population or herd mean for a cow of that age and season. With TIM, the estimated MY is undefined if no daily yields are recorded.

Milk, fat, and protein yields can be processed separately using single-trait best prediction or jointly using multi-trait best prediction. Replacement of M1, M2, to Mn with F1, F2, to Fn or P1, P2, to Pn gives the single-trait predictions for fat or for protein. Multi-trait predictions require larger vectors and matrices but similar algebra. Products of trait correlations and autoregressive correlations, for example, may provide the needed covariances.

=== Multiple-Trait Procedure (MTP) (Schaeffer & Jamrozik, 1996<ref>Schaeffer, L.R., and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. J. Dairy Sci. 79:2044-2055.</ref>) ===
The Multiple-Trait Procedure predicts 305-d lactation yields for milk, fat, protein and SCS, incorporating information about standard lactation curves and covariances between milk, fat, and protein yields and SCS. Test day yields are weighted by their relative variances, and standard lactation curves of cows of similar breed, region, lactation number, age, and season of calving are used in the estimation of lactation curve parameters for each cow. The multiple-trait procedure can handle long intervals between test days, test days with milk only recorded, and can make 305-d predictions on the basis of just one test day record per cow. The procedure also lends itself to the calculation of peak yield, day of peak yield, yield persistency, and expected test-day yields, which could be useful management tools for a producer on a milk recording program.

The MTP method is based upon Wilmink's model in conjunction with an approach incorporating standard curve parameters for cows with the same production characteristics. Wilmink's function for one trait is given by Equation 4.

Equation 4. Wilmink function for one trait (MTP).

y = A + B''t'' ± C''exp'' (-0.05''t'') + ''e''

where y is yield on day t of lactation, A, B, and C are related to the shape of the lactation curve.

The parameters A, B, and C need to be estimated for each yield trait. The yield traits have high phenotypic correlations, and MTP would incorporate these correlations. Use of MTP would allow for the prediction of yields even if data were not available on each test day for a cow.

The vector of parameters to be estimated for one cow are designated:
[[File:Vectro.png|center|thumb]]
where M, F, and P represent milk, fat, and protein, respectively, and S represents somatic cell score. The vector c is to be estimated from the available test-day records. Let c0 represent the corresponding parameters estimated across all cows with the same production characteristics as the cow in question.

Let
[[File:Vector2.png|center|thumb]]

be the vector of yield traits and somatic cell scores on test ''k'' at day ''t'' of the lactation.

The incidence matrix, ''Xk'', is constructed as follows:
[[File:Vector3.png|center|thumb|558x558px]]

The MTP equations are:
[[File:Equation55555.png|none|thumb|560x560px]]
and ''n'' is the number of tests for that cow. ''Rk'' is a matrix of order 4 that contains the variances and covariances among the yields on ''kth'' test at day ''t'' of lactation. The elements of this matrix were derived from regression formulas based on fitting phenotypic variances and covariances of yields to models with ''t'' and ''t2'' as covariables. Thus, element ''ij'' of ''Rk'' would be determined by

rij(t) = ß0ij + ß1ij (t) + ß2ij (t2)

G is a 12 x 12 matrix containing variances and covariances among the parameters in '''ĉ''' and represents the cow to cow variation in these parameters, which includes genetic and permanent environmental effects, but ignores genetic covariances between cows. The parameters for '''''G''''' and '''''Rk''''' vary depending on the breed, but must be known. Initially, these matrices were allowed to vary by region of Canada in addition to breed, but this meant that there could exist two cows with identical production records on the same days in milk, but because one cow was in one region and the other cow was in another region, then the accuracy of their predictions would be different. This was considered to be too confusing for dairy producers, so that regional differences in variance-covariance matrices were ignored and one set of parameters would be used for all regions for a particular breed. Estimation of G is described later.

If a cow has a test, but only milk yield is reported, then

y’k(Mk 0 0 0)

and
[[File:And.png|center|thumb|540x540px]]

The inverse of '''''Rk''''' is the regular inverse of the nonzero submatrix within '''''Rk''''', ignoring the zero rows and columns. Thus, missing yields can be accommodated in MTP.

Accuracy of predicted 305-d lactation totals depends on the number of test-day records during the lactation and DIM associated with each test. Thus, any prediction procedure will require reliability figures to be reported with all predictions, especially if fewer tests at very irregular intervals are going to be frequent in milk recording. At the moment, an approximate procedure is applied that uses the inverse elements of '''(X’R-1X + G-1) -1.'''

==== 1.1 Example calculations ====
Four test day records on a 25 month old, Holstein cow calving in June from Ontario are given in the Table 5 below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 5. Example test day data for a cow (MTP).'''''
|- style="background-color:#efefef;"
|'''Test no.'''
|'''DIM=''t'''''
|'''Exp(-0.05''t'')'''
|'''Milk (kg)'''
|'''Fat (kg)'''
|'''Protein (kg)'''
|'''SCS'''
|-
|1
|15
|0.47237
|28.8
|
|
|3.130
|-
|2
|54
|0.06721
|29.2
|1.12
|0.87
|2.463
|-
|3
|188
|0.000083
|23.7
|0.97
|0.78
|2.157
|-
|4
|250
|0.0000037
|20.8
|
|
|2.619
|}
</center>

Notice that two tests do not have fat and protein yields, and that intervals between tests are irregular and large. The vector of standard curve parameters based on all available comparable cow, is
[[File:Vector4.png|center|thumb]]
The R^(-1)_k matrices for each test day need to be constructed. These matrices are derived from regression equations. The equations for Holsteins were:
<center>
{| class="wikitable" style="text-align: center;"
|''rMM(t) =''
|71.0752 - 0.281201''t'' + 0.0004977''t2''
|-
|''rMF(t) =''
|2.4365 - 0.013274''t'' + 0.0000302''t2''
|-
|''rMP(t) =''
|2.0504 - 0.008286''t'' + 0.0000163''t2''
|-
|''rMS(t) =''
|<nowiki>-1.7993 + 0.013209</nowiki>''t'' - 0.000056''t2''
|-
|''rFF(t) =''
|0.1312 - 0.000725''t'' + 0.000001586''t2''
|-
|''rFP(t) =''
|0.0739 - 0.000386''t'' + 0.000000926''t2''
|-
|''rFS(t) =''
|<nowiki>- 0.0386 + 0.000292</nowiki>''t'' - 0.000001796''t2''
|-
|''rPP(t) =''
|0.066 - 0.000267''t'' + 0.0000005636''t2''
|-
|''rPS(t) =''
|<nowiki>- 0.0404 + 0.000369</nowiki>''t'' - 0.000001743''t2''
|-
|''rSS(t) =''
|3.0404 - 0.000083''t'' - 0.000006105''t2''
|}
</center>

The inverses of the residual variance-covariance matrices for yields for the four test days are as follows:
<center>
{| class="wikitable" style="text-align: center;"
|
|0.0151259
|0
|0
|0.0080354
|-
|'''R^(-1)_1''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0080354
|0
|0
|0.3334553
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.1685584
|0.345947
|<nowiki>-4.851935</nowiki>
|0.0254775
|-
|'''R^(-1)_2''' = =
|<nowiki>-0.345947</nowiki>
|26.830915
|<nowiki>-17.40281</nowiki>
|<nowiki>-0.041445</nowiki>
|-
|
|<nowiki>-4.851935</nowiki>
|<nowiki>-17.40281</nowiki>
|187.18579
|<nowiki>-0.584885</nowiki>
|-
|
|0.0254775
|<nowiki>-0.041445</nowiki>
|<nowiki>-0.584885</nowiki>
|0.3365425
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.2620161
|0.1479068
|<nowiki>-7.943903</nowiki>
|0.0316069
|-
|'''R^(-1)_3''' = =
|0.1479068
|54.446977
|<nowiki>-56.01333</nowiki>
|0.3306741
|-
|
|<nowiki>-7.943903</nowiki>
|<nowiki>-56.01333</nowiki>
|317.9609
|<nowiki>-0.92601</nowiki>
|-
|
|0.0316069
|0.3306741
|<nowiki>-0.92601</nowiki>
|0.3654369
|}
{| class="wikitable" style="text-align: center;"
|

|0.0329465
|0
|0
|0.0251039
|-
|'''R^(-1)_4''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0251039
|0
|0
|0.3981981
|}

Inverse matrix G^(-1) of order 12 is the same for all cows of the same breed:

[[File:Left 6x6.jpg|center|thumb|600x600px|Inverse matrix G^(-1) of order 12]]

</center>
Note that many covariances between different parameters of the lactation curves have been set to zero. When all covariances were included, the prediction errors for individual cows were very large, possibly because the covariances were highly correlated to each other within and between traits. Including only covariances between the same parameter among traits gave much smaller prediction errors.

The elements of the MTP equations of order 12 for this cow are shown in partitioned format also:

'''X’R-1X ='''
<center>[[File:Elements of the MTP equations of order 12.jpg|center|thumb|600x600px|Elements of the MTP equations of order 12]]
</center>
[[File:Equation7.png|center|thumb|632x632px]]

The solution vector for this cow is
[[File:Equation6666.png|center|thumb]]

To predict 305-day yields, Y305
[[File:Equation7777.png|none|thumb|551x551px]]
Equation 6 is used separately for each trait (milk, fat, protein, and SCS). The results for this cow were 7456 kg milk, 301 kg fat, and 239 kg protein. The result for SCS is divided by 305 to give an average daily SCS of 2.477.
</div>
</div>

= Appendices =
== Appendix 1 - Adjustment factors to calculate 24-hour yields using the Liu method ==
<div class="mw-collapsible mw-collapsed">
<div>
In Table 6 the adjustment factors to calculate 24-hour yields, using the Liu method, can be found. The description of the Liu method can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2.]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" |'''''Table 1. Adjustment factors to calculate 24-hour yields using the Liu method. Milking time (MT) is either 1 (PM) or 2 (AM), i = parity class, j= milking interval class and k = stage of lactation class.'''''
|- style="background-color:#efefef;"
|'''MT'''
|'''i'''
|'''j'''
|'''k'''
| colspan="2" |'''Milk yield (DMY)'''
| colspan="2" |'''Fat yield (DFY)'''
| colspan="2" |'''Protein yield (DPY)'''
|-
| colspan="4" |
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|-
|1
|1
|1
|1
|5.29333
|1.83283
|0.30911
|1.43518
|0.18984
|1.77461
|-
|1
|1
|1
|2
|4.17676
|1.97447
|0.2803
|1.56914
|0.12246
|2.00568
|-
|1
|1
|1
|3
|4.26476
|1.95945
|0.18826
|1.82468
|0.12624
|2.0137
|-
|1
|1
|1
|4
|3.41282
|2.01814
|0.25025
|1.64707
|0.12519
|1.99629
|-
|1
|1
|1
|5
|1.79548
|2.22665
|0.06578
|2.09515
|0.05249
|2.24065
|-
|1
|1
|1
|6
|3.7751
|1.95508
|0.12854
|1.93892
|0.11936
|2.00979
|-
|1
|1
|1
|7
|1.544
|2.1478
|0.06425
|2.06779
|0.0569
|2.13851
|-
|1
|1
|2
|1
|5.8584
|1.79409
|0.33193
|1.42953
|0.20756
|1.7288
|-
|1
|1
|2
|2
|5.45524
|1.84258
|0.32877
|1.43235
|0.21332
|1.74001
|-
|1
|1
|2
|3
|4.64052
|1.86706
|0.27155
|1.57017
|0.16439
|1.84539
|-
|1
|1
|2
|4
|2.86835
|2.06209
|0.18647
|1.79403
|0.10803
|2.0193
|-
|1
|1
|2
|5
|2.11336
|2.12055
|0.10435
|1.97206
|0.07193
|2.10651
|-
|1
|1
|2
|6
|2.00673
|2.0636
|0.1386
|1.83336
|0.06892
|2.06532
|-
|1
|1
|2
|7
|1.71752
|2.11269
|0.06501
|2.0379
|0.05569
|2.12881
|-
|1
|1
|3
|1
|2.80244
|2.02183
|0.17663
|1.72438
|0.11078
|1.96422
|-
|1
|1
|3
|2
|3.47396
|1.98268
|0.2135
|1.6805
|0.10471
|1.99092
|-
|1
|1
|3
|3
|2.81702
|2.04348
|0.20754
|1.71868
|0.1127
|1.98403
|-
|1
|1
|3
|4
|3.1989
|1.998
|0.21578
|1.6991
|0.10802
|1.99517
|-
|1
|1
|3
|5
|2.47055
|2.04826
|0.15418
|1.83151
|0.07492
|2.07547
|-
|1
|1
|3
|6
|1.923
|2.07728
|0.11783
|1.89678
|0.06457
|2.08391
|-
|1
|1
|3
|7
|1.85264
|2.0873
|0.13047
|1.86711
|0.071
|2.06917
|-
|1
|1
|4
|1
|2.75042
|1.96631
|0.24794
|1.61741
|0.09248
|1.95376
|-
|1
|1
|4
|2
|2.97505
|1.96711
|0.20029
|1.71842
|0.09381
|1.97081
|-
|1
|1
|4
|3
|2.33365
|2.02986
|0.17021
|1.79996
|0.07631
|2.03167
|-
|1
|1
|4
|4
|3.41505
|1.94107
|0.1845
|1.76799
|0.10989
|1.95456
|-
|1
|1
|4
|5
|2.67488
|1.97797
|0.13433
|1.85893
|0.09432
|1.97755
|-
|1
|1
|4
|6
|1.89907
|2.04841
|0.08715
|1.96251
|0.07132
|2.04225
|-
|1
|1
|4
|7
|1.80326
|2.03554
|0.1251
|1.86477
|0.06072
|2.04747
|-
|1
|1
|5
|1
|2.76763
|1.92863
|0.15754
|1.72474
|0.10187
|1.88749
|-
|1
|1
|5
|2
|3.36896
|1.92048
|0.2236
|1.64149
|0.12369
|1.8823
|-
|1
|1
|5
|3
|2.22763
|2.00452
|0.17614
|1.7474
|0.08019
|1.9782
|-
|1
|1
|5
|4
|2.44625
|1.97049
|0.17217
|1.74753
|0.0889
|1.94647
|-
|1
|1
|5
|5
|2.379
|1.97307
|0.15965
|1.76134
|0.0896
|1.94575
|-
|1
|1
|5
|6
|1.62948
|2.02491
|0.11021
|1.85546
|0.0852
|1.94593
|-
|1
|1
|5
|7
|1.45651
|2.0254
|0.07479
|1.92789
|0.05846
|2.00196
|-
|1
|1
|6
|1
|2.01088
|1.9497
|0.16548
|1.68143
|0.101
|1.85846
|-
|1
|1
|6
|2
|2.96605
|1.93064
|0.25841
|1.52566
|0.12097
|1.86061
|-
|1
|1
|6
|3
|2.2281
|1.96085
|0.19036
|1.69013
|0.08032
|1.9375
|-
|1
|1
|6
|4
|2.39473
|1.952
|0.17854
|1.72423
|0.06863
|1.97582
|-
|1
|1
|6
|5
|2.37955
|1.94127
|0.19579
|1.66419
|0.08447
|1.93156
|-
|1
|1
|6
|6
|0.36203
|2.12393
|0.14291
|1.75822
|0.03845
|2.04562
|-
|1
|1
|6
|7
|1.5702
|1.96794
|0.1336
|1.76796
|0.06449
|1.94829
|-
|1
|1
|7
|1
|3.93654
|1.82772
|0.2359
|1.61894
|0.15032
|1.76054
|-
|1
|1
|7
|2
|4.39662
|1.81581
|0.24969
|1.5881
|0.16909
|1.74794
|-
|1
|1
|7
|3
|3.78325
|1.82778
|0.19228
|1.71802
|0.12368
|1.8268
|-
|1
|1
|7
|4
|3.39116
|1.86302
|0.1969
|1.71838
|0.12282
|1.848
|-
|1
|1
|7
|5
|3.20111
|1.83255
|0.09893
|1.86309
|0.1044
|1.84257
|-
|1
|1
|7
|6
|3.75639
|1.78665
|0.25205
|1.56174
|0.14105
|1.76802
|-
|1
|1
|7
|7
|1.42153
|1.95649
|0.09226
|1.85882
|0.04636
|1.96245
|-
|1
|1
|8
|1
|2.3454
|1.90436
|0.14321
|1.77423
|0.10703
|1.82306
|-
|1
|1
|8
|2
|3.97557
|1.82746
|0.26651
|1.58374
|0.15298
|1.76385
|-
|1
|1
|8
|3
|4.26939
|1.80503
|0.22918
|1.64925
|0.12924
|1.81061
|-
|1
|1
|8
|4
|2.90779
|1.89861
|0.18578
|1.73968
|0.13948
|1.79679
|-
|1
|1
|8
|5
|2.8265
|1.87632
|0.19374
|1.67929
|0.12377
|1.80944
|-
|1
|1
|8
|6
|2.26312
|1.87397
|0.09917
|1.82528
|0.08819
|1.84453
|-
|1
|1
|8
|7
|0.31382
|2.04402
|0.05049
|1.95773
|0.02612
|1.99012
|-
|1
|2
|1
|1
|4.63752
|1.99615
|0.31102
|1.58962
|0.16637
|1.96686
|-
|1
|2
|1
|2
|5.56226
|1.91521
|0.26761
|1.64342
|0.16973
|1.94145
|-
|1
|2
|1
|3
|4.51983
|1.96962
|0.26221
|1.65088
|0.12245
|2.03857
|-
|1
|2
|1
|4
|4.51563
|1.93033
|0.18468
|1.80715
|0.15252
|1.94807
|-
|1
|2
|1
|5
|2.60334
|2.07338
|0.16011
|1.81257
|0.09892
|2.05493
|-
|1
|2
|1
|6
|2.86068
|1.98457
|0.15381
|1.79197
|0.08619
|2.04046
|-
|1
|2
|1
|7
|1.6596
|2.11753
|0.13089
|1.83687
|0.09908
|1.96479
|-
|1
|2
|2
|1
|3.94656
|2.03607
|0.23716
|1.6988
|0.19559
|1.88765
|-
|1
|2
|2
|2
|4.20525
|1.98621
|0.3553
|1.46663
|0.1657
|1.92175
|-
|1
|2
|2
|3
|3.31729
|2.04589
|0.29682
|1.57761
|0.12491
|2.00945
|-
|1
|2
|2
|4
|1.95977
|2.13926
|0.16059
|1.79846
|0.06713
|2.12835
|-
|1
|2
|2
|5
|1.49014
|2.14889
|0.10057
|1.90772
|0.05279
|2.14047
|-
|1
|2
|2
|6
|0.82235
|2.22517
|0.07573
|1.94963
|0.04014
|2.17549
|-
|1
|2
|2
|7
|1.53608
|2.08972
|0.11472
|1.81148
|0.0676
|2.03957
|-
|1
|2
|3
|1
|3.85525
|2.00429
|0.27991
|1.62403
|0.12863
|1.98973
|-
|1
|2
|3
|2
|4.1508
|1.9852
|0.3635
|1.47515
|0.13952
|1.97074
|-
|1
|2
|3
|3
|3.31493
|2.02332
|0.31131
|1.55183
|0.11703
|2.00696
|-
|1
|2
|3
|4
|2.47354
|2.0652
|0.20828
|1.71637
|0.09402
|2.04147
|-
|1
|2
|3
|5
|1.68517
|2.08809
|0.14418
|1.80246
|0.06917
|2.05808
|-
|1
|2
|3
|6
|1.316
|2.12714
|0.11206
|1.87179
|0.04723
|2.12486
|-
|1
|2
|3
|7
|0.4841
|2.20538
|0.04633
|2.02915
|0.02369
|2.18113
|-
|1
|2
|4
|1
|2.82623
|2.01819
|0.25826
|1.69268
|0.11251
|1.97665
|-
|1
|2
|4
|2
|3.24039
|1.9811
|0.36283
|1.50648
|0.11719
|1.96246
|-
|1
|2
|4
|3
|2.4545
|2.03386
|0.19627
|1.75339
|0.09698
|2.00807
|-
|1
|2
|4
|4
|2.46446
|2.01626
|0.17827
|1.76414
|0.08026
|2.02912
|-
|1
|2
|4
|5
|2.11339
|2.00724
|0.14884
|1.77964
|0.07749
|2.00585
|-
|1
|2
|4
|6
|1.51141
|2.04563
|0.11559
|1.82474
|0.06194
|2.02586
|-
|1
|2
|4
|7
|0.95936
|2.09963
|0.07044
|1.95281
|0.03645
|2.0993
|-
|1
|2
|5
|1
|3.36561
|1.97323
|0.2649
|1.65361
|0.13019
|1.92402
|-
|1
|2
|5
|2
|3.66222
|1.95479
|0.35065
|1.51028
|0.14652
|1.89882
|-
|1
|2
|5
|3
|3.20442
|1.96165
|0.28676
|1.58823
|0.12031
|1.93028
|-
|1
|2
|5
|4
|1.78673
|2.0426
|0.17183
|1.75198
|0.0678
|2.02025
|-
|1
|2
|5
|5
|1.61868
|2.01988
|0.11914
|1.80878
|0.06624
|1.99283
|-
|1
|2
|5
|6
|1.30123
|2.02218
|0.10515
|1.80653
|0.05345
|2.00292
|-
|1
|2
|5
|7
|0.65695
|2.08269
|0.06835
|1.89102
|0.0332
|2.0525
|-
|1
|2
|6
|1
|2.3773
|1.9669
|0.24867
|1.6336
|0.08319
|1.94741
|-
|1
|2
|6
|2
|2.82556
|1.95506
|0.31731
|1.51798
|0.12008
|1.89324
|-
|1
|2
|6
|3
|2.7235
|1.94883
|0.30621
|1.5177
|0.09365
|1.93764
|-
|1
|2
|6
|4
|1.77727
|1.98273
|0.17989
|1.69341
|0.07314
|1.95161
|-
|1
|2
|6
|5
|0.81041
|2.05295
|0.13961
|1.74391
|0.04468
|2.01091
|-
|1
|2
|6
|6
|0.72188
|2.0465
|0.09874
|1.79927
|0.03137
|2.03309
|-
|1
|2
|6
|7
|1.21598
|1.97942
|0.07065
|1.87211
|0.04484
|1.98491
|-
|1
|2
|7
|1
|3.55054
|1.89128
|0.27402
|1.61031
|0.10827
|1.89085
|-
|1
|2
|7
|2
|5.0062
|1.81574
|0.3119
|1.54857
|0.18009
|1.76865
|-
|1
|2
|7
|3
|3.95204
|1.84947
|0.30465
|1.53907
|0.16048
|1.789
|-
|1
|2
|7
|4
|2.36233
|1.9168
|0.18751
|1.70412
|0.09531
|1.88355
|-
|1
|2
|7
|5
|1.48851
|1.94443
|0.09973
|1.81041
|0.05904
|1.92497
|-
|1
|2
|7
|6
|1.22525
|1.94454
|0.06617
|1.87082
|0.05516
|1.91259
|-
|1
|2
|7
|7
|1.13847
|1.93756
|0.08109
|1.83388
|0.04706
|1.93165
|-
|1
|2
|8
|1
|4.09874
|1.87708
|0.20312
|1.73434
|0.15506
|1.83083
|-
|1
|2
|8
|2
|4.66403
|1.84302
|0.31808
|1.56093
|0.18049
|1.78288
|-
|1
|2
|8
|3
|3.24375
|1.89351
|0.2827
|1.59546
|0.13583
|1.83427
|-
|1
|2
|8
|4
|2.24175
|1.92084
|0.17795
|1.72611
|0.09636
|1.87438
|-
|1
|2
|8
|5
|1.63783
|1.93625
|0.1225
|1.78642
|0.0659
|1.90934
|-
|1
|2
|8
|6
|2.01753
|1.89095
|0.13742
|1.74752
|0.08289
|1.86553
|-
|1
|2
|8
|7
|0.97568
|1.97215
|0.05926
|1.88807
|0.04057
|1.95672
|-
|2
|1
|1
|1
|3.44076
|1.73133
|0.27759
|1.55037
|0.13323
|1.68913
|-
|2
|1
|1
|2
|4.99596
|1.64527
|0.2322
|1.58033
|0.17533
|1.62422
|-
|2
|1
|1
|3
|3.83372
|1.68144
|0.25087
|1.52033
|0.14525
|1.66706
|-
|2
|1
|1
|4
|3.87034
|1.68102
|0.20979
|1.60153
|0.13627
|1.68885
|-
|2
|1
|1
|5
|1.76134
|1.80424
|0.15241
|1.70485
|0.06231
|1.81524
|-
|2
|1
|1
|6
|0.79304
|1.89072
|0.09906
|1.80312
|0.03277
|1.89435
|-
|2
|1
|1
|7
|1.43535
|1.80614
|0.0593
|1.81589
|0.0407
|1.85002
|-
|2
|1
|2
|1
|3.72284
|1.68499
|0.19226
|1.66567
|0.1237
|1.66453
|-
|2
|1
|2
|2
|4.42667
|1.66508
|0.24314
|1.55652
|0.14361
|1.66251
|-
|2
|1
|2
|3
|2.7019
|1.75871
|0.32717
|1.38452
|0.11056
|1.72312
|-
|2
|1
|2
|4
|2.41538
|1.75937
|0.14575
|1.68355
|0.09038
|1.74138
|-
|2
|1
|2
|5
|1.65412
|1.81649
|0.13926
|1.70623
|0.0597
|1.81378
|-
|2
|1
|2
|6
|2.0843
|1.7735
|0.21052
|1.57508
|0.07244
|1.78566
|-
|2
|1
|2
|7
|1.43238
|1.80651
|0.08031
|1.78712
|0.05269
|1.81727
|-
|2
|1
|3
|1
|2.45314
|1.77068
|0.18152
|1.73443
|0.07657
|1.78025
|-
|2
|1
|3
|2
|3.01217
|1.70966
|0.19388
|1.66175
|0.05624
|1.80606
|-
|2
|1
|3
|3
|2.09997
|1.74945
|0.14493
|1.68277
|0.05446
|1.7922
|-
|2
|1
|3
|4
|2.36683
|1.71741
|0.12244
|1.71407
|0.06775
|1.75721
|-
|2
|1
|3
|5
|1.56776
|1.75755
|0.08776
|1.76946
|0.04244
|1.79675
|-
|2
|1
|3
|6
|1.63824
|1.75452
|0.09422
|1.76794
|0.04181
|1.80604
|-
|2
|1
|3
|7
|0.74114
|1.83421
|0.08039
|1.78306
|0.02347
|1.85596
|-
|2
|1
|4
|1
|1.47047
|1.78588
|0.17271
|1.69379
|0.06511
|1.74985
|-
|2
|1
|4
|2
|2.22168
|1.72985
|0.20701
|1.59429
|0.08178
|1.71455
|-
|2
|1
|4
|3
|2.50108
|1.69618
|0.16828
|1.61962
|0.08598
|1.70516
|-
|2
|1
|4
|4
|1.97141
|1.7202
|0.1446
|1.66357
|0.06856
|1.73201
|-
|2
|1
|4
|5
|1.17054
|1.75879
|0.1172
|1.69234
|0.04624
|1.75806
|-
|2
|1
|4
|6
|1.74755
|1.70968
|0.12562
|1.67603
|0.0629
|1.72333
|-
|2
|1
|4
|7
|0.52482
|1.80155
|0.07345
|1.75615
|0.02671
|1.79288
|-
|2
|1
|5
|1
|1.76464
|1.76219
|0.24301
|1.59094
|0.07156
|1.73136
|-
|2
|1
|5
|2
|1.99594
|1.73438
|0.1984
|1.5954
|0.06489
|1.73449
|-
|2
|1
|5
|3
|1.8804
|1.72362
|0.13019
|1.67977
|0.06783
|1.71916
|-
|2
|1
|5
|4
|1.83337
|1.71477
|0.11197
|1.70244
|0.05764
|1.73194
|-
|2
|1
|5
|5
|1.49752
|1.72615
|0.13128
|1.65461
|0.04656
|1.7433
|-
|2
|1
|5
|6
|1.3042
|1.7305
|0.07173
|1.75315
|0.04482
|1.7399
|-
|2
|1
|5
|7
|2.00868
|1.67669
|0.12298
|1.64761
|0.09175
|1.64669
|-
|2
|1
|6
|1
|0.84993
|1.75972
|0.12918
|1.74026
|0.0328
|1.74802
|-
|2
|1
|6
|2
|1.93666
|1.67406
|0.16606
|1.59943
|0.04535
|1.7106
|-
|2
|1
|6
|3
|2.12115
|1.64964
|0.19988
|1.50821
|0.05229
|1.68986
|-
|2
|1
|6
|4
|0.68831
|1.73901
|0.09674
|1.6838
|0.01696
|1.75787
|-
|2
|1
|6
|5
|1.13081
|1.69479
|0.06413
|1.72559
|0.04936
|1.67757
|-
|2
|1
|6
|6
|0.5893
|1.72537
|0.02598
|1.80138
|0.01591
|1.74082
|-
|2
|1
|6
|7
|0.72519
|1.71955
|0.03157
|1.78405
|0.02889
|1.71972
|-
|2
|1
|7
|1
|1.85937
|1.66064
|0.2416
|1.49676
|0.06807
|1.63599
|-
|2
|1
|7
|2
|1.8527
|1.64892
|0.2374
|1.43845
|0.06336
|1.6431
|-
|2
|1
|7
|3
|1.56905
|1.66084
|0.15434
|1.55598
|0.04336
|1.68109
|-
|2
|1
|7
|4
|0.74968
|1.69857
|0.13496
|1.56636
|0.02871
|1.6933
|-
|2
|1
|7
|5
|1.08222
|1.65925
|0.10847
|1.613
|0.03305
|1.67829
|-
|2
|1
|7
|6
|1.1124
|1.68059
|0.14267
|1.57525
|0.04416
|1.6776
|-
|2
|1
|7
|7
|0.88031
|1.6751
|0.10534
|1.60483
|0.04216
|1.66444
|-
|2
|1
|8
|1
|0.62802
|1.72402
|0.19225
|1.54631
|0.03247
|1.69368
|-
|2
|1
|8
|2
|0.83902
|1.68303
|0.15492
|1.53421
|0.05922
|1.61411
|-
|2
|1
|8
|3
|1.33727
|1.63407
|0.19835
|1.43309
|0.05874
|1.61141
|-
|2
|1
|8
|4
|1.06381
|1.64762
|0.11026
|1.58762
|0.04019
|1.64574
|-
|2
|1
|8
|5
|1.13714
|1.61716
|0.13322
|1.53166
|0.05648
|1.59149
|-
|2
|1
|8
|6
|1.19134
|1.60463
|0.11089
|1.54864
|0.06258
|1.56912
|-
|2
|1
|8
|7
|1.58872
|1.60204
|0.066
|1.64659
|0.04748
|1.63282
|-
|2
|2
|1
|1
|3.46775
|1.78609
|0.28956
|1.68515
|0.15003
|1.72171
|-
|2
|2
|1
|2
|5.69879
|1.67614
|0.3725
|1.5045
|0.19774
|1.64659
|-
|2
|2
|1
|3
|5.18985
|1.66571
|0.40124
|1.40574
|0.17828
|1.65793
|-
|2
|2
|1
|4
|3.43435
|1.74182
|0.20332
|1.66994
|0.11075
|1.76221
|-
|2
|2
|1
|5
|2.48643
|1.76219
|0.13714
|1.7396
|0.09636
|1.75624
|-
|2
|2
|1
|6
|1.41151
|1.82292
|0.15415
|1.6725
|0.06549
|1.80013
|-
|2
|2
|1
|7
|0.9096
|1.8409
|0.08811
|1.7823
|0.03467
|1.85275
|-
|2
|2
|2
|1
|1.85358
|1.83615
|0.28355
|1.64765
|0.06055
|1.83138
|-
|2
|2
|2
|2
|3.81188
|1.74978
|0.25972
|1.62799
|0.11238
|1.7646
|-
|2
|2
|2
|3
|3.16717
|1.76679
|0.29832
|1.53409
|0.09407
|1.78959
|-
|2
|2
|2
|4
|2.33664
|1.78934
|0.22694
|1.60101
|0.07273
|1.80371
|-
|2
|2
|2
|5
|2.01675
|1.79303
|0.10664
|1.79792
|0.06062
|1.8184
|-
|2
|2
|2
|6
|1.80809
|1.80081
|0.13659
|1.70935
|0.07335
|1.79213
|-
|2
|2
|2
|7
|1.01661
|1.8295
|0.0548
|1.84688
|0.03414
|1.84213
|-
|2
|2
|3
|1
|2.01474
|1.8142
|0.21867
|1.74325
|0.05359
|1.83088
|-
|2
|2
|3
|2
|3.53989
|1.71985
|0.28196
|1.60868
|0.10823
|1.73763
|-
|2
|2
|3
|3
|3.38412
|1.69907
|0.27409
|1.56164
|0.11042
|1.71397
|-
|2
|2
|3
|4
|2.2171
|1.74622
|0.16076
|1.70107
|0.07372
|1.75906
|-
|2
|2
|3
|5
|1.11799
|1.80944
|0.11087
|1.75678
|0.03792
|1.81891
|-
|2
|2
|3
|6
|1.40464
|1.76033
|0.10048
|1.72933
|0.05342
|1.75745
|-
|2
|2
|3
|7
|0.11328
|1.8972
|0.04052
|1.87101
|0.00787
|1.88753
|-
|2
|2
|4
|1
|2.59777
|1.74476
|0.28154
|1.66509
|0.10763
|1.71072
|-
|2
|2
|4
|2
|3.53853
|1.69511
|0.38311
|1.46839
|0.13243
|1.66523
|-
|2
|2
|4
|3
|2.80538
|1.70587
|0.26686
|1.55787
|0.1126
|1.68024
|-
|2
|2
|4
|4
|2.18191
|1.72068
|0.18333
|1.65612
|0.085
|1.71029
|-
|2
|2
|4
|5
|1.23383
|1.7716
|0.12824
|1.71179
|0.04845
|1.76628
|-
|2
|2
|4
|6
|0.85652
|1.79279
|0.0763
|1.79314
|0.03563
|1.78528
|-
|2
|2
|4
|7
|0.97995
|1.77178
|0.0797
|1.7577
|0.03846
|1.77043
|-
|2
|2
|5
|1
|2.47016
|1.74985
|0.32061
|1.60073
|0.10455
|1.71058
|-
|2
|2
|5
|2
|3.76194
|1.68979
|0.32787
|1.54675
|0.11781
|1.69109
|-
|2
|2
|5
|3
|2.61421
|1.70766
|0.20307
|1.64866
|0.08315
|1.71378
|-
|2
|2
|5
|4
|1.6809
|1.74028
|0.16795
|1.66491
|0.06202
|1.73305
|-
|2
|2
|5
|5
|1.31241
|1.75722
|0.14383
|1.68302
|0.05338
|1.74562
|-
|2
|2
|5
|6
|1.66563
|1.71781
|0.12721
|1.69231
|0.06147
|1.72101
|-
|2
|2
|5
|7
|0.87471
|1.74991
|0.07882
|1.71706
|0.04173
|1.73246
|-
|2
|2
|6
|1
|1.70055
|1.72832
|0.20839
|1.67759
|0.06001
|1.71779
|-
|2
|2
|6
|2
|3.20558
|1.65143
|0.33676
|1.47797
|0.09642
|1.6546
|-
|2
|2
|6
|3
|1.5827
|1.71538
|0.19719
|1.62038
|0.05324
|1.71254
|-
|2
|2
|6
|4
|1.7692
|1.69473
|0.14854
|1.66225
|0.05758
|1.69946
|-
|2
|2
|6
|5
|1.33003
|1.70542
|0.10726
|1.69398
|0.04565
|1.7096
|-
|2
|2
|6
|6
|1.01266
|1.71155
|0.09376
|1.70285
|0.04005
|1.70822
|-
|2
|2
|6
|7
|0.9856
|1.70091
|0.06454
|1.73063
|0.0394
|1.69796
|-
|2
|2
|7
|1
|2.02441
|1.67788
|0.30435
|1.5407
|0.08673
|1.63673
|-
|2
|2
|7
|2
|1.43949
|1.71143
|0.30098
|1.47963
|0.06527
|1.67295
|-
|2
|2
|7
|3
|1.68946
|1.66442
|0.24777
|1.47116
|0.06594
|1.64834
|-
|2
|2
|7
|4
|1.10967
|1.68591
|0.15663
|1.60109
|0.04949
|1.67069
|-
|2
|2
|7
|5
|0.77866
|1.70882
|0.11248
|1.64389
|0.03402
|1.70215
|-
|2
|2
|7
|6
|0.67502
|1.69719
|0.10289
|1.62419
|0.03507
|1.67744
|-
|2
|2
|7
|7
|0.65216
|1.70336
|0.05545
|1.73388
|0.02233
|1.72102
|-
|2
|2
|8
|1
|1.33877
|1.67358
|0.18369
|1.64385
|0.06055
|1.63818
|-
|2
|2
|8
|2
|0.71697
|1.71038
|0.25461
|1.49037
|0.04798
|1.66397
|-
|2
|2
|8
|3
|2.13197
|1.62429
|0.2393
|1.47673
|0.08136
|1.6065
|-
|2
|2
|8
|4
|1.16932
|1.66188
|0.13759
|1.60108
|0.0463
|1.64856
|-
|2
|2
|8
|5
|1.48369
|1.62387
|0.12547
|1.58988
|0.06919
|1.5925
|-
|2
|2
|8
|6
|1.18879
|1.65442
|0.10031
|1.62813
|0.07392
|1.58846
|-
|2
|2
|8
|7
|0.58052
|1.68546
|0.02696
|1.7382
|0.01982
|1.70519
|}
</center>
</div>
</div>

== Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme ==
<div class="mw-collapsible mw-collapsed">
<div>
=== Abstract ===
Based on comments on imprecision of the estimation method for 24-hour fat % in AM/PM milk recording schemes the regression formula was extended and re-estimated. Non-linearity for the existing effects of protein % of the milk sample, interval before sampling, milk amount of sample, milk amount of previous milking and interval before the previous milking was incorporated by using polynomials. Extensions were made by adding the effects of time of sampling, parity and month of sampling as class variables and lactation stage as polynomial. In total a reduction of the standard deviation of the difference between true and estimated 24-hour fat % of 2.4% was reached (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

'''''Keywords''''': estimation, fat %, AM/PM.

=== Introduction ===
The AM/PM milk recording routine is based on only one morning (a.m.) or evening (p.m.) milk sample which are collected in an alternating way. A condition to take part in this AM/PM milk recording in The Netherlands is that on farm electronic milk measurements (EMM) are available. EMM-data consists of time of milking and milk quantity of every milking. Based on one milk sample and the EMM-data the 24-hour fat % is estimated (Peeters & Galesloot, 2002<ref name=":2">Peeters, R. and P. Galesloot, 2002.Estimating daily fat yield from a single milking on test day for herds with a robotic milking system. J. Dairy Sci. 85, 682-688.</ref>). Also for farms with an automatic milking system (AMS) this estimation is used when only one milk sample is available for analysis on milk composition.

Based on comments from farmers on fluctuations in 24-hour fat % preliminary research was conducted. This showed that the current estimation caused an underestimation of 24-hour fat % based on an a.m.-sample of 0.09% while the estimate based on a p.m.-sample was overestimated by 0.05%. Possible causes for this fluctuation are differences in milk-fat synthesis between day- and night-time as was shown by Gilbert et al. (1972) <ref>Gilbert, G.R., G.L. Hargrove and M. Kroger, 1972. Diurnal variations in milk yield, fat yield, milk fat % and milk protein % by the test interval method. J. Dairy Sci. 56, 409-410.</ref>and Lee & Wardorp (1984)<ref>Lee, A.J. and Wardorp, 1984. Predicting daily milk yield, fat percent, and protein percent from morning or afternoon tests. J. Dairy Sci. 67, 351-360.</ref>. Other factors of imprecision in the current estimation can be caused by lactation stage and parity, two factors that are accounted for in the method of Liu et al. (2000)<ref>Liu, Z., R. Reents, F. Reinhardt and K Kuwan, 2000. Approaches to estimating daily yield from single milk testing schemes and use of a.m.-p.m. records in test-day model genetic evaluation in dairy cattle. J. Dairy Sci. 83, 2672-2682.</ref>.

The objective of this research is to re-estimate the regression formula which is used to estimate the 24-hour fat %s in AM/PM milk recording and AMS recordings with only one sample. By testing for non-linearity of current effects and introducing new explanatory variables the aim is to increase the accuracy of the estimated 24-hour fat %.

=== Material and Methods ===
The data needed for the objective had to meet a number of criteria. The most important criteria were that the data comprised:

* differences in interval between milking times;
* different milking times;
* multiple samples per cow per herd test date;
* milking time and quantity of all milkings;

Only data of farms that use an AMS met all of these criteria. Therefore the research was conducted on data of all farms that used an AMS from January 20th 2001 until July 1st 2004. Records with only one sample per herd test date were excluded from the analysis.

In order to estimate as well as validate the new regression formula the each herd test date was assigned at random into two separate datasets. Dataset 1 was used for estimation and contained 371.528 samplings on 50.591 cows on 537 farms. Dataset 2 was used for validation and contained 371.885 milkings on 50.643 cows on 538 farms. Some characteristics of variables of both datasets are presented in Table 1.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" |'''''Table 1. Characteristics of variables in dataset 1 (estimation) and dataset 2 (validation).'''''
|-
| rowspan="2" |'''Variable'''
| colspan="2" |'''Dataset 1 (estimation)'''
| colspan="2" |'''Dataset 2 (validation)'''
|-
|'''Mean'''
|'''Std'''
|'''Mean'''
|'''Std'''
|-
|Sample milk amount (kg)
|10.1
|3.1
|10.1
|3.1
|-
|Sample fat (%)
|4.40
|0.76
|4.41
|0.76
|-
|Sample protein (%)
|3.49
|0.35
|3.49
|0.35
|-
|Time at sampling
|12.29
|7.24
|12.31
|7.24
|-
|Interval before sample (min)
|520
|154
|521
|155
|-
|Interval before prev. milking (min)
|526
|158
|527
|159
|}
</center>

=== Methods ===
The analysis started with the currently used regression formula which uses the effects: fat %, protein %, milk amount of sampling, interval before sampling, milk amount of the previous milking and interval before the previous milking (Peeters & Galesloot, 2002<ref name=":2" />). All these effects are considered to be linear. As an extra check of the data this regression formula was re-estimated and compared to the currently used regression formula. In order to estimate the regression formula first of all the 24-hour fat % was determined by using a weighted average of all milk samples for that cow on that herd test date.

Subsequently, a number of changes to the regression formula were tested for their effect on the accuracy of the 24-hour fat %. The changes that are tested are:

# non-linearity of the current effects;
# effect of time at sampling;
# effect of lactation stage;
# effect of parity;
# month of milk recording;

The effects were all tested in a similar way by plotting the residuals of the regression formula without the effect that is tested to the tested effect. Based on this plot a possible relation between residual and effect becomes clear and the best way of incorporating the effect is shown. The conclusion if an effect had a positive effect on the accuracy of the regression formula was based on the standard deviation of the difference between estimated and true 24-hour fat %. Also the correlation between the two fat %s and the b-factor (regression coefficient) of the linear regression between the two fat %s were considered.

=== Results ===
The regression coefficients of the re-estimated regression formula differed slightly from the estimates by Peeters & Galesloot (2002)<ref name=":1" />, probably due to the different dataset.

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %.
[[File:Imagefig1.png|center|thumb|''Figure 1a: Average residual per class for the variables sample fat %'']]
[[File:Imagefig1b.png|center|thumb|''Figure 1b: Sample protein %'' ]]
[[File:Imagefig1c.png|center|thumb|''Figure 1c : Interval before sampling'']]
[[File:Imagefig1d.png|center|thumb|''Figure 1d : Interval before previous milking'']]
[[File:Imagefig1e.png|center|thumb|''Figure 1e : Sample milk amount'']]
[[File:Imagefig1f.png|center|thumb|''Figure 1f: Milk amount before sampling'']]

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %. Of all variables, only fat % of the milk sample (Figure 1a) seemed to be linear. A 2nd order polynomial fitted the interval before the previous milking. The other variables, i.e. protein % of the milk sample, interval before sampling, milk amount of sample and milk amount of the previous milking were described by a 3rd order polynomial. For all variables except fat % of the sample higher order polynomials were found significant. This however was caused by the large amount of data and no longer a possible biological effect since it also had no effect on the accuracy of the estimation.

The effect of time of sampling showed a large amount of variability over time. Using a polynomial to fit the data was therefore difficult. Estimation of the effect by hourly intervals was a good alternative as is shown in Figure 2. Lactation stage had mainly an effect in the first 50 days of lactation as is shown by Figure 3. A 3rd order polynomial fitted the data properly.
[[File:Imagefig2.png|center|thumb|''Figure 2. Average residual per class for time of sampling (minutes after midnight).'']]
[[File:Imagefig33.png|center|thumb|''Figure 3. Average residual per class for lactation stage (days).'']]

The effects of parity and month of milk sampling were both considered as class variables. For parity the effects of parity 1 to 6 and 7 or higher were considered. Table 2 shows that mainly for the lower parities the estimated 24-hour fat % was overestimated. Also the months May to October, usually the pasture period, showed an overestimation of 24-hour fat %.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" |'''''Table 2. Effect of parity and month of sampling on estimated 24-hour fat % (*100).'''''
|-
|'''Parity'''
|'''Estimate'''
|'''Month of sampling'''
|'''Estimate'''
|-
|1
|<nowiki>-6.58</nowiki>
|January
|<nowiki>-0.24</nowiki>
|-
|2
|<nowiki>-3.56</nowiki>
|February
|<nowiki>-0.28</nowiki>
|-
|3
|<nowiki>-1.42</nowiki>
|June
|<nowiki>-0.54</nowiki>
|-
|4
|<nowiki>-0.48</nowiki>
|April
|<nowiki>-0.27</nowiki>
|-
|5
|<nowiki>-0.35</nowiki>
|May
|<nowiki>-2.07</nowiki>
|-
|6
|<nowiki>-0.35</nowiki>
|June
|<nowiki>-3.36</nowiki>
|-
|7+
|<nowiki>-0.00</nowiki>
|July
|<nowiki>-4.32</nowiki>
|-
|
|
|August
|<nowiki>-5.52</nowiki>
|-
|
|
|September
|<nowiki>-4.74</nowiki>
|-
|
|
|October
|<nowiki>-2.24</nowiki>
|-
|
|
|November
|<nowiki>-0.97</nowiki>
|-
|
|
|December
|<nowiki>-0.00</nowiki>
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" |'''''Table 3. Statistics of the difference between true and estimated 24-hour fat % for six regression formulas (current, re-estimated + five steps), each also including preceding steps.'''''
|-
|style="text-align: left;"|'''Regression'''
|'''Std.'''
|'''Min'''
|'''Max'''
|'''Cor'''
|'''b-factor'''
|-
|style="text-align: left;"|Current, re-estimated
|0.2856
|<nowiki>-1.840</nowiki>
|2.224
|0.898
|0.807
|-
|style="text-align: left;"|Non-linearity
|0.2820
|<nowiki>-1.890 </nowiki>
|2.198
|0.901
|0.812
|-
|style="text-align: left;"|Time of sampling
|0.2817
|<nowiki>-1.877 </nowiki>
|2.211
|0.901
|0.813
|-
|style="text-align: left;"|Lactation stage
|0.2803
|<nowiki>-1.883 </nowiki>
|2.196
|0.902
|0.814
|-
|style="text-align: left;"|Parity
|0.2794
|<nowiki>-1.887 </nowiki>
|2.179
|0.903
|0.816
|-
|style="text-align: left;"|Month of sampling
|0.2788
|<nowiki>-1.868 </nowiki>
|2.175
|0.903
|0.817
|}
</center>

Table 3 shows some statistics of the difference between the true and estimated 24-hour fat % based on dataset 2 (validation) of the different regression formulas. Each of the five changes to the regression formula had a (minor) positive effect on either the standard deviation of the difference between the true and estimated 24-hour fat % (Std.), the correlation (Cor) between the two fat %s, the b-factor of the linear regression between the two fat %s or a combination of the these. All changes together reduced the standard deviation with 2.4% from 0.2856 to 0.2788, increased the correlation from 0.898 to 0.903 and increased the b-factor from 0.807 to 0.817.

=== Conclusions ===
The regression formula to estimate the 24-hour fat % based on one milk sample was improved. Improvements were first of all considering non-linearity of the variables by using polynomials for protein % of the milk sample (3rd order), interval before sampling (3rd order), milk amount of sample (3rd order), milk amount of previous milking (3rd order) and interval before the previous milking (2nd order). Secondly, adding the effects of time of sampling (class variable), lactation stage (3rd order polynomial), parity (class variable) and month of sampling (class variable) gave a further reduction of the difference between true and estimated 24-hour fat %. The total reduction in standard deviation of the difference between true and estimated 24-hour fat % is 2.4% (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

</div>
</div>

== Appendix 3 - A unified Python implementation of standardized 305 day yield calculation methods ==
<div class="mw-collapsible mw-collapsed">
<div>
The ICAR guideline is translated into an open-source Python package that can serve as a reference implementation for 305-day yield calculation. In addition to implementing the methods described in the original guideline (with the exception of the multi-trait method, which will be added in future work), the package incorporates 14 lactation-curve models, including traditional parametric models, Bayesian fitting approaches, and an AI-based model. The package also provides tools to derive biologically relevant lactation characteristics such as time to peak, peak yield, cumulative yield, and persistency. The package is publicly available through PyPI and can be installed directly using pip install lactationcurve (van Leerdam et al., 2026). Extensive documentation was developed alongside the package to improve transparency and reproducibility [https://bovi-analytics.github.io/bovi/lactationcurve.html https://bovi-analytics.github.io/bovi/lactationcurve.html.]

Through a companioning website (https://tools.bovi-analytics.org<nowiki/>/), users can upload milk-recording data in CSV format, fit and visualize the implemented lactation-curve models, and compare different cumulative milk-yield methodologies on both test-day and fully daily-recorded lactations using metrics such as RMSE, Pearson correlation, MAPE, and MAE. Reference datasets are provided to allow organizations to benchmark their own calculations against alternative methodologies. In addition, downloadable PDF reports summarize the results through detailed statistics and scatterplots, both overall and stratified by parity.
</div>
</div>

Section 02 – Cattle Milk Recording

2026-07-22T17:59:36Z

Cmosconi:

= Overview =
<div class="mw-collapsible mw-collapsed">
<div>
== Introduction ==
Information about milk production traits is very important for managing and breeding dairy herds. The milk recording process starts with the collection of animal identification, a calving date of milking cows, the amount of milk given and the date with time or time frame of a day. A milk sample may be taken. The obtained milk sample is analysed for milk constituents. The results of the analysis plus the data about milk yield and time of milking are stored in a database. Subsequently a number of parameters, cumulative yields and indices are calculated and stored in the database and, finally, reported to the farmer

This Section 2 of the ICAR Guidelines focuses on the milk recording process for dairy cattle.

== Scope ==
Figure 1 gives a pictorial summary of the main elements of this guideline.

In summary, this section of the ICAR Guidelines covers the milk recording process from the enrolment of a herd for milk recording, through to the delivery of information which a herd owner can use to assist in a range of decisions.
[[File:Scope of Section 2 - Dairy cattle milk recording..png|thumb|Figure 1. Scope of Section 2 -Dairy cattle milk recording.|center|524x524px]]

Not covered in this section are:
# Standards and guidelines for ICAR approval of milk recording devices. Please consult [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices|Section 11]] for this subject.
# Standards and guidelines for ICAR approval of ID devices. Please consult [[Section 10 – Identification Device Certification|Section 10]] for this subject.
# Standards and guidelines for preparation of milk samples and for quality assurance of milk analysis. Please consult [[Section 12 – Milk Analysis|Section 12]] for this subject.
# Standards and guidelines for in-line milk analysis on the farm. Please consult [[Section 13 – On-farm Milk Analysis|Section 13]] for this subject.

== Enrolment ==

Enrolment of new herds in the recording process should involve an agreement between the farmer and the recording organisation regarding technical and financial questions such as:

# General information about the recording programme itself, i.e.
#* Herd and cow identification.
#* Scope of recorded data, including database setup as required by the user.
#* Scheduling recording.
#* Data capture and processing.
#* Recording methods and intervals.
#* Milk measuring and meters.
#* Sampling and sample transport.
#* Reports (outcomes) and supporting decisions.
# Definition of supervision scheme and other quality assurance and plausibility checking steps.
# Fee structure and invoicing.
# Approval of technicians by milk recording organisations (MROs) so as to give them free access to farms for all recording and supervision actions.

In cases where the owner of the recorded cows or his employees carry out the recording itself, it is up to the organisation to decide upon, and provide for, any necessary training.

== Standard and Guidelines for Milk Recording ==
These standards and guidelines for milk recording are valid for all milking systems, including AMS where applicable.
====General Standards and Guidelines for milk recording====
#ICAR-approved (electronic) milk meters and sampling devices must be used on the recording day (see [https://wiki.icar.org/index.php/Section_11_%E2%80%93_Testing,_Approval_and_Checking_of_Measuring,_Recording_and_Sampling_Devices#Procedure_1:_Procedure_for_Application_for_Testing_of_Measuring,_Recording_and_Sampling_Devices_or_Sensor_Systems Procedure 1 of Section 11 - Guidelines for Testing, Approval and Checking of Milk Recording Devices]). The list of approved milk meters, jars and AMS and automatic milk sampler/tray combinations sampling devices can be found on the [https://www.icar.org/index.php/certifications/icar-certifications-for-milk-meters-for-cow-sheep-goats/ ICAR web page].
#Milk weights are recorded for each milking of the recording period. The measurement may be done using any of the ICAR approved recording devices, or by weighing. The minimum accuracy of the measurement is 0.2 kg.
#Where milk constituents are analysed, the equipment used must meet ICAR standards for accuracy. Please consult [[Section 12 – Milk Analysis|Sections 12]] and [[Section 13 – On-farm Milk Analysis|Section 13]] of the Guidelines for details.
#The accuracy of the equipment used for milk recording and sampling must be checked by an agency approved by the member organisations, on a regular and systematic basis using methods approved by ICAR. The list of methods is given in [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices#Procedure 6: Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices|Procedure 6 of Section 11]] - Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices.
#All analyses of the constituents of a milk sample must be carried out on the same milk sample.
#These samples should ideally represent the 24-hour milking period.
#If milk samples do not represent a 24-hour period, the results of milk analyses must be corrected to a 24-hour period by a method approved by ICAR (see [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]).
#In cases where the duration of recording deviates from 24 hours, the results must be converted into 24-hour yields. Only approved 24-hour yield calculation methods can be used. The appropriate methodology is described in [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]
#As date of recording, we recommend to use the date on which the last sample was taken. As alternative, the date of the first sample can be used.
#Calculation methods
##The quantities of milk and milk constituents shall be calculated according to one of the methods outlined in this section of the ICAR Guidelines (see [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Standard methods for calculating 24 hour yields]).
##Member organisations should keep the ICAR Secretariat informed about the calculation methods being used by the records processing operations in their organisation or country and shall be responsible for ensuring that the records are corrected and calculated as specified in this section of the ICAR Guidelines.
====Standards and Guidelines for milk recording using AMS====
This subsection covers systems where milk weights, milk quality or other traits of the cows are monitored constantly and automatically. This can be done in both automatic and manually operated milking systems.

Requirements:
*Animal identification is automatic and reliable. Farm transponders can also be used for automatic identification if they are linked to the cow’s official identification in farm software.
*All individual milkings must be recorded from all AMSs in the farm and transmitted to the recording database for calculation, interrupted milkings included.
*For official milk recording purposes, the data file obtained from electronic milk meters must contain the following: 1) Cow ID, 2) Milking time stamp, 3) Milk weight and 4) Sampling stamp to mark the milking where the sample comes from.
*All milkings within the recording period may be sampled, and in this case the samples should be analysed separately. Alternatively, a one-milking sample can be taken for each cow, followed by fat correction calculation.
*All cows in milk on the recording day have to be sampled. The sampling device must remain in operation until all cows are sampled. When the number of available sampling devices is smaller than the number of AMS units, sampling may need to be prolonged beyond one day to allow complete sampling of all cows. In that case, the sampling device has to be moved between AMS units.
*During sampling, the automatic sampler must be monitored to make sure there are vials left for the next cows.
*24-hour yield calculations must be carried out by a MRO, independently of the AMS manufacturer. This is done in order to guarantee harmonisation of calculation methods between the different brands of equipment and software.
*Data of all milkings over a given time period must be collected for the 24-hour milk yield calculation. A 96-hour data collection period is recommended.
Recommendations:
#Ideally, data of all milkings should be collected and used to compute lactation yield.
#Description of formats to exchange data recorded by an AMS can be requested from the manufacturer or the ICAR ADE data exchange standard for milking data can be used.
#In the case of milk recording method B (see [[Section 02 – Cattle Milk Recording#Recording|chapter 1.4 "Recording]]") with AMS, the milk recording organization should make sure that the farmer knows how to load or transfer data.
#Data can be extracted by: 1) manual operation by MRO Technician’s or Farmer (file extraction), 2) automated system and data transfer through an Application Programming Interface (API), 3) another data transfer and exchange system.
#Raw milk recording data from the AMS must be easily accessible for MRO data processing.
#For official milk recording purposes, the data file obtained from electronic milk meters may also contain the following: 1) Vial ID (this is obligatory with M sampling scheme), 2) Milking duration, 3) Milking speed, 4) Incomplete milking in automatic milking systems and 5) Other relevant data measured or reported by the equipment.
#Individual milkings should be tested for milk secretion rate in order to detect interrupted and unrecorded milkings, which in turn have an effect on the calculated 24-hour yields. If there is an interrupted milking or a milking that follows an interrupted milking at the beginning of the recording period, these two milkings must be excluded from the calculations. During the recording period they can be excluded but do not need to be.
#It is recommended to individually sample all milkings within the 24-hour recording period for 24-hour fat content calculation due to the high variability of milking frequency and milk fat content. In cases where sampling all milkings is not possible, please consult Chapter 2 of [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 - Computing 24-hour Yields] (for approved correction calculation methods).
#It is recommended to sample only milkings with a preceding interval longer than 4 hours.
====Authorisation to record====
It is recommended that professional milk recording technicians are trained and certified before they carry out recordings on their own. Ideally, such training includes a period of supervised work with a certified technician. Where such a certification system is in place, it is not allowed to record without an authorisation.

It is also recommended that frequent training is given to milk recording technicians on new technologies and equipment, safety instructions and data quality issues.

In B and C recording, farmers or their employees doing the practical recording need to be capable of operating the recording equipment correctly (e.g. milk meters, data capture tools) and are familiar with recording techniques.

It is recommended to have a conformation test from a certified recording agency and that frequent training take place.
====Cows to be recorded====
In a recorded herd, all milk-producing cows must be recorded. If a herd is divided into groups, all animals in the group have to be recorded on the same recording scheme. If different recording schemes are practiced on the farm all cows must be recorded according to the standards for recording and sampling intervals in table 3.

Acceptable reasons for missing data are discussed below, in 5.5. Missing results and/or abnormal intervals are reported [[Section 02 – Cattle Milk Recording#Missing results|here]].

===Identification (ID)===
====Herd ID====
Each herd in milk recording must be allocated a unique permanent identification number.
====Animal ID====
An official milk recording system must be based on a clearly identifiable and unique animal ID. It is recommended that one identification scheme for the whole country is used. Animal identification must also be in accordance with national and international regulation (e.g. EU member countries with EU legislation - 1760/2000 for cattle), and with relevant parts of currently valid ICAR Guidelines. The animal must be marked with an ICAR approved identification device or system. If the ID of imported animals is changed, the connection to the original ID must be maintained. Management numbers for cows can be used aside the official ID.
====Identification of the sample vial====
The sample, the milk weight and the cow ID must be linked at the milking.

Vials can be identified according to:
#Vial placement in the sampling unit.
#Cow or sample ID written on the vials.
#Barcoded vial with printed cow ID.
#Barcoded vial with cow ID registered at the milking.
#RFID vial with cow ID registered at the milking.
=====Sample identification without electronic equipment=====
Samples are identified according to their placement in the sampling unit. Additionally, sample or cow numbers can be written on the vials with a waterproof marker. If this marking is not done, there must be a sure and efficient way to identify sample No. 1 (e.g. different colour) and the sequence of other samples.

Each sampling unit must be connected to a list of samples where cow ID is given for each sample. Each transportation box also has to carry the relevant herd ID’s and, preferably, the sampling dates.
=====Barcoded vials=====
Samples are identified according to the barcode on the vial label.

If the label contains cow and/or herd ID, no electronic equipment is needed at the recording. The samples can be sent to the laboratory without accompanying sample lists or herd ID markings on the box.

If the label contains a random sample ID number, the cow ID must be connected with it on the farm. This is done with a barcode reader and computer programmes making the connection possible.
=====Vials with RFID=====
Samples are identified according to the RFID chip in the vial. This system requires the use of RFID readers and specific computer programmes creating a file where the cow and vial ID’s are connected.
=====Automatic sampling systems=====
In automatic milking systems (AMS), ICAR approved automatic samplers have to be used. Sample identification in these systems can be based on vial placement, barcode or RFID. The file with corresponding cow ID is in the management programme of the milking system. Data transfer is carried out with specific software and via a specific interface from the AMS to the MRO.
=====Sample ID in the laboratory=====
For impartiality and better quality, it is recommended that the samples are identified without cow ID and sent to the laboratory anonymously and the analysis results are merged afterwards in the data processing centre.
====Connection of the sample to milking and 24 h yield====
=====Sample and milk weight from the same milking=====
The ideal situation is that the sample and milk weight represent the same milking.
=====Sample from one milking, milk weight from two=====
A corrected analysis is routinely attached to the 24-hour yield.
=====Sample from one milking, milk weight from two or more, corrected by intervals=====
In this case, a 24-hour-yield is also combined with a one-milking sample, but the 24‑hour yield is obtained by correcting the recorded milkings according to the length of the preceding milking intervals. For example, if a cow has produced 20 kg milk in two milkings and the preceding intervals total 20 hours, her 24-hour yield is calculated as 20 kg * (24 h/20 h) = 24 kg. A corrected analysis is attached to this 24‑hour yield.
=====Sample from one milking or day, milk weight from several days=====
With electronic milk meters, it is possible to use the milk production from several days. This gives better accuracy of milk yield estimation; the highest accuracy with uncorrected milk weights is reached using a 4-day average. The problem is that the sample results become disconnected from the milk yield and a loss in fat and protein yield accuracy will occur. Ideally, fat and protein production should be connected to the recording day even in AMS.

In this case, there are three options to connect samples to the 24-hour yield:
#Milk weight is estimated from a longer measurement period but for fat and protein yield estimation only the milk yield on sampling day is used.
#Information only from the recording day for constituents in milk and milk yield estimation.
#Combination of multiple day milk yield with constituents from sampling. See ICAR procedures for using data from more than one day (Lazenby ''et al''., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>, estimation of fat and protein yield (Galesloot and Peeters , 2000)<ref name=":1">Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>.
The analysis data are merged with milk weights in the laboratory or data processing centre and the date of the analysis must be known.

=== Traits to be recorded ===

==== Definition of milking speed and box time ====

===== Introduction =====
Automated Milking Systems (AMS) do measure many traits. The definition of these traits might be different per brand of AMS. Data of these traits is often used by e.g. milk recording organisations, herdbooks or management software providers. When organisations store these data in their databases and use for certain services, it is important to know how these traits are defined.

These definitions could be used by milk recording organisations etc. to take into account differences between traits measured by different brands of AMS. These definitions could also be used by manufacturers of AMS to take into account for product development, to get more alignment in trait definitions between different brands of AMS.

Aim of this document is to propose a harmonized definition of some traits measured by AMS.

At this stage, the traits milking speed and box time are taken into account. Traits related to teat coordinates are described in Section 5 (Conformatoin Recording) of the ICAR guidelines.

==== Average milking speed ====
Definition = AverageMilkingSpeed (gr/min) = {TotalMilkYield / TotalMilkingTime}

* Total milk yield (kg) = Sum of all quarter level milk yields (kg)
* Total milking time = Last Take-off time (of any teat) - Begin of milk flow (of any teat)

Recommendations for manufacturers:

* Exclude any pre-treatment time from milking time.
* Provide take-off settings (threshold in gr/min at take-off, user-defined or default) and settings for the beginning of the measurement period, as milking time will be influenced by take-off settings and by the definition of the beginning of the milk flow.

Recommendations for data users:

* Don't report milking sessions with kick-off´s, interrupted and re-attached milkings because milking time will vary for these milkings.

==== Box time ====
Different types of box time:

* Milking
* Feed-only
* Pass-through
* Selection
* Training

Definition = {End box time - Begin box time} (HH:MM:SS)

* Begin box time = datetime of recognition of animal
* End box time = datetime when cow has exited the box (which might be different from opening of the gate), best to detect when cow has actually left the box

Additional data is needed to understand the status and completeness of the milking visit (Wethal and Heringstad, 2019). Registered issues during the milking are e.g.

* ff: at least 1 teat cup kicked off
* TeatNotFound: unable to find at least 1 of the teats for milking
* IncompleteMilking/FailedMilking: Minimum of 1 teat was registered as incompletely milked.
* The expected milk yield for a milking session depends on previous milkings. Settings like yield less than 80% of expectation for a teat, the milking session would be recorded as having an incompletely milked teat.
* Manual interaction like teat manually attached or milking finished manually.

Recommendations for manufacturers:

* Make the codes available that express if a milking was successful and the cause if the milking was not successful.
* Uniform names and definitions for interrupted, incomplete or failed milkings as well.

Recommendations for data users:

* Check the availability of a code that expresses if a milking was successful and the cause if the milking was not successful. The meaning of the code can be used to consider if the box time record has to be used for the intended purpose or not.
* To check if there is any extra box time due to feeding concentrates, e.g. through user specific settings such as 'PriorityFeeding'.

=== Traits to be recorded ===
In official milk recording, the following data have to be recorded, wherever available:

# Identification of each cow in the herd, even if they remain in the herd for a very short time.
# Birth date, sex, breed and parents of each animal when known.
# All services and embryo flushings and transfers: date, recipient, sire, dam of the embryo.
# All animal deaths and movements between farms and owners.
# Recording dates and locations.
# Milk yields for each cow and recording date.
# Fat content in milk for each cow and sampling date.

It is recommended to record also the following:

# Protein content in milk for each cow and sampling date.
# Milk somatic cell count for each cow and sampling date.
# Other results obtained from milk analysis.
# Milking duration and milking speed where possible.
# Milking times during recording.
# Recording methods and respective symbols used in records.
# Information about cow during the rearing period.

=== Recording method ===
The recording method for the herd consists of using five different symbols for:

# Responsibility for the practical recording.
# Sampling scheme.
# Recording interval.
# Sampling interval (if different from the above).
# Number of milkings per day (especially any deviation from 2x milking).

The symbols in Table 2 should be used:<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Symbols for milk recording schemes.''
|- style="background-color:#efefef; text-align:center;"

|'''Responsibility for recording'''
|'''Sampling scheme'''
|'''Recording interval (weeks)'''
|'''Sampling interval (weeks)'''
|'''Number of milkings per day'''
|-
| style="text-align:center;" | A
| style="text-align:center;" | P
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | B
| style="text-align:center;" | E
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | C
| style="text-align:center;" | Z
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" |
| style="text-align:center;" | T
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" |
| style="text-align:center;" | M
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:center;" | R x
|-
| style="text-align:center;" |
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | S x
|}
</center>

As an example: Recording method is CP36, 2x means that this is a recording where records/ samples are taken partly by the owner (farmer), and partly by a technician from the MRO, where the recording frequency is every 3 weeks, where the sampling frequency is every 6 weeks, and where the number of milkings per day is 2. If a national nomenclature system is used, it should be possible to transfer this system into ICAR nomenclature.

The reference milk recording method is by a representative of the recording organisation, measuring and sampling every four weeks, with proportional sampling and two milkings per day (AP44, 2x).

Recording other than by the reference method must be indicated using the appropriate symbols.

It is recommended that a limit is set for changing the recording method e.g. so that normally it is only possible to change the method twice per year.

It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

In the next sections the symbols are explained:
====Responsibility for the recording====
This symbol indicates who is responsible for measuring the milk yields and taking samples in the herd.
#Representative of the MRO (Method A; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Farmer or his/her representative (Method B; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Mixed responsibility (Method C; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
====ICAR Standards for sampling schemes====
=====Proportional sampling (P)=====
Samples and milk weights are taken at each milking during the recording day. The sampled amount corresponds to the milk yield of each milking. This is achieved by the use of a pipette in equal number of pipetting at each milking or of a specially designed tool which ensures proportional sampling to create one mixed sample. This is the default sampling scheme with no necessary correction to the analysis results, all other schemes must be reported.
=====Equal measure sampling (E)=====
Samples and milk weights are taken at each milking during the recording day. The amount of the sample is measured to be equal at each milking and mixed into one sample. The analysis results for fat should be corrected if one of the milking intervals is shorter than 10 or longer than 14 hours.
=====Multiple sampling (M)=====
Samples are taken at more than one milking during the recording day while milk weights are taken at each milking or over several days. Samples from different milkings are not mixed but they are kept in distinct vials so that each cow has at least two samples. The analysis results must be corrected to correspond to the 24-hour fat and protein yields. For example: a cow is milked 3x during 24 hours and 2 or 3 separate samples are taken, kept and analysed in different vials. This is the gold standard for AMS. It produces the most accurate results but is more expensive.
=====One-milking sampling with milk weights from more than one milking (Z)=====
Samples are taken from one milking during the recording day while milk weights are taken at each milking or over several days. The analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Alternated one-milking recording (T)=====
Samples and milk weights are taken during one milking, alternating between morning and evening milkings. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Constant one-milking recording (C)=====
Samples and milk weights are taken during one milking, constantly during morning or evening milking. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====In-line analysis recording (I)=====
Milk is not sampled but its constituents are continuously analysed by a stationary analyser.
====ICAR Standards for recording and sampling intervals====

<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Standards for recording and sampling intervals.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| rowspan="2" style="text-align:center;" |'''Recording or sampling interval (weeks)'''
| rowspan="2" style="text-align:center;" |'''Minimum number of recordings or samplings per year'''
| colspan="2" style="text-align:center;" |'''Interval between recordings or samplings (days)'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| rowspan="10" style="text-align:center;" |Reference method
| style="text-align:center;" |1
| style="text-align:center;" |44
| style="text-align:center;" |4
| style="text-align:center;" |10
|-
| style="text-align:center;" |2
| style="text-align:center;" |22
| style="text-align:center;" |10
| style="text-align:center;" |18
|-
| style="text-align:center;" |3
| style="text-align:center;" |15
| style="text-align:center;" |16
| style="text-align:center;" |26
|-
| style="text-align:center;" |4
| style="text-align:center;" |11
| style="text-align:center;" |22
| style="text-align:center;" |37
|-
| style="text-align:center;" |5
| style="text-align:center;" |9
| style="text-align:center;" |32
| style="text-align:center;" |46
|-
| style="text-align:center;" |6
| style="text-align:center;" |8
| style="text-align:center;" |38
| style="text-align:center;" |53
|-
| style="text-align:center;" |7
| style="text-align:center;" |7
| style="text-align:center;" |44
| style="text-align:center;" |60
|-
| style="text-align:center;" |8
| style="text-align:center;" |6
| style="text-align:center;" |50
| style="text-align:center;" |70
|-
| style="text-align:center;" |9
| style="text-align:center;" |5
| style="text-align:center;" |55
| style="text-align:center;" |75
|-
| style="text-align:center;" |Daily
| style="text-align:center;" |310
| style="text-align:center;" |1
| style="text-align:center;" |3
|}
</center>

====ICAR standards for number of milkings per day====

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 3. Symbols for number of milkings per day.''
|- style="background-color:#efefef; text-align:center;"
|'''Number of milkings per day'''
|'''Symbol'''
|-
| style="text-align:center;" | Once per day milking
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | Two milkings
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | Three milkings
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" | Four milkings
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" | Continuous milking (e.g. AMS)
| style="text-align:center;" | R x
|-
| style="text-align:center;" | Regular milkings not at the same times on each day (e.g. 10 milkings per week)
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" | Shown as the average number of milkings per day.
| style="text-align:center;" |
|-
| style="text-align:center;" | Animals that are both milked and suckled. (Number of times milked to prefix the S)
| style="text-align:center;" | S x
|}
</center>

Where a herd is dry for a period of the year, the minimum number of recordings should be adjusted proportionately to the production period.

Minimum number of herd recordings should be at least 85% of the normal number of recordings.

=== Missing results and/or abnormal intervals ===
{{anchor|Missing_results}}A recorded 24-hour yield is the best estimate of the yield and the constituents of the milk, weighed, sampled and recorded within 24 hours on the day of recording.
#When herds are normally milked at intervals such that the recording day is other than 24 hours, the yields shall be adjusted to a 24-hour interval using the following procedure (or other procedures approved by the ICAR):
#*Divide 24 by the interval, then multiply by the yield. For example:
#**For a 25 hour interval (24/25) x 35 kg = 33.6 kg
#**For a 20 hour interval (24/20) x 35 kg = 42.0 kg
#A recording is a set of daily test values for a given animal on a given day of recording, one or some or all of them can be missed (missing values)
#Missing values can be due to:
#*Out of range.
#*Sickness.
#*Disaster.
#*No sample analysis results.
#The number of the official and complete (milk, fat and protein) recordings in the lactation or other accumulated yield should be reported.
#Permitted range of the daily recorded values is given in Table 5. Outside of these ranges, the daily recorded<ref>'''Note:''' High fat breeds have breed average higher than 5.0 for fat %.</ref> value will be considered as a missing value.

<center>
{| class="wikitable"
! colspan="7" style="text-align:left;" | ''Table 5. Permitted range of the daily recorded values.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| colspan="2" style="text-align:center;" |'''Milk (kg)'''
| colspan="2" style="text-align:center;" |'''Fat %'''
| colspan="2" style="text-align:center;" |'''Protein %'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| style="text-align:center;" | Main Dairy Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 1.5
| style="text-align:center;" | 9.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 7.0
|-
| style="text-align:center;" | High Fat1 Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 2.0
| style="text-align:center;" | 12.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 9.0
|}
</center>1Note: High fat breeds have breed average higher than 5.0 for fat %The true daily recorded values collected from animals labelled by the farmer as sick, injured or under treatment must be used in the computation of the lactation record unless the milk yield is less than 50% of the previous milk yield or less than 60% of the predicted yield. In such a case, the whole set of daily recorded values may be considered as missing.

Estimates of the missing values of a daily recording can be computed by using interpolation procedures or by more sophisticated procedures approved by ICAR

== Samples ==

=== Representative sample ===
The milk sample has to represent the complete milking linked to it. This is achieved by mixing the milk thoroughly or pouring it into another vessel right before sampling.

Sampling scheme P requires using a pipette for making the sample proportional between different milkings.

With sampling scheme E, it is advisable to use a measuring cup to make sure the sample parts actually are equal.

Immediately after sampling, the vials have to be preserved, capped, shaken and marked. Samples should be stored cool and dark.

=== Transport ===
Samples should be transported for analysis to a laboratory as soon as possible after sampling.

The samples need to be packed for transport and handled during transport in a manner that guarantees that sample IDs are not compromised or mixed. It is also recommended to protect the packages from external interference.

The packing material must be clean and disposable or easy to clean.

During transportation, it is recommended that the temperature of the samples stays below +10°C.

== Database ==
Storing the recorded data in a milk recording database is an indispensable part of the recording. It is recommended to use the quickest possible means to store the data in the database in order to ensure up-to-date breeding values and management applications. Where computerised data capture is possible, it should not take more than five days after the recording to have the complete recording data set in the database.

The application of the Guidelines in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield], together with other parts of the Guidelines, ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

The guidelines on storage of data collected by the milk recording process are:

# For every recording, cow identification (ID), 24-hour milk yield or individual milk yields with a minimum of 0.2 kg (or the equivalent thereof) milk accuracy and recording date have to be stored.
# Where possible, it is advisable to store each milking separately. The data stored can include milk yield, time and date of milking, and milking scheme.
# Analysed results of the milk sample are stored, namely: sample ID, fat content (or percentage), sample status, sample type. Optional data can be stored on protein and/or lactose content, somatic cell count and additional analyses.
# Analysis results can be linked to one or more milkings of the cow.
# In case of storage or performance problems it might be necessary to remove old data of individual cow milkings from the database.
# Recording day information is the yield over 24 hours and should at least be kept in the database for the current lactation and the previous lactation.
# If recording day information is changed after batch processing it should be marked with a user-ID and time stamp.
# Yields are stored in kg or lbs or, in the case of fat and protein contents, in percent units.

The necessary additional information about how the results have been obtained include:

# Who did the recording (certified technician, farmer etc.).
# Herd and/or cow milking frequency.
# How many milkings were measured.
# How many milkings were sampled.
# Sampling scheme when sampling.
# Daily yield calculation method used.
# Recording and sampling intervals.
# It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

Basic checks for recording data:

# Farm (herd) ID: identified by a unique key.
# Animal ID: has to be unique in database.
# Format of animal ID: compliant to international standards of identification and registration.
# Recording date: less than or equal to today, greater than last recording date.
# Milk yield: stored with one decimal.
# 24 hour milk yield within range ( Table 5).
# Fat and protein content: e.g. within a range of +/- 3 standard deviation of population average (Table 5).
# Calving date: greater than birthday of cow (e.g. greater than birthday of cow + 20 months).
# Calving date: less than or equal to today.
# Sample analysis

This section of the ICAR Guidelines examines how observations are performed on farms and how data are collected, analysed and reported back to farmers. It forms an integral part with other sections of the ICAR Guidelines. It ensures that samples are analysed to the relevant degree of accuracy for the purposes of milk recording, breeding value prediction and other areas of usage. ICAR members operate in a range of situations, ranging from places with almost fully automated recording systems to areas with no roads and electricity. Therefore, the guidelines only demand standards that can be followed, irrespective of production situations and recommend more advanced options, where possible or required. Under the guidelines some practices might not be permitted while other practices are tolerated but not recommended.

== Yield calculations ==
This section covers 24-hour yields and accumulated yields for milk, fat, protein and somatic cells. It also describes the procedure for acceptance of new methods not previously mentioned in the guidelines.

The basic requirements for all calculation methods are that rounding shall only take place at the last step of the computation.

=== Lactation period ===

==== Commencement of the lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, is considered to commence is:

# The day that the cow calves (calving date), or
# In the absence of a calving date, the best estimate of the day that the cow commenced milk production.

A (valid) calving is defined as a parturition taking place:

# After the mid-point of the gestation period if a service has been recorded, or,
# After at least 75% of the normal gestation period has elapsed since the previous calving recorded if no service event has been recorded.

Any parturition falling outside the above definition shall be recorded as an abortion and shall not start a new lactation period.

For cows of dairy breeds the normal gestation length shall be deemed to be 280 days unless more specific breed information is available for use.

If the first recording is done on the calving date or within the first 4 days after calving, the milk yield and constituents at the first recording should not form part of the official lactation record, especially for automated milking systems (AMS) with multiple recorded days.

==== Completion of lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, has been completed is or:

# The day that the cow ceases to give milk (goes dry) or
# The day the cow gives less than 3.0 kg/day or 1.0 kg/milking in a recording (unless recorded sick) or
# When it is common practice not to record the dry-off date, the day of the midpoint between the last recording with the cow in milk and the first recording day with the animal dry may be assumed to be the dry-off date.

The lactation period ends on whichever date above occurs first.

Cows may be recorded as absent or sick on the recording day, without the lactation period being defined as terminated.

=== Production period ===
In the case where yield records are calculated on the basis of a period of production, usually a year, the record should be expressed as a ‘production period record‘ (symbol PP).

The production period begins the day after the end of the previous production period and ends as defined by the length (in days) of the production period.

=== Additional notes ===
For any ICAR method the interval between two consecutive recordings must routinely fulfil the value for the acceptable range on the herd level.

If the first recording occurs within 14 days from calving, then no adjustment is required to the first recorded value when computing the accumulated record. If the first recording occurs 15 to 95 days from calving, then an adjustment procedure may be applied.

If the 305th day of a lactation falls before the last recording, the interpolation method should be used also for the last period to compute the yields.

=== Standard methods for calculating 24 hour yields ===
The ICAR approved methods are presented in '''[https://www.icar.org/Guidelines/02-Procedure-1-Computing-24-Hour-Yield.pdf Procedure 1 of Section 2]'''. They include:

1. Methods for calculating daily yields from AM/PM milkings:

# Method of Delorenzo and Wiggans (1986)<ref>Delorenzo, M.A., and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. [https://www.journalofdairyscience.org/article/S0022-0302(86)80678-6/pdf J Dairy Sci 69; 2386]</ref>
# Method of Liu et al. (2019). Please note that in 2022 the method of Liu et al. (2000)<ref name=":0">Liu, Z., R. Reents, F. Reinhardt and K. Kuwan. 2000. Approaches to Estimating Daily Yield from Single Milk Testing Schemes and Use of a.m.-p.m. Records in Test-Day Model Genetic Evaluation in Dairy Cattle. [https://www.journalofdairyscience.org/article/S0022-0302(00)75161-7/pdf J. Dairy Sci. 83:2672-2682].</ref> has been updated to the method of Liu et al. (2019). We recommend to organisations that currently have implemented the method of Liu et al. (2000)<ref name=":0" /> to update to method of Liu et al. (2019).
# Method of Kyntäjä et al. (2021)<ref name=":3">1. Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. [https://www.icar.org/Documents/technical_series/ICAR-Technical-Series-no-25-Virtual-Meeting/Kyntaja.pdf ICAR Technical Series no. 25: 171-175.]</ref>

2. Methods to estimate 24h yield from Automatic Milking Systems:

# Using data on more than one day (Lazenby et al., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Using data on 1 day (Bouloc et al., 2002)<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Estimation of fat and protein yield (Galesloot and Peeters, 2000)<ref>Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>
# Sampling period (Hand et al., 2004<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D.F. 2004. Comparison of Protocols to Estimate 24 Hour Percent Fat and Protein. Presented at 34th ICAR session, Sousse, Tunisia, June, 2004. Proceedings of the 34th ICAR Meeting EAAP Publication No. 113:219-224</ref>; Bouloc et al., 2004)

3. Standard methods to estimate 24h yield from electronic milk meters:

# Estimation of 24-hour milk yield
# Using data on more than one day (Hand et al., 2006)<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. [https://doi.org/10.3168/jds.S0022-0302(06)72240-8 J. Dairy Sci. 89:1723-1726]</ref>
# Estimation of 24-hour fat and protein yield

=== Standard methods for calculating accumulated yields ===
The ICAR approved methods are presented in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_2_%E2%80%93_Computing_of_Accumulated_Lactation_Yield Procedure 2 of Section 2]. They include:

# Test Interval Method (TIM) (Sargent, 1968)<ref>Sargent, F.D., V.H. Lyton, and O.G. Wall, Jr . 1968. Test interval method of calculating Dairy Herd Improvement Association records. [https://doi.org/10.3168/jds.S0022-0302(68)86943-7 J. Dairy Sci. 51:170].</ref>
# Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987)<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. [https://doi.org/10.1016/0301-6226(87)90049-2 Livest. Prod. Sci. 17:l].</ref>
# Best prediction (VanRaden, 1997)<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. [https://doi.org/10.3168/jds.S0022-0302(97)76268-4 J. Dairy Sci. 80:3015-3022].</ref>
# Multiple-Trait Procedure (MTP) (Schaeffer and Jamrozik, 1996)<ref>Schaeffer, L.R. and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. [https://doi.org/10.3168/jds.S0022-0302(96)76578-5 J. Dairy Sci. 79:2044-2055.]</ref>

=== Procedure to approve new methods ===

# All parties interested in seeking approval for any new accumulated yield calculation method will notify the ICAR Secretariat and provide a description of the proposed method.
# These parties will provide a detailed report including statistical details, scientific references and other relevant data to the ICAR Dairy Cattle Milk Recording Working Group.
# The ICAR Dairy Cattle Milk Recording Working Group will then consider the proposal and recommend that it be conditionally approved, approved or rejected.
# The final steps will consist of approval by the General Assembly and publication in the guidelines. .

== Reporting ==
This subsection covers reports, data files, statistics and calculated key figures provided to farmers for breeding and management purposes.

It is recommended that farmers are given reports after each recording and at the end of the recording year or another longer recording period. These reports should contain data on both cow and herd level. In bigger herds, it is also advisable to present results by management groups or otherwise chosen cow groups within the herd. The reporting may be done on paper, through web pages and/or in the form of data files or electronic reports.

Where data files are distributed or direct access given to the results in the database, care must be taken that data ownership is clearly defined. This also includes defining who has access to data and how this access can be authorised.

ICAR members are advised to prepare annual statistics in a reasonable timeframe after closing the recording year. The minimum data requirements are what is needed for the ICAR [https://my.icar.org/stats/list Dairy Cattle Yearly Enquiry on-line database].

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 5. Examples of key figures for herd to be used by farmers and other users.''
|- style="background-color:#efefef; text-align:center;"
|style="text-align:left |'''Key figure'''
|style="text-align:left |'''Explanation'''
|-
| style="text-align:left;" | 12-month rolling average yield
| style="text-align:center;" | Total milk, fat and protein produced during the 365 (366) days preceding the recording divided by the average number of cows for the same period.
|-
| style="text-align:left;" | Average 305-day yield
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations finished during the reporting period divided with the number of finished 305-day lactations.
|-
| style="text-align:left;" | Average 305-day yield within a period
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations during the reporting period divided with the average number of cows on a 305-day lactation within the reporting period.
|-
| style="text-align:left;" | Average annual yield
| style="text-align:center;" | Total milk, fat and protein produced during the recording year divided by the average number of cows for the same recording year.
|-
| style="text-align:left;" | Average calving interval
| style="text-align:center;" | The average preceding intervals of all calvings second and more during the reporting period.
|-
| style="text-align:left;" | Average fat, protein or lactose contents in milk
| style="text-align:center;" | Total fat, protein and lactose yields divided by the total milk yield, usually expressed with two decimals.
|-
| style="text-align:left;" | Average lactation yield
| style="text-align:center;" | Total milk, fat and protein produced within lactations of any length finished during the reporting period divided with the number of finished lactations.
|-
| style="text-align:left;" | Average lactation yield within a period
| style="text-align:center;" | Total milk, fat and protein produced during the reporting period divided with the average number of cows in milk within the reporting period.
|-
| style="text-align:left;" | Average number of cows
| style="text-align:center;" | Average number of cows in the herd (or group) on a given day during the reporting period. Usually expressed with one decimal.
|-
| style="text-align:left;" | Average somatic cell count
| style="text-align:center;" | The average of all individual cow somatic cell counts weighted for individual milk yields.
|-
| style="text-align:left;" | Daily milk, fat and protein yields
| style="text-align:center;" | 1) Total daily milk, fat and protein yields divided by number of cows, or 2) Total daily milk, fat and protein yields divided by number of cows in milk.
|-
| style="text-align:left;" | Energy Corrected Milk (ECM)
| style="text-align:center;" | Calculated according to a national standard.
Example from the Nordic countries:

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + milk yield, kg * 0.7832)/3.14

or, if lactose has been analysed

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + lactose yield * 16.54 + milk yield, kg * 0.0207)/3.14.

From solids expressed as %:

ECM = [(fat content, % * 383 + protein content, % * 242 + 783.2)/3140]* milk yield, kg

or, if lactose has been analysed

ECM = [(fat content, % * 383 + protein content, % * 242 + lactose content, % * 165.4 + 20.7)/3140]* milk yield, kg.
|-
| style="text-align:left;" | Number of lactations
| style="text-align:center;" | Total number of finished lactations in the herd (or group) during the reporting period.
|-
| style="text-align:left;" | Reporting period
| style="text-align:center;" | The period presented in the given report. The most usual options are: one day, one recording interval, lactation, rolling 365 days, recording or calendar year, and the cow’s lifetime.
|}
</center>

== Decisions ==

As a result of the recording process and reports prepared on the basis of its results, decisions can be made on one or more of the following:

=== Short term impact: day-to-day management decisions taken on farms ===

# Decisions about bulk milk quality.
# Feeding decisions - daily diet based on group or individual performance.
# Pasture management decisions.
# Grouping decisions - placing cows in different management or feeding groups.
# Culling decisions - decisions on the sale or slaughter of cattle.
# Mating decisions.
# Decisions regarding programmes of certification for milk and milk products.
# Decisions based on data flow from MRO’s to farms and vice versa.

=== Medium-term impact ===

# Farmers’ decisions based on advisory services, veterinarians, independent experts and other services.
# Decisions about production planning on farms (herd development).

=== Long-term impact ===
# Breeding programme and selection decisions - breeding partners informed by genetic evaluation ([[Section 09 – Dairy Cattle Genetic Evaluation|Section 9)]] based on milk recording results.
# Decisions based on herd book and breeder association activities and deciding on business actions related to breeding animals, i.e. in some countries animal recording data are required for international trade with breeding animals.

=== Strategic decisions ===
# Research programmes concerning management, recording and breeding.
# Political decisions about possible subsidies in dairy cattle breeding at the governmental level and implementing measurements according to agriculture policy.

== Quality control ==
This Section together with other parts of the Guidelines ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

=== Bulk tank data comparison ===
It is a recommended practice to compare milk recording data with dairy deliveries and bulk tank milk contents. This can be done on the recording day or over a longer period of time. The calculation is done as follows:

# Comparison ratio = Total recorded milk yield, kg /Total milk produced, kg. This comparison is used where there is a reliable estimate of the farm use of milk.
# Quick comparison ratio = Total recorded milk yield, kg/ Total milk delivered, kg. This comparison is used where farm use of milk is not estimated.
# Content comparison = Recorded average fat / Bulk tank average fat
# Comparison ratio for fat = Total recorded fat yield, kg/ Total fat produced, kg
# Total recorded milk yield, kg = Ʃ (Individual milk yield, kg)
# Total milk delivered, kg = Total milk delivered, litres * milk density kg/litre
# Total milk produced, kg = (Total milk delivered, litres + Milk used or discarded on the farm, litres) * milk density kg/litre
# Total fat produced, kg = Total milk produced, kg x (Bulk tank fat percent/100)
# Recorded average fat = Ʃ [Individual milk yield kg x (Individual fat percent/100)]/Ʃ (Individual milk yield, kg)

The recommended acceptable range for comparison ratios is 0.95 - 1.05, and for quick comparison ratios 0.90 - 1.00, with due regard to herd size.

=== One day bulk tank data comparison ===
Milk yields and fat yields or contents are compared on the recording day. Comparing the contents is routinely possible where every delivery is sampled or by taking a bulk tank sample (see point [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Bulk_tank_data_comparison 1.10] above for how the comparison is done.)

=== Bulk tank data comparison over a longer period ===
Milk yields and fat yields or contents are compared over a longer period of time, e.g. 4 months or 12 months. This option requires a routine to obtain the applicable data from the dairies or milk buyers. Farm use of milk may be taken into account where applicable.

=== Bulk tank sample ===
Bulk tank samples can be used to verify the milk contents analysis obtained in milk recording. A sample is taken from a well-mixed bulk tank on the recording day. It must represent the milk of the whole 24-hour period. Bulk tank fat and protein contents are then compared to the weighted averages of the fat and protein percent obtained from milk recording. Normally, the difference between the values should not be more than 5%.

=== Supervised or repeated recording ===
Supervised recording is a tool designed to verify that individual cow records are reliable. It is based on repeating the herd recording as soon as possible after the original recording, and the obtained results are compared with the original recording. It is obligatory for ICAR Certificate of Quality (CoQ) holders to practice regular supervision, irrespective of recording methods used.

It is recommended that the supervised recording will follow immediately after the original recording, but for a good reason it can be postponed for up to 7 days.

The farmer and any other staff doing the original recording must not know that a supervised recording will follow. The technician who performs the supervised recording should not be the same person who did the original recording.

Usually supervised recording is done by recording the whole herd again, using the same sampling scheme and recording method (or a reference method) as in the previous recording. When herd size exceeds 200 cows, it is also allowed to do a supervised recording to selected, or randomised groups of animals in the herd.

Choosing the herds for supervised recording may be random or based on preselection. Traits for this preselection may include high yield, great increase in yield, presence of bull dams in the herd, and general suspicions about the correctness of herd results.

The traits compared in supervised recording must include milk and fat. Comparing protein is also recommended.

=== Supervision - example of comparison calculations ===

# Milk, fat and protein yields per cow are calculated for both the original and the supervised milking.
# Individual cow records where results between supervised recording and the original recording differ outside the norms might be excused where a good explanation can be given for exclusion (illness, heat, missed milking)
# Deviations (%) are calculated for each cow and yield constituent according to the formula: deviation = (supervised yield/unsupervised yield)*100-100
# Herd averages of the absolute values for each yield constituent are calculated.
# If the supervised recording occurs within 2 days of the original recording, the acceptable difference in herd averages are 7% for milk and protein and 9% for fat.
# If the supervised recording occurs between 3 and 7 days after the original recording, the acceptable difference of the aforementioned herd averages are 9% for milk and protein and 12% for fat.

The limits mentioned in these examples are typically applied by some of the member organisations, and are not meant to be understood as exact norms. Such norms should be laid down by each member organisation.

=== Evaluation of recording data ===
It is recommended that data quality is evaluated for each herd recording day. When such an evaluation is applied, the following features of the data have to be included:

# Person responsible for the recording.
# ICAR approval and calibration status of the recording equipment if owned by the farmer.
# Number of herd recordings per time period and/or recording interval.
# Number of herd samplings per time period and/or sampling interval.

The following features are also recommended to be included if possible:

# Deviation of milk and fat yields from dairy deliveries.
# Deviation of milk and fat yields from previous or predicted yields.
# Standard deviation of individual cow records.
# Number of recorded and/or sampled milkings within the recording day.
# Number of cows missed or not recorded in the recording.
</div>
</div>
= Procedures =
== Procedure 1: Computing 24-hour Yields ==
<div class="mw-collapsible mw-collapsed">
<div>
=== Methods to calculate 24-hour yield for milk yield and fat percentage from a single milking ===

==== Method of Delorenzo & Wiggans (1986)<ref>Delorenzo, M.A. and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. J. Dairy Sci. 69: 2386-2394.</ref> ====
Daily milk (DMY) and fat yield (DFY) estimates are based on measured yield and milking frequency. An adjustment factor accounts for differences in the average milking interval (expressed in decimal hours) between the preceding milking and the measured milking, and the time of day of the measured milking (started in a.m. or p.m.). For 2X milking, an additional adjustment is applied to milk yield for the interaction between milking interval and stage of lactation, with mid lactation (158 DIM) set to zero. Milking interval does not affect protein and solids non fat (SNF) percentages and so the percentages for the sampled milking are used for test-day estimates. Protein yield is calculated from the measured percentage and the adjusted milk yield.

The prediction of DMY and DFY from single milking on morning or evening in herds milked twice a day requires factors, that are the reciprocal of the proportion of total yield expected from single milkings in relation to the milking interval.

We propose to derive these coefficients (intercept, slope, etc.) for each country separately.

===== Adjustment of milking interval =====
The milking interval is the interval between milking time for the observed milking and the milking time preceding the observed milking. The milking interval is divided into 15-minutes classes. Factors for milk and fat yields may be calculated to each class using Equation 1:

''Equation 1. Factors for milk and fat yields.''
[[File:Equation 1.png|none|thumb|397x397px]]

===== Adjustment of lactation stage =====
Because the lactation stage of the cow has an influence on the effect of different milking intervals on milk production a second adjustment is made for every interval class through a covariate of days in milk as addition:

Covariate x (days in milk - 158)

===== Estimating sample day yields =====
Formulas for prediction sample day yields and percentages in herds with two milkings are:

''Equation 2. Equation for predicting 24-hour milk yield.''
[[File:Equation2.png|none|thumb|428x428px]]

''Equation 3. Equation for predicting 24-hour fat percentage.''
[[File:Equation3.png|none|thumb|431x431px]]

''Equation 4. Equation for predicting 24-hour fat yield.''
[[File:Equation4.png|none|thumb]]

''Equation 5. Equation for predicting 24-hour protein yield.''
[[File:Equation5.png|none|thumb|316x316px]]

===== Calculation examples =====

====== Practical Application ======
Two sets of factors are available for estimating DMY from a single milking, each for morning or evening milking sampling. The factors are calculated from the formula as described above and given in Table 1.
<center>
{| class="wikitable"
| colspan="5" align="left" |'''''Table 1. Factor of milk yield and covariate for herds milked twice a day.'''''
|- style="background-color:#efefef;"
| rowspan="2" align="center" |'''Length of milking interval in hours (minutes in decimal)'''
| colspan="2" align="center" |'''Morning milking'''
| colspan="2" align="center" |'''Evening milking'''
|- style="background-color:#efefef;"
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
|-
| align="center" |< 9.00
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.594
| align="center" |0.00378
|-
| align="center" |9.00-9.24
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.534
| align="center" |0.00485
|-
| align="center" |9.25-9.49
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.477
| align="center" |0.00486
|-
| align="center" |9.50-9.74
| align="center" |2.411
| align="center" |0.00716
| align="center" |2.423
| align="center" |0.00511
|-
| align="center" |9.75-9.99
| align="center" |2.359
| align="center" |0.00726
| align="center" |2.370
| align="center" |0.00473
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |10.00-10.24
| align="center" |2.310
| align="center" |0.00458
| align="center" |2.321
| align="center" |0.00337
|-
| align="center" |10.25-10.49
| align="center" |2.262
| align="center" |0.00399
| align="center" |2.273
| align="center" |0.00214
|-
| align="center" |10.50-10.74
| align="center" |2.217
| align="center" |0.00294
| align="center" |2.227
| align="center" |0.00000
|-
| align="center" |10.75-10.99
| align="center" |2.173
| align="center" |0.00223
| align="center" |2.183
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |11.00-11.24
| align="center" |2.131
| align="center" |0.00000
| align="center" |2.140
| align="center" |0.00000
|-
| align="center" |11.25-11.49
| align="center" |2.091
| align="center" |0.00000
| align="center" |2.099
| align="center" |0.00000
|-
| align="center" |11.50-11.74
| align="center" |2.052
| align="center" |0.00000
| align="center" |2.060
| align="center" |0.00000
|-
| align="center" |11.75-11.99
| align="center" |2.014
| align="center" |0.00000
| align="center" |2.022
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |12.00
| align="center" |2.000
| align="center" |0.00000
| align="center" |2.000
| align="center" |0.00000
|-
| align="center" |12.01-12.24
| align="center" |1.978
| align="center" |0.00000
| align="center" |1.986
| align="center" |0.00000
|-
| align="center" |12.25-12.49
| align="center" |1.943
| align="center" |0.00000
| align="center" |1.951
| align="center" |0.00000
|-
| align="center" |12.50-12.74
| align="center" |1.910
| align="center" |0.00000
| align="center" |1.917
| align="center" |0.00000
|-
| align="center" |12.75-12.99
| align="center" |1.877
| align="center" |0.00000
| align="center" |1.884
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |13.00-13.24
| align="center" |1.846
| align="center" |0.00000
| align="center" |1.852
| align="center" |-0.00190
|-
| align="center" |13.25-13.49
| align="center" |1.815
| align="center" |0.00000
| align="center" |1.822
| align="center" |-0.00231
|-
| align="center" |13.50-13.74
| align="center" |1.786
| align="center" |-0.00167
| align="center" |1.792
| align="center" |-0.00308
|-
| align="center" |13.75-13.99
| align="center" |1.757
| align="center" |-0.00258
| align="center" |1.763
| align="center" |-0.00339
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |14.00-14.24
| align="center" |1.730
| align="center" |-0.00347
| align="center" |1.736
| align="center" |-0.00509
|-
| align="center" |14.25-14.49
| align="center" |1.703
| align="center" |-0.00363
| align="center" |1.709
| align="center" |-0.00471
|-
| align="center" |14.50-14.74
| align="center" |1.677
| align="center" |-0.00332
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |14.75-14.99
| align="center" |1.652
| align="center" |-0.00316
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |≥ 15.00
| align="center" |1.628
| align="center" |-0.00235
| align="center" |1.683
| align="center" |-0.00454
|}
</center>

For estimating daily fat percentage there is only one table independent of morning or evening sampling – refer to Table 2.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" |'''''Table 2. Factor of fat percentage for herds milked twice a day.'''''
|- style="background-color:#efefef;"
|'''Length of milking'''

'''interval in hours'''
|'''Fat (percentage'''

'''factor)'''
|-
|< 9.00
|0.919
|-
|9.00-9.24
|0.927
|-
|9.25-9.49
|0.934
|-
|9.50-9.74
|0.941
|-
|9.75-9.99
|0.948
|-
|
|
|-
|10.00-10.24
|0.955
|-
|10.25-10.49
|0.961
|-
|10.50-10.74
|0.968
|-
|10.75-10.99
|0.974
|-
|
|
|-
|11.00-11.24
|0.980
|-
|11.25-11.49
|0.986
|-
|11.50-11.74
|0.992
|-
|11.75-11.99
|0.997
|-
|
|
|-
|12.00
|1.000
|-
|12.01-12.24
|1.003
|-
|12.25-12.49
|1.008
|-
|12.50-12.74
|1.013
|-
|12.75-12.99
|1.018
|-
|
|
|-
|13.00-13.24
|1.023
|-
|13.25-13.49
|1.028
|-
|13.50-13.74
|1.033
|-
|13.75-13.99
|1.037
|-
|
|
|-
|14.00-14.24
|1.042
|-
|14.25-14.49
|1.046
|-
|14.50-14.74
|1.050
|-
|14.75-14.99
|1.054
|-
|≥ 15.00
|1.058
|}
</center>

Milking-interval factors are calculated using Equation 1, where the intercept and slope are as in Table 3.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 3. Slope and intercept for milk yield and fat yield.'''''
|- style="background-color:#efefef;"
| rowspan="2" |'''Trait'''
| colspan="2" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started in a.m.'''
|'''For measured milking started in p.m.'''
|-
|Milk yield
|0.0654
|0.0634
|0.0363
|-
|Fat yield
|0.1965
|0.1939
|0.0254
|}
</center>
The milking interval has no significant influence on protein percentage. Therefore, the protein percentage of the sampled milking is used as the daily protein percentage.

====== Calculation of daily yields from morning milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Data for a cow from morning milking.'''''
|-
|Begin of recording:
|6:15
|(Morning milking)
|-
|Start of preceding milking:
|17:25
|
|-
|Length of milking interval:
|12 hours 50 minutes
|(Expressed as decimal 12.83)
|-
|Milk results at morning:
|12,0
|Milk-kg
|-
|
|4,12
|Fat-percentage
|-
|
|3,45
|Protein-percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 5. Factors for morning milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.877
|-
|The covariate is
|0
|-
|The factor for fat percentage from Table 2 is
|1.018
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 6. Example calculations for morning milking.'''''
|-
|The sample-day milk yield:
|1.877 x 12,0 kg + 0 x (120 - 158) = 22,5 kg
|-
|The sample-day fat percentage:
|1.018 x 4,12 = 4,19
|-
|The sample-day fat yield:
|22,5 kg x 0,0419 = 0,94 kg
|-
|The sample-day protein yield:
|22,5 kg x 0,0345 = 0,78 kg
|}
</center>

====== Calculation of daily yields from evening milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 7. Data for a cow from evening milking.'''''
|-
|Begin of recording:
|16:48
|Evening milking
|-
|Start of preceding milking:
|6:35
|
|-
|Length of milking interval:
|13 hours 47 minutes
|Expressed as decimal 13.78
|-
|Milk results at evening:
|14,0
|Milk kg
|-
|
|4,00
|Fat percentage
|-
|
|3,40
|Protein percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 8. Factors for evening milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.763
|-
|The covariate is
|<nowiki>-0,00339</nowiki>
|-
|The factor for fat percentage from Table 2 is
|1.037
|}
{| class="wikitable"
| colspan="2" |'''''Table 9. Example calculations for evening milking.'''''
|-
|The sample-day milk yield:
|1.763 x 14,0 kg - 0,00339 x (120 - 158) = 24,8 kg
|-
|The sample-day fat percentage:
|1.037 x 4,00 = 4,15
|-
|The sample-day fat yield:
|24,8 kg x 0,0415 = 1,03 kg
|-
|The sample-day protein yield:
|24,8 kg x 0,0340 = 0,84 kg
|}
</center>

====== Alternate recording of components and milk yield at both milkings ======
For this plan only the sample-day fat yield has to be calculated with regard to milking interval. The milk yield is the sum of evening and morning milk results.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 10. Example data for a cow from both milkings.'''''
|-
|Begin of recording evening:
|17:25
|
|-
|Milk results at evening:
|10:00
|Milk kg (only milking-yield)
|-
|Begin of recording morning:
|6:15
|
|-
|Milk results at morning:
|12:00
|Milk kg
|-
|
|4:20
|Fat percentage
|-
|
|3:50
|Protein percentage
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 11. Factor for fat percentage.'''''
|-
|Length of milking interval:
|12 hours 50 minutes (expressed

as decimal 12.83)
|-
|The factor for fat percentage from Table 2 is
|1.018.
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 12. Example calculation of daily yields.'''''
|-
|The sample-day milk yield:
|10,0 kg + 12,0 kg = 22,0 kg
|-
|The sample-day fat percentage:
|1.018 x 4,20 = 4,28
|-
|The sample-day fat yield:
|22,0 kg x 0,0428 = 0,94 kg
|-
|The sample-day protein yield:
|22,0 kg x 0,0350 = 0,77 kg
|}
</center>

====== Calculation for 3X Milking ======
For 3X herds, a single milking or two consecutive milkings may be weighed. The sample may be collected at one or both of these milkings. Stage of lactation × milking interval adjustments are not used for greater than 2× milking. These AM/PM factors for estimating daily yields in 3X herds should not be confused with factors that adjust 3X records to a 2X basis. Milking-interval factors are calculated using the same formula with the intercept and slope as in Table 13.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" align = "left" |'''''Table 13. Slope and intercept factors for 3X milking.'''''
|- style="background-color:#efefef;"
| rowspan="2" | '''Trait'''
| colspan="3" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started between 2 a.m. and 9:59 a.m.'''
|'''For measured milking started between 10 a.m. and 5:59 p.m.'''
|'''For measured milking started between 6:00 p.m. and 1:59 a.m.'''
|-
|Milk yield
|0.077
|0.068
|0.066
|0.0329
|-
|Fat yield
|0.186
|0.186
|0.182
|0.0186
|}
</center>
When two milkings are included for sampling, the intercepts and intervals for both milkings are included in determining a factor for calculated estimated milk yield that is applied to the total yield from both milkings as in Equation 6.

''Equation 6. Milking interval factor for 3X milking.''
[[File:Equation6.png|none|thumb|536x536px]]
Milk and fat percent factors are calculated separately based on the number of milkings weighed or sampled.

====== Calculation for 4X - 6X Milking ======
The intercept terms for calculating 3X factors (0.077, 0.068, and 0.066) are multiplied by the factor [3 / (milkings per day)] for use in calculating factors for milking frequencies greater than 3X.

==== Method of Liu et al. (2019) ====
A multiple regression method (MRM) is used for estimating 24-hour daily milk yield (DMY), daily fat yield (DFY) and daily protein yield (DPY) based on partial yields from either morning (AM) or evening (PM) milking. Fat percentage (DFP) or protein percentage (DPP) on a 24-hour daily basis are then derived using the estimated 24-hour daily yields. The MRM can be used as a reference method for estimating daily yields and component percentages.

The method of Liu et al. (2019) is an updated version of the method of Liu et al. (2000). The model is only used for farms with 2 time milkings during 24 hours.

The following formula is used to estimate DMY, DFY, DPY based on partial yields (PMY, PFY,PPY) from either morning (AM) or evening (PM) milking:

''Equation 7. Model for predicting 24-hour yield.''

''yijk = a + bijk * xijk''

where:

yijk is the estimated 24-hour daily yield (DMY, DFY or DPY);

xijk is AM or PM partial daily yield on a test day (PMY, PFY, or PPY).

Subscript '''''i''''' represents class of parity effect with 2 levels: first and higher parities.

Subscript '''''j''''' represents class of length of preceding milking interval with 8 levels for AM milking: < 720 minutes, < 740 minutes, < 760 minutes, < 780 minutes, < 800 minutes, < 820 minutes, < 840 minutes, >= 840 minutes and 8 levels for PM milking: < 600 minutes, < 620 minutes, < 640 minutes, < 660 minutes, < 680 minutes, < 700 minutes, < 720 minutes, >= 720 minutes.

Subscript '''''k''''' represents class of lactation stage with 7 classes: < 60 days, < 120 days, < 180 days, < 240 days, < 300 days, < 360 days, >= 360 days.

'''''a''''' is the estimated intercept for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

'''''b'''''ijk is the estimated slope for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

The factors for '''''a''''' and '''''b'''''ijk can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Appendix_1_-_Adjustment_factors_to_calculate_24-hour_yields_using_the_Liu_method Appendix 1].

For a given yield trait a total number of 112 formulae are to be estimated for calculating 24-hour daily yield based on partial yield from either AM or PM milking. Component percentage for fat (DFP) and protein (DPP), on a 24-hour basis is calculated by dividing estimated fat or protein yield by estimated daily milk yield:[[File:Imagefinal.png|center|thumb|339x339px]]

===== Calculation example with method of Liu et al. (2019) =====
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" align = "left" |'''''Table 14. Data from an evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="6" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="6" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="6" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow'''

'''ID'''
|'''Calving date'''
|'''Lactation number'''
| colspan="2" |'''Milk yield (kg)'''
|'''Fat content (%)'''
|'''Protein content (%)'''
|'''Fat yield (kg)'''
|'''Protein yield (kg)'''
|'''Index1'''
|-
|A
|01.01.2020
|1
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1132
|-
|B
|01.01.2020
|2
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1232
|-
|C
|27.03.2020
|1
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1131
|-
|D
|27.03.2020
|2
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1231
|-
|
|
|
|
|
|
|
|
|
|
|}
'''1''' Index is marked in the Appendix table.
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 15. Calculation of 24-hour daily yield and components for evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="3" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="3" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="3" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow ID'''
|'''DMY (kg)'''
|'''DFY (kg)'''
| colspan="2" |'''DPY (kg)'''
|'''DFP (%)'''
|'''DPP (%)'''
|-
|A
|3,47396+25,0

<nowiki>*</nowiki> 1,98268 = 53,0401 ≈ '''53,0'''
|0,2135+0,995

<nowiki>*</nowiki> 1,68050 = 1,8855975
| colspan="2" |0,10471+0,8325* 1,99092 = 1,7621509
|1,8855975 / 53,04096*100

≈ '''3,55'''
|1,7621509 / 53,04096*100

≈ '''3,32'''
|-
|B
|4,15080+25,0* 1,98520 = 53,7808 ≈ '''53,8'''
|0,3635+0,995

<nowiki>*</nowiki> 1,47515 = 1,8312743
| colspan="2" |0,13952+0,8325* 1,97074 = 1,7801611
|1,8312743 / 53,7808*100

≈ '''3,41'''
|1,7801611 / 53,7808*100

≈ '''3,31'''
|-
|C
|2,80244+33,1

<nowiki>*</nowiki> 2,02183 = 69,72501 ≈ '''69,7'''
|0,17663+1,3339 * 1,72438 = 2,4767805
| colspan="2" |0,11078+1,1122 * 1,96422 = 2,2953855
|2,4767805 / 69,725013*100

≈ '''3,55'''
|2,2953855 / 69,725013*100

≈ '''3,29'''
|-
|D
|3,85525+33,1 * 2,00429 = 70,19725 ≈ '''70,2'''
|0,27991+1,3339 * 1,62403 = 2,4462036
| colspan="2" |0,12863+1,1122* 1,98973 = 2,3416077
|2,4462036 / 70,7197249*100 ≈ '''3,48'''
|2,3416077 / 70,7197249*100 ≈ '''''3,34'''''
|-
|
|
|
|
|
|
|
|}
</center>
'''Note''' that intercepts and slopes of the applied regression formulae are underscored.

===== Fat correction for equal measure sampling =====
With Equal measure sampling, it is advisable to use Equation 8 (or the like) to correct fat contents:

Equation 8. Fat correction for equal measure sampling.

Fat, % = Analysed fat, % + 0.69 – 1.3 x (morning milk/ 24-hour milk)

The relation of morning milk to 24-hour milk is to be calculated to at least four decimals.

==== 1.1 Method of Kyntäjä & Nokka (2021)<ref name=":3" />: 24-hour correction factors for fat percentage ====
This method can be applied to calculate 24-hour correction factors for fat percentage, in case the milk recording is based on two milkings, with at least one known milk yield and one sample. A 24-hour recording day is assumed.

The conventional way to calculate correction factors is based on a data set where all milkings have been recorded and analysed separately. This approach requires a lot of effort and extra analysis, and is not cheap to organise. Organisations that have access to a large number of records may be able to use those data to calculate correction factors even if they have no extra analysis.

Requirements for the data set:

# The data set has to be large enough. Every single factor needs to be based on at least 10,000 or, even better, 100,000 observations.
# Each individual data set must contain at least one preceding milking interval, milk weight, and analysed sample. If it contains more milk weights, intervals etc. that is even better. It is also good to include breed, lactation number, days in milk and other data that may have an effect on the factors.

===== Calculation example of the method of Kyntäjä & Nokka (2021)<ref>Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. ICAR Technical Series no. 25: 171-175.</ref> =====

====== The accumulated data set ======
Since 2003, Finland had accumulated a data set of 7.5 million recordings with data on the time of the sampled and preceding milking as reported by the farmer, the lab analysis results, and the 24-hour milk yield. Grouped according to the preceding interval, the analysed fat content gives a nice sigmoid curve with the highest fat content found after a 540 to 630 minutes’ interval (9 to 10.5 hours) and the lowest at 810 to 930 minutes (13.5 to 15.5 hours).
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 16. Average analysed milk fat percentage by preceding interval class, 2003 – 2020.'''''
|- style="background-color:#efefef;"
|'''Interval before'''

'''Sampling (minutes)'''
|'''Number of samples'''
|'''Median interval in the class'''
|'''Average fat content analysed (%)'''
|-
|<510
|93,577
|495
|4.20
|-
|510-539
|19,523
|525
|4.70
|-
|540-569
|111,268
|555
|4.79
|-
|570-599
|253,807
|585
|4.83
|-
|600-629
|1,461,587
|615
|4.75
|-
|630-659
|919,968
|645
|4.66
|-
|660-689
|1,168,683
|675
|4.56
|-
|690-719
|223,877
|705
|4.42
|-
|720-749
|517,447
|735
|4.28
|-
|750-779
|212,428
|765
|4.16
|-
|780-809
|924,014
|795
|4.12
|-
|810-839
|698,463
|825
|4.09
|-
|840-869
|1,104,778
|855
|4.07
|-
|870-899
|154,561
|885
|4.05
|-
|900-929
|77,024
|915
|4.07
|-
|>929
|26,977
|945
|4.13
|}
</center>

The results were also divided into subgroups according to lactation number, phase of lactation, and breed. The effect of the preceding milk interval on milk fat seems to be bigger with older cows and in the beginning of lactation. It was also bigger with Ayrshire cows as compared with Holsteins. At this point, however, the decision was made not to take these factors into account when calculating new correction factors.

====== Calculation of new factors ======
The results above were turned into a simple set of correction factors, dependent solely on the preceding interval. In order to do this, two assumptions were made:

# A 24-hour recording day was assumed. This way, we can deduce the second milking interval from the one we know and mirror the fat percent for that milking.
# Milk secretion rate was assumed to be constant around the 24-hour period. This allows us to deduce the share of the 24-hour yield produced at each milking.

These assumptions allow us to create the new correction factors by mirroring the milk yield and milk fat content in the milking whose actual data we have not got. This way, we get the following formula:

Equation 9. Correction factor.
[[File:Equation9.png|none|thumb|545x545px]]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left" |'''''Table 17. Calculation of the mirrored milking and the correction factors'''''
|- style="background-color:#efefef;"
|'''Interval before sampling (minutes)'''
|'''Average fat in the sampled milking (%)'''
|'''Share of 24-hour milk in the sampled milking'''
|'''Mirrored interval (minutes)'''
|'''Average fat in the mirrored milking (%)'''
|'''Calculated 24-hour average fat(%)'''
|'''Correction factor'''
|-
|<510
|4.21
|0.34
|>929
|4.14
|4.16
|0.989
|-
|510-539
|4.77
|0.36
|900-929
|4.08
|4.33
|0.907
|-
|540-569
|4.82
|0.39
|870-899
|4.05
|4.35
|0.903
|-
|570-599
|4.84
|0.41
|840-869
|4.07
|4.38
|0.906
|-
|600-629
|4.76
|0.43
|810-839
|4.09
|4.37
|0.919
|-
|630-659
|4.66
|0.45
|780-809
|4.12
|4.36
|0.936
|-
|660-689
|4.56
|0.47
|750-779
|4.16
|4.35
|0.953
|-
|690-719
|4.43
|0.49
|720-749
|4.29
|4.36
|0.984
|-
|720-749
|4.29
|0.51
|690-719
|4.43
|4.36
|1.016
|-
|750-779
|4.16
|0.53
|660-689
|4.56
|4.35
|1.046
|-
|780-809
|4.12
|0.55
|630-659
|4.66
|4.36
|1.059
|-
|810-839
|4.09
|0.57
|600-629
|4.76
|4.37
|1.070
|-
|840-869
|4.07
|0.59
|570-599
|4.84
|4.38
|1.076
|-
|870-899
|4.05
|0.61
|540-569
|4.82
|4.35
|1.073
|-
|900-929
|4.08
|0.64
|510-539
|4.77
|4.33
|1.062
|-
|>929
|4.14
|0.66
|<510
|4.21
|4.16
|1.006
|}
</center>

=== Methods to calculate 24-hour yields in Automatic Milking Systems ===

==== General remarks about calculation of 24-hour milk yield ====
It is characteristic for AMS systems that individual cows set their own milking rhythm, thus making it largely irrelevant to use the traditional model of measuring milk yields and sampling at all milkings in the herd during the recording day. In order to determine how much an individual cow’s real 24-hour milk, fat and protein yield is, more complex calculations are required, especially with milk fat that varies considerably from milking to milking. For protein content and cell counts, no correction is needed for a one-milking sample.

The basic idea with calculating a 24-hour milk yield from AMS data is that milk yields per milking are converted into milk yield per time unit (minute or hour) during the preceding interval. This milk yield per time unit is then converted into milk yield in 24 hours. In order to do this, the data set must also contain time stamps for each milking.

How many milkings or how long a measurement period is used for creating 24-hour yields depends on the milk recording organisation. The fewer milkings are used the more random variance there will be in the individual cow milk yields. The absolute minimum is two milkings with preceding intervals, while a measuring period of 96 hours is recommended.

The sampled milking must always be inside the milk yield measurement period. For the calculation of fat and protein yields, it is recommended to use only those milk yields that are from the same period or day. With Z sampling, the 24-hour fat and protein yields may be calculated based on a shorter measurement period than what is used for calculating the 24-hour milk yields.

==== Calculation of milk yield using data of several days (Lazenby ''et al''., 2002<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Automatic Milking Systems (AMS). The average of most recent milk weights can be calculated using a number of preceding milkings or a number of preceding days. If number of milkings is used, the optimal estimate of the milking rate is obtained using an average of current milking together with the 12 most recent milkings back in time. The optimal estimate is the maximum value of the difference curve at which the correlation with the ‘true’ 24-hour milk yield is greatest and the variance across milkings is minimized. If number of days is used, the optimal estimate of the milking rate is obtained using an average of all milkings occurred in the last 96 hours (4 most recent days). In Table 18 the percent of maximum difference for various number of milkings and days is reported. The optimal estimate is independent from stage of lactation and parity.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 18. Percent maximum for different number of days and milkings.'''''
|- style="background-color:#efefef;"
|'''Days'''
|'''Percent Max.'''
|'''Current milking'''

'''+ most recent milkings'''
|'''Percent max.'''
|-
|1
|49.38
|10
|97.85
|-
|2
|77.26
|11
|99.08
|-
|3
|92.34
|12
|99.70
|-
|4
|98.91
|13
|99.81
|-
|5
|98.50
|14
|99.40
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table19.png|center|thumb|911x911px]]
Therefore, 24-hour yield estimation using most recent milkings (1+12) is computed using Equation 10.

''Equation 10. 24-hour yield estimation using 12 previous milkings from AMS.''
[[File:Equation10.png|none|thumb|527x527px]]
and, 24-hour yield estimation using all milkings occurred in the last 96 hours (most recent 4 days), all milking in the last 4 days are included is computed using Equation 11.

''Equation 11. 24 hours yield estimation using milkings from the last 96 hours from AMS''
[[File:Equation11.png|none|thumb|534x534px]]

===== Advantages and disadvantages of this method =====
In terms of Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between milk weights and contents may arise if contents are recorded on one day only. Moreover, some cows may begin or finish their lactation during the period of recording. In this case the computation of milk yield must be adapted. The number of data that need to be validated is higher (for instance, contents have short interval between two milkings).

==== Calculation of milk yield using data on 1 day (Bouloc ''et al''., 2002<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
When the number of milkings is reduced to milkings obtained during one day only, the accuracy of the estimation of the true performance is the same as classical milk recording methods with the same interval between two test days. For instance, Milk Yield estimated from all the milkings recorded during 24 hours, and with an interval between two test days of four weeks has the same accuracy as A4.

==== Calculation of fat and protein yield (Galesloot & Peeters, 2000<ref name=":1" />) ====
Calculation of fat and protein percent must be based on milk weights at time of sampling. The 24-hour protein percentage can be predicted by the protein percentage of the sample without adjustment. However, the 24-hour fat percentage is more difficult to predict, as levels of fat percent are inversely proportional to the amount of milk yield. It is important then to have a close connection between time of samples and actual milk yields.

The Peeters and Galesloot method is a multiple linear regression model for estimating 24-hour fat percent and yields from one-sampled milking during the AMS sampling period. Six different statistical models were tested. This method takes into account fat percent, protein percent, milk weight and milking interval of the sampled milking, milking interval and milk weight of the previous milking (simple model). Another model, based on six different classification of variables (Ca - Cf) such as, time of sampled milking, interval preceding the sampled milking, ratio of fat to protein percent, parity, lactation stage, can be applied (complex model).

===== Simple model =====
24-hour Fat% = b0 + b1* Fat%(n) + b2* Prot%(n) + b3* Int(n) + b4* Int(n-1) + b5* Milk(n) + b6* Milk (n-1) + e

b0= Intercept, b1 to b6 = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, e = Residual effect.

===== Complex model =====
24-hour Fat%i = b0i + b1i* Fat%(n) + b2i* Prot%(n) + b3i* Int(n) + b4i* Int(n-1) + b5i* Milk(n) + b6i* Milk(n-1) + ei

b0i = Intercept, b1i to b6i = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, ei = Residual effect

i = subclass of classification for class variables Cx for x = a, b, c, d, e, f

Ca = Day Time of sampled milking (h) 0-5.59, 6.00-11.59, 12.00-17.59, 18.00-23.59

Cb = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440

Cc = Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

Cd = Parity 1, 2, ≥ 3

Ce = Lactation stage 1-99, 100-199, ≥200

Cf = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440 and Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

The best prediction of 24-hour fat percent and 24-hour fat yields from this method, includes fat percent, protein percent, milk weight and milking interval of the sampled milking, milk weight and milking interval of the preceding milking and the interaction between milking interval, the ratio of fat to protein percent of the sampled milking (complex model corresponding to Cf classification).

The Peeters and Galesloot method has been updated by Roelofs et al. (2006)<ref>Peeters, R. and P. J. B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. J Dairy Sci. 85:682-688.</ref>. The Roelofs method is described in [[Section 02 – Cattle Milk Recording#Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme|Appendix 2]] of this Section.

N.B. This method has been developed by CRV. CRV has available a set of parameters, estimated with this method. For more information about costs and advice on application of this method, please contact CRV. ICAR has no benefit from the application of this method or any other method described in these guidelines.

==== Calculation example of 24-hour fat and protein yields with sampling scheme M ====
With this method, all milkings in a 24-hour recording period must be sampled. The obtained separate analysis results are then used to compute a 24-hour yield of milk solids, and a weighted average of their content.

Individual milkings (last 96 hours) and recording day contents:
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left" |'''''Table 20. Calculation of 24-hour fat and protein contents with sampling scheme M.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY/MM/DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat%'''
|'''Protein%'''
|-
|1
|2021/09/09
|20:45
|525
|13.7
|26.1
|
|
|-
|2
|2021/09/10
|5:30
|617
|16.0
|25.9
|
|
|-
|3
|2021/09/10
|15:47
|720
|18.7
|26.0
|
|
|-
|4
|2021/09/11
|3:25
|645
|16.8
|26.0
|
|
|-
|5
|2021/09/11
|14:10
|899
|18.3
|20.3
|
|
|-
|6
|2021/09/11
|23:27
|557
|14.6
|26.2
|
|
|-
|7
|2021/09/12
|10:51
|684
|17.4
|25.4
|4.53
|3.17
|-
|8
|2021/09/12
|19:44
|533
|14.1
|26.5
|4.92
|3.18
|-
|9
|2021/09/13
|1:35
|351
|9.9
|28.2
|5.92
|3.07
|}
</center>

For example, calculation of fat% on recording day:

24-hour Fat% = (9.9 kg milk x 5.92% fat + 14.1 kg milk x 4.92 % fat + 17.4 kg milk x 4.53 % fat) / (9.9 + 14.1 + 17.4) kg milk = 5.00 %

To calculate the 24-hour fat yield, the calculated 24-hour milk yield is multiplied by the fat content thus obtained (5.00 %).

The same method is used for protein, somatic cell count, urea, lactose and other milk constituents.

Estimation of milk contents: It is recommended to set the robot not to take samples if the preceding milking of the individual cow is not more than 4 hours earlier. If such milkings occur the milk sampled from them is not suitable for 24-hour fat calculation.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left"|'''''Table 21. Calculation of 24-hour fat and protein contents with sampling scheme M where one milking interval was shorter than 4 hours.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY-MM-DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat %'''
|'''Protein%'''
|-
|1
|2021/11/12
|20:05
|590
|15.4
|26.4
|
|
|-
|2
|2021/11/13
|6:31
|626
|16.3
|26.0
|
|
|-
|3
|2021/11/13
|17:12
|641
|17.1
|26.7
|
|
|-
|4
|2021/11/14
|4:40
|688
|17.5
|25.4
|
|
|-
|5
|2021/11/14
|15:11
|631
|16.4
|26.0
|
|
|-
|6
|2021/11/15
|2:25
|674
|16.5
|24.5
|
|
|-
|7
|2021/11/15
|9:47
|452
|10.8
|23.9
|
|
|-
|8
|2021/11/15
|18:30
|523
|13.6
|26.0
|4.71
|3.36
|-
|9
|2021/11/15
|21:15
|165
|3.1
|18.8
|5.161
|3.481
|-
|10
|2021/11/16
|7:49
|634
|16.5
|26.0
|4.47
|3.21
|}
1 Time between two consecutive milkings shorter than 4 hours, data not taken into account for calculation of milk contents.
</center>

Calculation of the fat content of milk during the recording day:

24-hour Fat% = (16.5 kg milk x 4.47 % fat + 13.6 kg milk x 4.71 % fat) / (16.5 kg + 13.6 kg) = 4.57 %

The same method is used for protein, somatic cells, urea, lactose and other milk constituents.

=== Methods to calculate 24-hour yields from electronic milk meters ===

==== Using data on more than one day (Hand ''et al''., 2006<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. J. Dairy Sci. 89:1723–1726.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Electronic Milk Meters. The average of most recent milk weights can be calculated using a number of preceding days. Table 22 reports the concordance correlations for a range of multiple-day averages. As soon as at least the 3 preceding days are used in the calculation, the concordance correlation reaches a high value of at least 0.981. There are no significant differences between 3, 4, 5, 6 and 7-day averages. The correlations are independent from stage of lactation and parity. Thus, 24-hour yields can be the average of from 3 to 7 daily milkings previous to the test day when fat and protein samples were taken.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 22. Concordance correlations for different multiple-day averages.'''''
|- style="background-color:#efefef;"
|'''Multiple-day average'''
|'''Concordance correlation'''
|-
|1
|0.957
|-
|2
|0.975
|-
|3
|0.981
|-
|4
|0.981
|-
|5
|0.982
|-
|6
|0.981
|-
|7
|0.981
|-
|10
|0.979
|-
|14
|0.977
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table20.png|center|thumb|923x923px]]

Therefore, 24-hour yield estimation averaging over 5 days is given by Equation 12.

''Equation 12. 24-hour yield estimation averaging over 5 days.''
[[File:Equation12.png|center|thumb|601x601px]]

===== Advantages and disadvantages of this method =====
Concerning Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between Milk weights and contents have been shown. The estimation bias increases proportionally to the number of days use to compute the 24-hour average. Thus, this method is recommended only if milk weight is the only variable of interest. If milk contents are of interest then the milk weight should be calculated using the milkings from the same day of sampling.

==== Estimation of 24-hour fat and protein yield ====
Fat and protein yields should be determined from the 24-hour yield on the day of sampling, and not the averaged value.

=== Calculation of daily fat percentage from single samples by Gerke et al., 2025 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Gerke.xlsx here]

Constant access to the automatic milking system (AMS) leads to varying milking frequency of cows and subsequently varying milking interval lengths (MI) and milk yield (MY) of single milkings. This influences milk production and can result in variable milk composition in individual milkings during the day. Therefore, the fat percentage from one sampled milking must be adjusted before it can be used as a daily value. The method described specifies the data required and the calculation procedure for deriving a corrected 24 h milk fat percentage from a single sample on test day (TD) in AMS herds.

==== Model specification ====
The multiple linear regression includes transformation, interaction, and polynomial parameters to model non-linearity and thereby improve prediction accuracy. Beside F% of a single milking (''m'') on TD, the model focused on lactation characteristics and milk recording data of up to 4 preceding milkings. With milking intervals ranging between 4 and 20 hours, the method can be applied to milk recording samples from cows with 2 or 3 milkings whose milking intervals lengths (MI) before sampling accumulate to less than 24 h.

The functional form of the model described below specifies the data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample:[[File:Image A.png|center|thumb|636x636px|'''Data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample''']]
</div>where:

DF% = estimated 24 h fat percentage on TD

''m'' = sampled milking on TD

''m-x'' = x milkings before the milking where the sample was taken (x: 1-3)

F% = fat percentage of the sampled milking ''m''

MY(''m'') = milk yield (kg) of ''m''

MI(''m'') = length of time interval (min) preceding the sampled milking ''m''

MY(''m''-x) = milk yields of the 1-3 preceding milkings of ''m''

MI(''m''-x) = milking interval length corresponding to MY(''m''-x)

DIM = days in milk on TD ranging between 5 and 330 d

Parity = parity class (e.g primiparous = 1 and multiparous = 0)

Daytime = time-of-day group of ''m'' (e.g. morning/noon/evening)

e = residual error

The method and its implementation are described in detail by Gerke et al. (2025).

==== Calculation and examples ====
The mathematical notation, with the corresponding regression coefficients in Table 1 for calculating the daily fat percentage (DF%):[[File:Calculating the daily fat percentage (DF%).jpg|center|Calculating the daily fat percentage (DF%)|thumb|511x511px]][[File:Calculating the daily fat percentage (DF%) 2.jpg|center|frame|'''Table 1. Coefficients for regression formula.''']]
</div>
[[File:Example data required for estimating 24 h fat percentage (DF%).jpg|alt=Example data required for estimating 24 h fat percentage (DF%)|center|frame|'''Table 2.''' '''Example data required for estimating 24 h fat percentage (DF%)''']]
Based on the data assembled on TD (Table 2), the corrected 24 h fat percentage (DF%) can be calculated using the mathematical formula und its corresponding coefficients listed in Table 1 as shown in the following examples:
[[File:Corrected 24 h fat percentage.jpg|alt=Corrected 24 h fat percentage|center|thumb|661x661px|'''Corrected 24 h fat percentage''']]

=== Reference ===
Gerke, J. S., Kammer, M., Werner, A., Köstler, R., Piepenburg, J., Mayerhofer, M., … Duda, J. (2025). Estimating daily fat percentage from single samples in herds with automatic milking system using a regression model. ''Livestock Science'', ''293'', 105649. doi: 10.1016/j.livsci.2025.105649

=== Calculation of daily fat percentage from single samples by Jenko et al., 2008, 2010 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Jenko.xlsx here]

This method estimates daily milk yield (DMY), daily fat yield (DFY), and daily protein yield (DPY) in the alternate one-milking recording (T) scheme. Daily fat percentage (DFP) and daily protein percentage (DPP) are then derived from the daily yield (DY) estimates. Utilizing this method allows us to remove the risk of underestimating high and overestimating low DY and contents.

The following formula is used to estimate the DY from the partial yield (PY) and the estimated PY/DY ratio (y):

DY=PYi/yi

where the subscript i is either morning (a.m.) or evening (p.m.).

The value of y is calculated based on the milking interval in minutes (MI), estimated intercept (µ) and regression coefficients (b1 and b2) for yield traits in a.m. or p.m. milking using the following equations for DMY and DPY:

'''Equation 1. Model for milk yield and protein yield.'''

yi = µ + b1 × MI

and for DFY

'''Equation 2. Model for fat yield.'''

yi = µ + b1 × MI + b2 × MI2

The intercept and regression coefficients can be either estimated from the data with records from both a.m. and p.m. milking or the estimates from Table 1 can be applied.

'''Table 1. Intercept and regression coefficients for calculation of daily yield.'''
{| class="wikitable"
|'''Daily yield'''
|'''Milking'''
|'''µ'''
|'''b1'''
|'''b2'''
|-
|DMY
|a.m.
|0,1081000000
|0,0005503000
|
|-
|
|p.m.
|0,0884200000
|0,0005683000
|
|-
|DPY
|a.m.
|0,1124000000
|0,0005419000
|
|-
|
|p.m.
|0,0966400000
|0,0005593000
|
|-
|DFY .
|a.m.
|0,5903000000
|<nowiki>-0,0005093000</nowiki>
|0,0000005377
|-
|
|p.m.
|0,1574000000
|0,0006705000
|<nowiki>-0,0000002744</nowiki>
|}
Finally, daily fat percentage (DFP) and daily protein percentage (DPP) are calculated from the estimated DY:

DFP=DFY/DMY × 100

DPP=DPY/DMY × 100

==== Calulation example with method of Jenko et al. (2008, 2010) ====
Example of the calculations of daily yields from morning milking and evening milking is presented in tables 3 and 4. Data from the Delorenzo and Wiggans method is used in the calculations (Table 2).

'''Table 2. Data for morning and evening milking.'''
{| class="wikitable"
|'''Milking'''
|'''a.m.'''
|'''p.m.'''
|-
|Beginning of recording
|06:15
|20:22
|-
|Start of preceding milking
|17:25
|06:35
|-
|Milking interval (min)
|770
|827
|-
|'''Milking results'''
|
|
|-
|Milk (kg)
|12,00
|14,00
|-
|Protein (%)
|3,45
|3,40
|-
|Fat (%)
|4,12
|4,00
|}

'''Table 3. Calculation of partial yield (PY) and calculation of y value.'''
{| class="wikitable"
|Trait
|Milking
|PY (%)
|PY (kg)
|y
|-
|Milk
|a.m.
|
|12,00
|0,1081000000 + 0,0005503000 x 770 = 0,531831
|-
|
|p.m.
|
|14,00
|0,0884200000 + 0,0005683000 x 827 = 0,558404
|-
|Protein
|a.m.
|3,45
|12,00 / 3,45 = 0,41
|0,1124000000 + 0,0005419000 x 770 = 0,529663
|-
|
|p.m.
|3,40
|14,00 / 3,40 = 0,48
|0,0966400000 + 0,0005593000 x 827 = 0,559181
|-
|Fat
|a.m.
|

4,12
|12,00 / 4,12 = 0,49
|0,5903000000 -0,0005093000 x 770 + 0,0000005377 x 7702 = 0,516941
|-
|
|p.m.
|

4,00
|12,00 / 4,00 = 0,56
|0,1574000000 +0,0006705000 x 827 - 0,0000002744 x 8272 = 0,524233
|}

'''Table 4. Calculation of daily yield (DY, kg) and daily components (DY, %).'''
{| class="wikitable"
|Trait
|DY
|Milking
|DY (kg)
|DY (%)
|-
|Milk
|DMY
|a.m.
|12,00 / 0,531831 = 22,56356
|
|-
|
|
|p.m.
|14,00 / 0,531831 = 25,07145
|
|-
|Protein
|DPY
|a.m.
|0,41 / 0,529663 = 0,781629
|(0,781629 / 22,56356) x 100 = 3,46
|-
|
|
|p.m.
|0,48 / 0,559181 = 0,851245
|(0,851245 / 25,07145) x 100 = 3,40
|-
|Fat
|DFY
|a.m.
|0,49 / 0,516941 = 0,956395
|(0,956395 / 22,56356) x 100 = 4,24
|-
|
|
|p.m.
|0,56 / 0,524233 = 1,068227
|(1,068227 / 25,07145) x 100 = 4,26
|}

==== References ====

* Jenko, J., Perpar, T., Logar, B., Sadar, M., Ivanovič, B., Jeretina, J., Verbič, J., Podgoršek, P. 2008. Comparison of different models for estimating daily yields from a.m./p.m. milkings in Slovenian dairy scheme. Presented at the 36th ICAR Session, Niagara Falls, New York, United States, June 16-20, 2008.
* Jenko, J., Perpar, T., Gorjanc G., Babnik, D. 2010. Evaluation of different approaches for the estimation of daily yield from single milk testing scheme in cattle, J. Dairy Res., 77 (2010), pp. 137-143; DOI: 10.1017/S0022029909990586

</div>
</div>

== Procedure 2 – Computing of Accumulated Lactation Yield ==
<div class="mw-collapsible mw-collapsed">
<div>
=== The Test Interval Method (TIM) (Sargent, 1968<ref>Sargent, F. D., V. H. Lyton, and 0. G. Wall, J r . 1968. Test interval method of calculating Dairy Herd Improvement Association records. J. Dairy Sci. 51:170.</ref>) ===
Test Interval Method is the reference method for calculating accumulated yields. Another adaptation of the method is the Centering Date Method where the yields from the preceding recording are used until the mid point of the recording interval and then substituted by the yields from the following recording.

The following equations are used to compute the lactation record for milk yield (MY), for fat (and protein) yield (FY), and for fat (and protein) percent (FP).
[[File:Equation1111.png|none|thumb|653x653px]]
Where:
M1, M2, Mn are the weights in kilograms, given to one decimal place, of the milk yielded in the 24 hours of the recording day.

F1, F2, Fn are the fat yields estimated by multiplying the milk yield and the fat percent (given to at least two decimal places) collected on the recording day.

I1, I2, In-1 are the intervals, in days, between recording dates.

I0 is the interval, in days, between the lactation period start date and the first recording date.

In is the interval, in days, between the last recording date and the end of the lactation period.

The equation applied for fat yield and percentage must be applied for any other milk components such as protein and lactose.

Details of how to apply the formulae are shown in Table 3 using the example data in Table 1, below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" align = "left" |'''''Table 1. Raw data used in example (TIM).'''''
|- style="background-color:#efefef;"
| colspan="6" align = "left"|'''Data:'''

'''Calving March 25'''
|- style="background-color:#efefef;"
|
|'''Date of'''

'''recording'''
|'''Number'''

'''of days'''
|'''Quantity of milk'''

'''weighed in kg'''
|'''Fat'''

'''percentage'''
|'''Fat'''

'''in grams'''
|-
|April
|8
|14
|28.2
|3.65
|1 029
|-
|May
|6
|28
|24.8
|3.45
|856
|-
|June
|5
|30
|26.6
|3.40
|904
|-
|July
|7
|32
|23.2
|3.55
|824
|-
|August
|2
|26
|20.2
|3.85
|778
|-
|August
|30
|28
|17.8
|4.05
|721
|-
|September
|25
|26
|13.2
|4.45
|587
|-
|October
|27
|32
|9.6
|4.65
|446
|-
|November
|22
|26
|5.8
|4.95
|287
|-
|December
|20
|28
|4.4
|5.25
|231
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left"|'''''Table 2. Lactation period summary (TIM).'''''
|-
|Beginning of lactation:
|March 26
|-
|End of lactation:
|January 3
|-
|Duration of lactation period:
|284 days
|-
|Number of testings (weighings):
|10
|}
</center>
<center>
{| class="wikitable"
| colspan="8" |'''''Table 3. Computations using Test Interval Method.'''''
|- style="background-color:#efefef;"
| colspan="3" rowspan="2" |'''Interval'''

'''both days included'''
|
| colspan="2" |'''Daily production'''
| colspan="2" |'''Sum'''
|- style="background-color:#efefef;"
|'''Days'''
|'''Kg milk'''
|'''Grams of fat'''
|'''Kg milk'''
|'''Kg fat'''
|-
|Mar 26
|<nowiki>-</nowiki>
|Apr 8
|14
|28.2
|1 029
|395
|14.410
|-
|Apr 9
|<nowiki>-</nowiki>
|May 6
|28
|(28.2+24.8)/2
|(1 029+856) /2
|742
|26.389
|-
|May 7
|<nowiki>-</nowiki>
|June 5
|30
|(24.8+26.6) /2
|(856+904) /2
|771
|26.400
|-
|June 6
|<nowiki>-</nowiki>
|July 7
|32
|(26.6+23.2) /2
|(904+824) /2
|797
|27.648
|-
|July 8
|<nowiki>-</nowiki>
|Aug. 2
|26
|(23.2+20.2) /2
|(824+778) /2
|564
|20.817
|-
|Aug. 3
|<nowiki>-</nowiki>
|Aug 30
|28
|(20.2+17.8) /2
|(778+721) /2
|532
|20.980
|-
|Aug 31
|<nowiki>-</nowiki>
|Sept. 25
|26
|(17.8+13.2) /2
|(721+587) /2
|403
|17.008
|-
|Sept. 26
|<nowiki>-</nowiki>
|Oct. 27
|32
|(13.2+9.6) /2
|(587+446) /2
|365
|16.541
|-
|Oct. 28
|<nowiki>-</nowiki>
|Nov. 22
|26
|(9.6+5.8) /2
|(446+287) /2
|200
|9.536
|-
|Nov. 23
|<nowiki>-</nowiki>
|Dec. 20
|28
|(5.8+4.4) /2
|(287+231) /2
|143
|7.253
|-
|Dec. 21
|<nowiki>-</nowiki>
|Jan. 3
|14
|4.4
|231
|62
|3.234
|-
|
|
|
|284
|
|
|4973
|190.216
|-
| colspan="8" |
|-
| colspan="8" |Total quantity of milk: 4 973. kg
|-
| colspan="8" |Total quantity of fat: 190 kg
|-
| colspan="8" |Average fat percentage (190.216 / 4973) x 100 = 3.82%
|}
</center>

=== Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. Livest. Prod. Sci. 17:l.</ref>) ===
With the method 'Interpolation using Standard Lactation Curves' missing test day yields and 305 day projections are predicted. The method makes use of separate standard lactation curves representing the expected course of the lactation, for a certain herd production level, age at calving and season of calving and yield trait. By interpolation using standard lactation curves, the fact that after calving milk yield generally increases and subsequently decreases is taken into account. The daily yields are predicted for fixed days of the lactation: day 0, 10, 30, 50 etc.

The cumulative yield is calculated as follows in :
[[File:Equation2222222.png|none|thumb|474x474px]]
where:

yi = the i-th daily yield;

INTi = the interval in days between the daily yields yi and yi+1;

''n'' = total number of daily yields (measured daily yields and predicted daily yields).

The next example illustrates the calculation of a record in progress. The cow was tested at day 35 and day 65 of the lactation. To determine the lactation yield, daily milk yields are determined for day 0, 10, 30 and 50 of the lactation, by means of the standard lactation curves. The daily yields are in Table 4.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Measured and derived daily yields, used to calculate the record in progress in the example (ISLC).'''''
|- style="background-color:#efefef;"
|'''Day of lactation'''
|'''Milk (kg)'''
|'''Note'''
|-
|0
|25.9
|Predicted
|-
|10
|27.8
|Predicted
|-
|30
|31.7
|Predicted
|-
|35
|31.8
|Measured
|-
|50
|32.9
|Interpolated using standard lactation curve
|-
|65
|33.0
|Measured
|}
</center>

Next, the record in progress can be calculated by means of the formula for a cumulative yield as follows:

[(10 - 1) * 25.9 + (10+1) * 27.8] / 2 +

[(20 - 1) * 27.8 + (20+1) * 31.7] / 2 +

[(5 - 1) * 31.7 + (5+1) * 31.8] / 2 +

[(15 - 1) * 31.8 + (15+1) * 32.9] / 2 +

[(15 - 1) * 32.9 + (15+1) * 33.0] / 2 = 2005.3 kg.

This corresponds to the surface below the line through the predicted and measured daily yields (see Figure 1).
[[File:Figure1.png|center|thumb|621x621px|''Figure 1. Example of calculation of record in progress.'']]

=== Best prediction (BP) (VanRaden, 1997<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. J. Dairy Sci. 80:3015-3022.</ref>) ===
Recorded milk weights are combined into a lactation record using standard selection index methods. Let vector y contain M1, M2, to Mn and let E('''y''') contain corresponding the expected values for each recorded day. The E(y) are obtained from standard lactation curves for the population or for the herd and should account for the cow's age and other environmental factors such as season, milking frequency, etc. The yields in '''y''' covary as a function of the recording interval between them (I). Diagonal elements in Var(y) are the population or herd variance for that recording day and off diagonals are obtained from autoregressive or similar functions such as Corr(M1, M2)=0.995I for first lactations or 0.992I for later lactations. Covariances of one observation with the lactation yield, for example Cov(M1, MY), are the sum of 305 individual covariances. E(MY) is the sum of 305 daily expected values. Lactation milk yield is then predicted as Equation 3:
[[File:Equation333333.png|none|thumb|640x640px]]
With best prediction, predicted milk yields have less variance than true milk yields. With TIM, estimated yields have more variance than true yields. The reason is that predicted yields are regressed toward the mean unless all 305 daily yields are observed. With best prediction, the predicted MY for a lactation without any observed yields is E(MY) which is the population or herd mean for a cow of that age and season. With TIM, the estimated MY is undefined if no daily yields are recorded.

Milk, fat, and protein yields can be processed separately using single-trait best prediction or jointly using multi-trait best prediction. Replacement of M1, M2, to Mn with F1, F2, to Fn or P1, P2, to Pn gives the single-trait predictions for fat or for protein. Multi-trait predictions require larger vectors and matrices but similar algebra. Products of trait correlations and autoregressive correlations, for example, may provide the needed covariances.

=== Multiple-Trait Procedure (MTP) (Schaeffer & Jamrozik, 1996<ref>Schaeffer, L.R., and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. J. Dairy Sci. 79:2044-2055.</ref>) ===
The Multiple-Trait Procedure predicts 305-d lactation yields for milk, fat, protein and SCS, incorporating information about standard lactation curves and covariances between milk, fat, and protein yields and SCS. Test day yields are weighted by their relative variances, and standard lactation curves of cows of similar breed, region, lactation number, age, and season of calving are used in the estimation of lactation curve parameters for each cow. The multiple-trait procedure can handle long intervals between test days, test days with milk only recorded, and can make 305-d predictions on the basis of just one test day record per cow. The procedure also lends itself to the calculation of peak yield, day of peak yield, yield persistency, and expected test-day yields, which could be useful management tools for a producer on a milk recording program.

The MTP method is based upon Wilmink's model in conjunction with an approach incorporating standard curve parameters for cows with the same production characteristics. Wilmink's function for one trait is given by Equation 4.

Equation 4. Wilmink function for one trait (MTP).

y = A + B''t'' ± C''exp'' (-0.05''t'') + ''e''

where y is yield on day t of lactation, A, B, and C are related to the shape of the lactation curve.

The parameters A, B, and C need to be estimated for each yield trait. The yield traits have high phenotypic correlations, and MTP would incorporate these correlations. Use of MTP would allow for the prediction of yields even if data were not available on each test day for a cow.

The vector of parameters to be estimated for one cow are designated:
[[File:Vectro.png|center|thumb]]
where M, F, and P represent milk, fat, and protein, respectively, and S represents somatic cell score. The vector c is to be estimated from the available test-day records. Let c0 represent the corresponding parameters estimated across all cows with the same production characteristics as the cow in question.

Let
[[File:Vector2.png|center|thumb]]

be the vector of yield traits and somatic cell scores on test ''k'' at day ''t'' of the lactation.

The incidence matrix, ''Xk'', is constructed as follows:
[[File:Vector3.png|center|thumb|558x558px]]

The MTP equations are:
[[File:Equation55555.png|none|thumb|560x560px]]
and ''n'' is the number of tests for that cow. ''Rk'' is a matrix of order 4 that contains the variances and covariances among the yields on ''kth'' test at day ''t'' of lactation. The elements of this matrix were derived from regression formulas based on fitting phenotypic variances and covariances of yields to models with ''t'' and ''t2'' as covariables. Thus, element ''ij'' of ''Rk'' would be determined by

rij(t) = ß0ij + ß1ij (t) + ß2ij (t2)

G is a 12 x 12 matrix containing variances and covariances among the parameters in '''ĉ''' and represents the cow to cow variation in these parameters, which includes genetic and permanent environmental effects, but ignores genetic covariances between cows. The parameters for '''''G''''' and '''''Rk''''' vary depending on the breed, but must be known. Initially, these matrices were allowed to vary by region of Canada in addition to breed, but this meant that there could exist two cows with identical production records on the same days in milk, but because one cow was in one region and the other cow was in another region, then the accuracy of their predictions would be different. This was considered to be too confusing for dairy producers, so that regional differences in variance-covariance matrices were ignored and one set of parameters would be used for all regions for a particular breed. Estimation of G is described later.

If a cow has a test, but only milk yield is reported, then

y’k(Mk 0 0 0)

and
[[File:And.png|center|thumb|540x540px]]

The inverse of '''''Rk''''' is the regular inverse of the nonzero submatrix within '''''Rk''''', ignoring the zero rows and columns. Thus, missing yields can be accommodated in MTP.

Accuracy of predicted 305-d lactation totals depends on the number of test-day records during the lactation and DIM associated with each test. Thus, any prediction procedure will require reliability figures to be reported with all predictions, especially if fewer tests at very irregular intervals are going to be frequent in milk recording. At the moment, an approximate procedure is applied that uses the inverse elements of '''(X’R-1X + G-1) -1.'''

==== 1.1 Example calculations ====
Four test day records on a 25 month old, Holstein cow calving in June from Ontario are given in the Table 5 below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 5. Example test day data for a cow (MTP).'''''
|- style="background-color:#efefef;"
|'''Test no.'''
|'''DIM=''t'''''
|'''Exp(-0.05''t'')'''
|'''Milk (kg)'''
|'''Fat (kg)'''
|'''Protein (kg)'''
|'''SCS'''
|-
|1
|15
|0.47237
|28.8
|
|
|3.130
|-
|2
|54
|0.06721
|29.2
|1.12
|0.87
|2.463
|-
|3
|188
|0.000083
|23.7
|0.97
|0.78
|2.157
|-
|4
|250
|0.0000037
|20.8
|
|
|2.619
|}
</center>

Notice that two tests do not have fat and protein yields, and that intervals between tests are irregular and large. The vector of standard curve parameters based on all available comparable cow, is
[[File:Vector4.png|center|thumb]]
The R^(-1)_k matrices for each test day need to be constructed. These matrices are derived from regression equations. The equations for Holsteins were:
<center>
{| class="wikitable" style="text-align: center;"
|''rMM(t) =''
|71.0752 - 0.281201''t'' + 0.0004977''t2''
|-
|''rMF(t) =''
|2.4365 - 0.013274''t'' + 0.0000302''t2''
|-
|''rMP(t) =''
|2.0504 - 0.008286''t'' + 0.0000163''t2''
|-
|''rMS(t) =''
|<nowiki>-1.7993 + 0.013209</nowiki>''t'' - 0.000056''t2''
|-
|''rFF(t) =''
|0.1312 - 0.000725''t'' + 0.000001586''t2''
|-
|''rFP(t) =''
|0.0739 - 0.000386''t'' + 0.000000926''t2''
|-
|''rFS(t) =''
|<nowiki>- 0.0386 + 0.000292</nowiki>''t'' - 0.000001796''t2''
|-
|''rPP(t) =''
|0.066 - 0.000267''t'' + 0.0000005636''t2''
|-
|''rPS(t) =''
|<nowiki>- 0.0404 + 0.000369</nowiki>''t'' - 0.000001743''t2''
|-
|''rSS(t) =''
|3.0404 - 0.000083''t'' - 0.000006105''t2''
|}
</center>

The inverses of the residual variance-covariance matrices for yields for the four test days are as follows:
<center>
{| class="wikitable" style="text-align: center;"
|
|0.0151259
|0
|0
|0.0080354
|-
|'''R^(-1)_1''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0080354
|0
|0
|0.3334553
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.1685584
|0.345947
|<nowiki>-4.851935</nowiki>
|0.0254775
|-
|'''R^(-1)_2''' = =
|<nowiki>-0.345947</nowiki>
|26.830915
|<nowiki>-17.40281</nowiki>
|<nowiki>-0.041445</nowiki>
|-
|
|<nowiki>-4.851935</nowiki>
|<nowiki>-17.40281</nowiki>
|187.18579
|<nowiki>-0.584885</nowiki>
|-
|
|0.0254775
|<nowiki>-0.041445</nowiki>
|<nowiki>-0.584885</nowiki>
|0.3365425
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.2620161
|0.1479068
|<nowiki>-7.943903</nowiki>
|0.0316069
|-
|'''R^(-1)_3''' = =
|0.1479068
|54.446977
|<nowiki>-56.01333</nowiki>
|0.3306741
|-
|
|<nowiki>-7.943903</nowiki>
|<nowiki>-56.01333</nowiki>
|317.9609
|<nowiki>-0.92601</nowiki>
|-
|
|0.0316069
|0.3306741
|<nowiki>-0.92601</nowiki>
|0.3654369
|}
{| class="wikitable" style="text-align: center;"
|

|0.0329465
|0
|0
|0.0251039
|-
|'''R^(-1)_4''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0251039
|0
|0
|0.3981981
|}

Inverse matrix G^(-1) of order 12 is the same for all cows of the same breed:

[[File:Left 6x6.jpg|center|thumb|600x600px|Inverse matrix G^(-1) of order 12]]

</center>
Note that many covariances between different parameters of the lactation curves have been set to zero. When all covariances were included, the prediction errors for individual cows were very large, possibly because the covariances were highly correlated to each other within and between traits. Including only covariances between the same parameter among traits gave much smaller prediction errors.

The elements of the MTP equations of order 12 for this cow are shown in partitioned format also:

'''X’R-1X ='''
<center>[[File:Elements of the MTP equations of order 12.jpg|center|thumb|600x600px|Elements of the MTP equations of order 12]]
</center>
[[File:Equation7.png|center|thumb|632x632px]]

The solution vector for this cow is
[[File:Equation6666.png|center|thumb]]

To predict 305-day yields, Y305
[[File:Equation7777.png|none|thumb|551x551px]]
Equation 6 is used separately for each trait (milk, fat, protein, and SCS). The results for this cow were 7456 kg milk, 301 kg fat, and 239 kg protein. The result for SCS is divided by 305 to give an average daily SCS of 2.477.
</div>
</div>

= Appendices =
== Appendix 1 - Adjustment factors to calculate 24-hour yields using the Liu method ==
<div class="mw-collapsible mw-collapsed">
<div>
In Table 6 the adjustment factors to calculate 24-hour yields, using the Liu method, can be found. The description of the Liu method can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2.]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" |'''''Table 1. Adjustment factors to calculate 24-hour yields using the Liu method. Milking time (MT) is either 1 (PM) or 2 (AM), i = parity class, j= milking interval class and k = stage of lactation class.'''''
|- style="background-color:#efefef;"
|'''MT'''
|'''i'''
|'''j'''
|'''k'''
| colspan="2" |'''Milk yield (DMY)'''
| colspan="2" |'''Fat yield (DFY)'''
| colspan="2" |'''Protein yield (DPY)'''
|-
| colspan="4" |
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|-
|1
|1
|1
|1
|5.29333
|1.83283
|0.30911
|1.43518
|0.18984
|1.77461
|-
|1
|1
|1
|2
|4.17676
|1.97447
|0.2803
|1.56914
|0.12246
|2.00568
|-
|1
|1
|1
|3
|4.26476
|1.95945
|0.18826
|1.82468
|0.12624
|2.0137
|-
|1
|1
|1
|4
|3.41282
|2.01814
|0.25025
|1.64707
|0.12519
|1.99629
|-
|1
|1
|1
|5
|1.79548
|2.22665
|0.06578
|2.09515
|0.05249
|2.24065
|-
|1
|1
|1
|6
|3.7751
|1.95508
|0.12854
|1.93892
|0.11936
|2.00979
|-
|1
|1
|1
|7
|1.544
|2.1478
|0.06425
|2.06779
|0.0569
|2.13851
|-
|1
|1
|2
|1
|5.8584
|1.79409
|0.33193
|1.42953
|0.20756
|1.7288
|-
|1
|1
|2
|2
|5.45524
|1.84258
|0.32877
|1.43235
|0.21332
|1.74001
|-
|1
|1
|2
|3
|4.64052
|1.86706
|0.27155
|1.57017
|0.16439
|1.84539
|-
|1
|1
|2
|4
|2.86835
|2.06209
|0.18647
|1.79403
|0.10803
|2.0193
|-
|1
|1
|2
|5
|2.11336
|2.12055
|0.10435
|1.97206
|0.07193
|2.10651
|-
|1
|1
|2
|6
|2.00673
|2.0636
|0.1386
|1.83336
|0.06892
|2.06532
|-
|1
|1
|2
|7
|1.71752
|2.11269
|0.06501
|2.0379
|0.05569
|2.12881
|-
|1
|1
|3
|1
|2.80244
|2.02183
|0.17663
|1.72438
|0.11078
|1.96422
|-
|1
|1
|3
|2
|3.47396
|1.98268
|0.2135
|1.6805
|0.10471
|1.99092
|-
|1
|1
|3
|3
|2.81702
|2.04348
|0.20754
|1.71868
|0.1127
|1.98403
|-
|1
|1
|3
|4
|3.1989
|1.998
|0.21578
|1.6991
|0.10802
|1.99517
|-
|1
|1
|3
|5
|2.47055
|2.04826
|0.15418
|1.83151
|0.07492
|2.07547
|-
|1
|1
|3
|6
|1.923
|2.07728
|0.11783
|1.89678
|0.06457
|2.08391
|-
|1
|1
|3
|7
|1.85264
|2.0873
|0.13047
|1.86711
|0.071
|2.06917
|-
|1
|1
|4
|1
|2.75042
|1.96631
|0.24794
|1.61741
|0.09248
|1.95376
|-
|1
|1
|4
|2
|2.97505
|1.96711
|0.20029
|1.71842
|0.09381
|1.97081
|-
|1
|1
|4
|3
|2.33365
|2.02986
|0.17021
|1.79996
|0.07631
|2.03167
|-
|1
|1
|4
|4
|3.41505
|1.94107
|0.1845
|1.76799
|0.10989
|1.95456
|-
|1
|1
|4
|5
|2.67488
|1.97797
|0.13433
|1.85893
|0.09432
|1.97755
|-
|1
|1
|4
|6
|1.89907
|2.04841
|0.08715
|1.96251
|0.07132
|2.04225
|-
|1
|1
|4
|7
|1.80326
|2.03554
|0.1251
|1.86477
|0.06072
|2.04747
|-
|1
|1
|5
|1
|2.76763
|1.92863
|0.15754
|1.72474
|0.10187
|1.88749
|-
|1
|1
|5
|2
|3.36896
|1.92048
|0.2236
|1.64149
|0.12369
|1.8823
|-
|1
|1
|5
|3
|2.22763
|2.00452
|0.17614
|1.7474
|0.08019
|1.9782
|-
|1
|1
|5
|4
|2.44625
|1.97049
|0.17217
|1.74753
|0.0889
|1.94647
|-
|1
|1
|5
|5
|2.379
|1.97307
|0.15965
|1.76134
|0.0896
|1.94575
|-
|1
|1
|5
|6
|1.62948
|2.02491
|0.11021
|1.85546
|0.0852
|1.94593
|-
|1
|1
|5
|7
|1.45651
|2.0254
|0.07479
|1.92789
|0.05846
|2.00196
|-
|1
|1
|6
|1
|2.01088
|1.9497
|0.16548
|1.68143
|0.101
|1.85846
|-
|1
|1
|6
|2
|2.96605
|1.93064
|0.25841
|1.52566
|0.12097
|1.86061
|-
|1
|1
|6
|3
|2.2281
|1.96085
|0.19036
|1.69013
|0.08032
|1.9375
|-
|1
|1
|6
|4
|2.39473
|1.952
|0.17854
|1.72423
|0.06863
|1.97582
|-
|1
|1
|6
|5
|2.37955
|1.94127
|0.19579
|1.66419
|0.08447
|1.93156
|-
|1
|1
|6
|6
|0.36203
|2.12393
|0.14291
|1.75822
|0.03845
|2.04562
|-
|1
|1
|6
|7
|1.5702
|1.96794
|0.1336
|1.76796
|0.06449
|1.94829
|-
|1
|1
|7
|1
|3.93654
|1.82772
|0.2359
|1.61894
|0.15032
|1.76054
|-
|1
|1
|7
|2
|4.39662
|1.81581
|0.24969
|1.5881
|0.16909
|1.74794
|-
|1
|1
|7
|3
|3.78325
|1.82778
|0.19228
|1.71802
|0.12368
|1.8268
|-
|1
|1
|7
|4
|3.39116
|1.86302
|0.1969
|1.71838
|0.12282
|1.848
|-
|1
|1
|7
|5
|3.20111
|1.83255
|0.09893
|1.86309
|0.1044
|1.84257
|-
|1
|1
|7
|6
|3.75639
|1.78665
|0.25205
|1.56174
|0.14105
|1.76802
|-
|1
|1
|7
|7
|1.42153
|1.95649
|0.09226
|1.85882
|0.04636
|1.96245
|-
|1
|1
|8
|1
|2.3454
|1.90436
|0.14321
|1.77423
|0.10703
|1.82306
|-
|1
|1
|8
|2
|3.97557
|1.82746
|0.26651
|1.58374
|0.15298
|1.76385
|-
|1
|1
|8
|3
|4.26939
|1.80503
|0.22918
|1.64925
|0.12924
|1.81061
|-
|1
|1
|8
|4
|2.90779
|1.89861
|0.18578
|1.73968
|0.13948
|1.79679
|-
|1
|1
|8
|5
|2.8265
|1.87632
|0.19374
|1.67929
|0.12377
|1.80944
|-
|1
|1
|8
|6
|2.26312
|1.87397
|0.09917
|1.82528
|0.08819
|1.84453
|-
|1
|1
|8
|7
|0.31382
|2.04402
|0.05049
|1.95773
|0.02612
|1.99012
|-
|1
|2
|1
|1
|4.63752
|1.99615
|0.31102
|1.58962
|0.16637
|1.96686
|-
|1
|2
|1
|2
|5.56226
|1.91521
|0.26761
|1.64342
|0.16973
|1.94145
|-
|1
|2
|1
|3
|4.51983
|1.96962
|0.26221
|1.65088
|0.12245
|2.03857
|-
|1
|2
|1
|4
|4.51563
|1.93033
|0.18468
|1.80715
|0.15252
|1.94807
|-
|1
|2
|1
|5
|2.60334
|2.07338
|0.16011
|1.81257
|0.09892
|2.05493
|-
|1
|2
|1
|6
|2.86068
|1.98457
|0.15381
|1.79197
|0.08619
|2.04046
|-
|1
|2
|1
|7
|1.6596
|2.11753
|0.13089
|1.83687
|0.09908
|1.96479
|-
|1
|2
|2
|1
|3.94656
|2.03607
|0.23716
|1.6988
|0.19559
|1.88765
|-
|1
|2
|2
|2
|4.20525
|1.98621
|0.3553
|1.46663
|0.1657
|1.92175
|-
|1
|2
|2
|3
|3.31729
|2.04589
|0.29682
|1.57761
|0.12491
|2.00945
|-
|1
|2
|2
|4
|1.95977
|2.13926
|0.16059
|1.79846
|0.06713
|2.12835
|-
|1
|2
|2
|5
|1.49014
|2.14889
|0.10057
|1.90772
|0.05279
|2.14047
|-
|1
|2
|2
|6
|0.82235
|2.22517
|0.07573
|1.94963
|0.04014
|2.17549
|-
|1
|2
|2
|7
|1.53608
|2.08972
|0.11472
|1.81148
|0.0676
|2.03957
|-
|1
|2
|3
|1
|3.85525
|2.00429
|0.27991
|1.62403
|0.12863
|1.98973
|-
|1
|2
|3
|2
|4.1508
|1.9852
|0.3635
|1.47515
|0.13952
|1.97074
|-
|1
|2
|3
|3
|3.31493
|2.02332
|0.31131
|1.55183
|0.11703
|2.00696
|-
|1
|2
|3
|4
|2.47354
|2.0652
|0.20828
|1.71637
|0.09402
|2.04147
|-
|1
|2
|3
|5
|1.68517
|2.08809
|0.14418
|1.80246
|0.06917
|2.05808
|-
|1
|2
|3
|6
|1.316
|2.12714
|0.11206
|1.87179
|0.04723
|2.12486
|-
|1
|2
|3
|7
|0.4841
|2.20538
|0.04633
|2.02915
|0.02369
|2.18113
|-
|1
|2
|4
|1
|2.82623
|2.01819
|0.25826
|1.69268
|0.11251
|1.97665
|-
|1
|2
|4
|2
|3.24039
|1.9811
|0.36283
|1.50648
|0.11719
|1.96246
|-
|1
|2
|4
|3
|2.4545
|2.03386
|0.19627
|1.75339
|0.09698
|2.00807
|-
|1
|2
|4
|4
|2.46446
|2.01626
|0.17827
|1.76414
|0.08026
|2.02912
|-
|1
|2
|4
|5
|2.11339
|2.00724
|0.14884
|1.77964
|0.07749
|2.00585
|-
|1
|2
|4
|6
|1.51141
|2.04563
|0.11559
|1.82474
|0.06194
|2.02586
|-
|1
|2
|4
|7
|0.95936
|2.09963
|0.07044
|1.95281
|0.03645
|2.0993
|-
|1
|2
|5
|1
|3.36561
|1.97323
|0.2649
|1.65361
|0.13019
|1.92402
|-
|1
|2
|5
|2
|3.66222
|1.95479
|0.35065
|1.51028
|0.14652
|1.89882
|-
|1
|2
|5
|3
|3.20442
|1.96165
|0.28676
|1.58823
|0.12031
|1.93028
|-
|1
|2
|5
|4
|1.78673
|2.0426
|0.17183
|1.75198
|0.0678
|2.02025
|-
|1
|2
|5
|5
|1.61868
|2.01988
|0.11914
|1.80878
|0.06624
|1.99283
|-
|1
|2
|5
|6
|1.30123
|2.02218
|0.10515
|1.80653
|0.05345
|2.00292
|-
|1
|2
|5
|7
|0.65695
|2.08269
|0.06835
|1.89102
|0.0332
|2.0525
|-
|1
|2
|6
|1
|2.3773
|1.9669
|0.24867
|1.6336
|0.08319
|1.94741
|-
|1
|2
|6
|2
|2.82556
|1.95506
|0.31731
|1.51798
|0.12008
|1.89324
|-
|1
|2
|6
|3
|2.7235
|1.94883
|0.30621
|1.5177
|0.09365
|1.93764
|-
|1
|2
|6
|4
|1.77727
|1.98273
|0.17989
|1.69341
|0.07314
|1.95161
|-
|1
|2
|6
|5
|0.81041
|2.05295
|0.13961
|1.74391
|0.04468
|2.01091
|-
|1
|2
|6
|6
|0.72188
|2.0465
|0.09874
|1.79927
|0.03137
|2.03309
|-
|1
|2
|6
|7
|1.21598
|1.97942
|0.07065
|1.87211
|0.04484
|1.98491
|-
|1
|2
|7
|1
|3.55054
|1.89128
|0.27402
|1.61031
|0.10827
|1.89085
|-
|1
|2
|7
|2
|5.0062
|1.81574
|0.3119
|1.54857
|0.18009
|1.76865
|-
|1
|2
|7
|3
|3.95204
|1.84947
|0.30465
|1.53907
|0.16048
|1.789
|-
|1
|2
|7
|4
|2.36233
|1.9168
|0.18751
|1.70412
|0.09531
|1.88355
|-
|1
|2
|7
|5
|1.48851
|1.94443
|0.09973
|1.81041
|0.05904
|1.92497
|-
|1
|2
|7
|6
|1.22525
|1.94454
|0.06617
|1.87082
|0.05516
|1.91259
|-
|1
|2
|7
|7
|1.13847
|1.93756
|0.08109
|1.83388
|0.04706
|1.93165
|-
|1
|2
|8
|1
|4.09874
|1.87708
|0.20312
|1.73434
|0.15506
|1.83083
|-
|1
|2
|8
|2
|4.66403
|1.84302
|0.31808
|1.56093
|0.18049
|1.78288
|-
|1
|2
|8
|3
|3.24375
|1.89351
|0.2827
|1.59546
|0.13583
|1.83427
|-
|1
|2
|8
|4
|2.24175
|1.92084
|0.17795
|1.72611
|0.09636
|1.87438
|-
|1
|2
|8
|5
|1.63783
|1.93625
|0.1225
|1.78642
|0.0659
|1.90934
|-
|1
|2
|8
|6
|2.01753
|1.89095
|0.13742
|1.74752
|0.08289
|1.86553
|-
|1
|2
|8
|7
|0.97568
|1.97215
|0.05926
|1.88807
|0.04057
|1.95672
|-
|2
|1
|1
|1
|3.44076
|1.73133
|0.27759
|1.55037
|0.13323
|1.68913
|-
|2
|1
|1
|2
|4.99596
|1.64527
|0.2322
|1.58033
|0.17533
|1.62422
|-
|2
|1
|1
|3
|3.83372
|1.68144
|0.25087
|1.52033
|0.14525
|1.66706
|-
|2
|1
|1
|4
|3.87034
|1.68102
|0.20979
|1.60153
|0.13627
|1.68885
|-
|2
|1
|1
|5
|1.76134
|1.80424
|0.15241
|1.70485
|0.06231
|1.81524
|-
|2
|1
|1
|6
|0.79304
|1.89072
|0.09906
|1.80312
|0.03277
|1.89435
|-
|2
|1
|1
|7
|1.43535
|1.80614
|0.0593
|1.81589
|0.0407
|1.85002
|-
|2
|1
|2
|1
|3.72284
|1.68499
|0.19226
|1.66567
|0.1237
|1.66453
|-
|2
|1
|2
|2
|4.42667
|1.66508
|0.24314
|1.55652
|0.14361
|1.66251
|-
|2
|1
|2
|3
|2.7019
|1.75871
|0.32717
|1.38452
|0.11056
|1.72312
|-
|2
|1
|2
|4
|2.41538
|1.75937
|0.14575
|1.68355
|0.09038
|1.74138
|-
|2
|1
|2
|5
|1.65412
|1.81649
|0.13926
|1.70623
|0.0597
|1.81378
|-
|2
|1
|2
|6
|2.0843
|1.7735
|0.21052
|1.57508
|0.07244
|1.78566
|-
|2
|1
|2
|7
|1.43238
|1.80651
|0.08031
|1.78712
|0.05269
|1.81727
|-
|2
|1
|3
|1
|2.45314
|1.77068
|0.18152
|1.73443
|0.07657
|1.78025
|-
|2
|1
|3
|2
|3.01217
|1.70966
|0.19388
|1.66175
|0.05624
|1.80606
|-
|2
|1
|3
|3
|2.09997
|1.74945
|0.14493
|1.68277
|0.05446
|1.7922
|-
|2
|1
|3
|4
|2.36683
|1.71741
|0.12244
|1.71407
|0.06775
|1.75721
|-
|2
|1
|3
|5
|1.56776
|1.75755
|0.08776
|1.76946
|0.04244
|1.79675
|-
|2
|1
|3
|6
|1.63824
|1.75452
|0.09422
|1.76794
|0.04181
|1.80604
|-
|2
|1
|3
|7
|0.74114
|1.83421
|0.08039
|1.78306
|0.02347
|1.85596
|-
|2
|1
|4
|1
|1.47047
|1.78588
|0.17271
|1.69379
|0.06511
|1.74985
|-
|2
|1
|4
|2
|2.22168
|1.72985
|0.20701
|1.59429
|0.08178
|1.71455
|-
|2
|1
|4
|3
|2.50108
|1.69618
|0.16828
|1.61962
|0.08598
|1.70516
|-
|2
|1
|4
|4
|1.97141
|1.7202
|0.1446
|1.66357
|0.06856
|1.73201
|-
|2
|1
|4
|5
|1.17054
|1.75879
|0.1172
|1.69234
|0.04624
|1.75806
|-
|2
|1
|4
|6
|1.74755
|1.70968
|0.12562
|1.67603
|0.0629
|1.72333
|-
|2
|1
|4
|7
|0.52482
|1.80155
|0.07345
|1.75615
|0.02671
|1.79288
|-
|2
|1
|5
|1
|1.76464
|1.76219
|0.24301
|1.59094
|0.07156
|1.73136
|-
|2
|1
|5
|2
|1.99594
|1.73438
|0.1984
|1.5954
|0.06489
|1.73449
|-
|2
|1
|5
|3
|1.8804
|1.72362
|0.13019
|1.67977
|0.06783
|1.71916
|-
|2
|1
|5
|4
|1.83337
|1.71477
|0.11197
|1.70244
|0.05764
|1.73194
|-
|2
|1
|5
|5
|1.49752
|1.72615
|0.13128
|1.65461
|0.04656
|1.7433
|-
|2
|1
|5
|6
|1.3042
|1.7305
|0.07173
|1.75315
|0.04482
|1.7399
|-
|2
|1
|5
|7
|2.00868
|1.67669
|0.12298
|1.64761
|0.09175
|1.64669
|-
|2
|1
|6
|1
|0.84993
|1.75972
|0.12918
|1.74026
|0.0328
|1.74802
|-
|2
|1
|6
|2
|1.93666
|1.67406
|0.16606
|1.59943
|0.04535
|1.7106
|-
|2
|1
|6
|3
|2.12115
|1.64964
|0.19988
|1.50821
|0.05229
|1.68986
|-
|2
|1
|6
|4
|0.68831
|1.73901
|0.09674
|1.6838
|0.01696
|1.75787
|-
|2
|1
|6
|5
|1.13081
|1.69479
|0.06413
|1.72559
|0.04936
|1.67757
|-
|2
|1
|6
|6
|0.5893
|1.72537
|0.02598
|1.80138
|0.01591
|1.74082
|-
|2
|1
|6
|7
|0.72519
|1.71955
|0.03157
|1.78405
|0.02889
|1.71972
|-
|2
|1
|7
|1
|1.85937
|1.66064
|0.2416
|1.49676
|0.06807
|1.63599
|-
|2
|1
|7
|2
|1.8527
|1.64892
|0.2374
|1.43845
|0.06336
|1.6431
|-
|2
|1
|7
|3
|1.56905
|1.66084
|0.15434
|1.55598
|0.04336
|1.68109
|-
|2
|1
|7
|4
|0.74968
|1.69857
|0.13496
|1.56636
|0.02871
|1.6933
|-
|2
|1
|7
|5
|1.08222
|1.65925
|0.10847
|1.613
|0.03305
|1.67829
|-
|2
|1
|7
|6
|1.1124
|1.68059
|0.14267
|1.57525
|0.04416
|1.6776
|-
|2
|1
|7
|7
|0.88031
|1.6751
|0.10534
|1.60483
|0.04216
|1.66444
|-
|2
|1
|8
|1
|0.62802
|1.72402
|0.19225
|1.54631
|0.03247
|1.69368
|-
|2
|1
|8
|2
|0.83902
|1.68303
|0.15492
|1.53421
|0.05922
|1.61411
|-
|2
|1
|8
|3
|1.33727
|1.63407
|0.19835
|1.43309
|0.05874
|1.61141
|-
|2
|1
|8
|4
|1.06381
|1.64762
|0.11026
|1.58762
|0.04019
|1.64574
|-
|2
|1
|8
|5
|1.13714
|1.61716
|0.13322
|1.53166
|0.05648
|1.59149
|-
|2
|1
|8
|6
|1.19134
|1.60463
|0.11089
|1.54864
|0.06258
|1.56912
|-
|2
|1
|8
|7
|1.58872
|1.60204
|0.066
|1.64659
|0.04748
|1.63282
|-
|2
|2
|1
|1
|3.46775
|1.78609
|0.28956
|1.68515
|0.15003
|1.72171
|-
|2
|2
|1
|2
|5.69879
|1.67614
|0.3725
|1.5045
|0.19774
|1.64659
|-
|2
|2
|1
|3
|5.18985
|1.66571
|0.40124
|1.40574
|0.17828
|1.65793
|-
|2
|2
|1
|4
|3.43435
|1.74182
|0.20332
|1.66994
|0.11075
|1.76221
|-
|2
|2
|1
|5
|2.48643
|1.76219
|0.13714
|1.7396
|0.09636
|1.75624
|-
|2
|2
|1
|6
|1.41151
|1.82292
|0.15415
|1.6725
|0.06549
|1.80013
|-
|2
|2
|1
|7
|0.9096
|1.8409
|0.08811
|1.7823
|0.03467
|1.85275
|-
|2
|2
|2
|1
|1.85358
|1.83615
|0.28355
|1.64765
|0.06055
|1.83138
|-
|2
|2
|2
|2
|3.81188
|1.74978
|0.25972
|1.62799
|0.11238
|1.7646
|-
|2
|2
|2
|3
|3.16717
|1.76679
|0.29832
|1.53409
|0.09407
|1.78959
|-
|2
|2
|2
|4
|2.33664
|1.78934
|0.22694
|1.60101
|0.07273
|1.80371
|-
|2
|2
|2
|5
|2.01675
|1.79303
|0.10664
|1.79792
|0.06062
|1.8184
|-
|2
|2
|2
|6
|1.80809
|1.80081
|0.13659
|1.70935
|0.07335
|1.79213
|-
|2
|2
|2
|7
|1.01661
|1.8295
|0.0548
|1.84688
|0.03414
|1.84213
|-
|2
|2
|3
|1
|2.01474
|1.8142
|0.21867
|1.74325
|0.05359
|1.83088
|-
|2
|2
|3
|2
|3.53989
|1.71985
|0.28196
|1.60868
|0.10823
|1.73763
|-
|2
|2
|3
|3
|3.38412
|1.69907
|0.27409
|1.56164
|0.11042
|1.71397
|-
|2
|2
|3
|4
|2.2171
|1.74622
|0.16076
|1.70107
|0.07372
|1.75906
|-
|2
|2
|3
|5
|1.11799
|1.80944
|0.11087
|1.75678
|0.03792
|1.81891
|-
|2
|2
|3
|6
|1.40464
|1.76033
|0.10048
|1.72933
|0.05342
|1.75745
|-
|2
|2
|3
|7
|0.11328
|1.8972
|0.04052
|1.87101
|0.00787
|1.88753
|-
|2
|2
|4
|1
|2.59777
|1.74476
|0.28154
|1.66509
|0.10763
|1.71072
|-
|2
|2
|4
|2
|3.53853
|1.69511
|0.38311
|1.46839
|0.13243
|1.66523
|-
|2
|2
|4
|3
|2.80538
|1.70587
|0.26686
|1.55787
|0.1126
|1.68024
|-
|2
|2
|4
|4
|2.18191
|1.72068
|0.18333
|1.65612
|0.085
|1.71029
|-
|2
|2
|4
|5
|1.23383
|1.7716
|0.12824
|1.71179
|0.04845
|1.76628
|-
|2
|2
|4
|6
|0.85652
|1.79279
|0.0763
|1.79314
|0.03563
|1.78528
|-
|2
|2
|4
|7
|0.97995
|1.77178
|0.0797
|1.7577
|0.03846
|1.77043
|-
|2
|2
|5
|1
|2.47016
|1.74985
|0.32061
|1.60073
|0.10455
|1.71058
|-
|2
|2
|5
|2
|3.76194
|1.68979
|0.32787
|1.54675
|0.11781
|1.69109
|-
|2
|2
|5
|3
|2.61421
|1.70766
|0.20307
|1.64866
|0.08315
|1.71378
|-
|2
|2
|5
|4
|1.6809
|1.74028
|0.16795
|1.66491
|0.06202
|1.73305
|-
|2
|2
|5
|5
|1.31241
|1.75722
|0.14383
|1.68302
|0.05338
|1.74562
|-
|2
|2
|5
|6
|1.66563
|1.71781
|0.12721
|1.69231
|0.06147
|1.72101
|-
|2
|2
|5
|7
|0.87471
|1.74991
|0.07882
|1.71706
|0.04173
|1.73246
|-
|2
|2
|6
|1
|1.70055
|1.72832
|0.20839
|1.67759
|0.06001
|1.71779
|-
|2
|2
|6
|2
|3.20558
|1.65143
|0.33676
|1.47797
|0.09642
|1.6546
|-
|2
|2
|6
|3
|1.5827
|1.71538
|0.19719
|1.62038
|0.05324
|1.71254
|-
|2
|2
|6
|4
|1.7692
|1.69473
|0.14854
|1.66225
|0.05758
|1.69946
|-
|2
|2
|6
|5
|1.33003
|1.70542
|0.10726
|1.69398
|0.04565
|1.7096
|-
|2
|2
|6
|6
|1.01266
|1.71155
|0.09376
|1.70285
|0.04005
|1.70822
|-
|2
|2
|6
|7
|0.9856
|1.70091
|0.06454
|1.73063
|0.0394
|1.69796
|-
|2
|2
|7
|1
|2.02441
|1.67788
|0.30435
|1.5407
|0.08673
|1.63673
|-
|2
|2
|7
|2
|1.43949
|1.71143
|0.30098
|1.47963
|0.06527
|1.67295
|-
|2
|2
|7
|3
|1.68946
|1.66442
|0.24777
|1.47116
|0.06594
|1.64834
|-
|2
|2
|7
|4
|1.10967
|1.68591
|0.15663
|1.60109
|0.04949
|1.67069
|-
|2
|2
|7
|5
|0.77866
|1.70882
|0.11248
|1.64389
|0.03402
|1.70215
|-
|2
|2
|7
|6
|0.67502
|1.69719
|0.10289
|1.62419
|0.03507
|1.67744
|-
|2
|2
|7
|7
|0.65216
|1.70336
|0.05545
|1.73388
|0.02233
|1.72102
|-
|2
|2
|8
|1
|1.33877
|1.67358
|0.18369
|1.64385
|0.06055
|1.63818
|-
|2
|2
|8
|2
|0.71697
|1.71038
|0.25461
|1.49037
|0.04798
|1.66397
|-
|2
|2
|8
|3
|2.13197
|1.62429
|0.2393
|1.47673
|0.08136
|1.6065
|-
|2
|2
|8
|4
|1.16932
|1.66188
|0.13759
|1.60108
|0.0463
|1.64856
|-
|2
|2
|8
|5
|1.48369
|1.62387
|0.12547
|1.58988
|0.06919
|1.5925
|-
|2
|2
|8
|6
|1.18879
|1.65442
|0.10031
|1.62813
|0.07392
|1.58846
|-
|2
|2
|8
|7
|0.58052
|1.68546
|0.02696
|1.7382
|0.01982
|1.70519
|}
</center>
</div>
</div>

== Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme ==
<div class="mw-collapsible mw-collapsed">
<div>
=== Abstract ===
Based on comments on imprecision of the estimation method for 24-hour fat % in AM/PM milk recording schemes the regression formula was extended and re-estimated. Non-linearity for the existing effects of protein % of the milk sample, interval before sampling, milk amount of sample, milk amount of previous milking and interval before the previous milking was incorporated by using polynomials. Extensions were made by adding the effects of time of sampling, parity and month of sampling as class variables and lactation stage as polynomial. In total a reduction of the standard deviation of the difference between true and estimated 24-hour fat % of 2.4% was reached (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

'''''Keywords''''': estimation, fat %, AM/PM.

=== Introduction ===
The AM/PM milk recording routine is based on only one morning (a.m.) or evening (p.m.) milk sample which are collected in an alternating way. A condition to take part in this AM/PM milk recording in The Netherlands is that on farm electronic milk measurements (EMM) are available. EMM-data consists of time of milking and milk quantity of every milking. Based on one milk sample and the EMM-data the 24-hour fat % is estimated (Peeters & Galesloot, 2002<ref name=":2">Peeters, R. and P. Galesloot, 2002.Estimating daily fat yield from a single milking on test day for herds with a robotic milking system. J. Dairy Sci. 85, 682-688.</ref>). Also for farms with an automatic milking system (AMS) this estimation is used when only one milk sample is available for analysis on milk composition.

Based on comments from farmers on fluctuations in 24-hour fat % preliminary research was conducted. This showed that the current estimation caused an underestimation of 24-hour fat % based on an a.m.-sample of 0.09% while the estimate based on a p.m.-sample was overestimated by 0.05%. Possible causes for this fluctuation are differences in milk-fat synthesis between day- and night-time as was shown by Gilbert et al. (1972) <ref>Gilbert, G.R., G.L. Hargrove and M. Kroger, 1972. Diurnal variations in milk yield, fat yield, milk fat % and milk protein % by the test interval method. J. Dairy Sci. 56, 409-410.</ref>and Lee & Wardorp (1984)<ref>Lee, A.J. and Wardorp, 1984. Predicting daily milk yield, fat percent, and protein percent from morning or afternoon tests. J. Dairy Sci. 67, 351-360.</ref>. Other factors of imprecision in the current estimation can be caused by lactation stage and parity, two factors that are accounted for in the method of Liu et al. (2000)<ref>Liu, Z., R. Reents, F. Reinhardt and K Kuwan, 2000. Approaches to estimating daily yield from single milk testing schemes and use of a.m.-p.m. records in test-day model genetic evaluation in dairy cattle. J. Dairy Sci. 83, 2672-2682.</ref>.

The objective of this research is to re-estimate the regression formula which is used to estimate the 24-hour fat %s in AM/PM milk recording and AMS recordings with only one sample. By testing for non-linearity of current effects and introducing new explanatory variables the aim is to increase the accuracy of the estimated 24-hour fat %.

=== Material and Methods ===
The data needed for the objective had to meet a number of criteria. The most important criteria were that the data comprised:

* differences in interval between milking times;
* different milking times;
* multiple samples per cow per herd test date;
* milking time and quantity of all milkings;

Only data of farms that use an AMS met all of these criteria. Therefore the research was conducted on data of all farms that used an AMS from January 20th 2001 until July 1st 2004. Records with only one sample per herd test date were excluded from the analysis.

In order to estimate as well as validate the new regression formula the each herd test date was assigned at random into two separate datasets. Dataset 1 was used for estimation and contained 371.528 samplings on 50.591 cows on 537 farms. Dataset 2 was used for validation and contained 371.885 milkings on 50.643 cows on 538 farms. Some characteristics of variables of both datasets are presented in Table 1.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" |'''''Table 1. Characteristics of variables in dataset 1 (estimation) and dataset 2 (validation).'''''
|-
| rowspan="2" |'''Variable'''
| colspan="2" |'''Dataset 1 (estimation)'''
| colspan="2" |'''Dataset 2 (validation)'''
|-
|'''Mean'''
|'''Std'''
|'''Mean'''
|'''Std'''
|-
|Sample milk amount (kg)
|10.1
|3.1
|10.1
|3.1
|-
|Sample fat (%)
|4.40
|0.76
|4.41
|0.76
|-
|Sample protein (%)
|3.49
|0.35
|3.49
|0.35
|-
|Time at sampling
|12.29
|7.24
|12.31
|7.24
|-
|Interval before sample (min)
|520
|154
|521
|155
|-
|Interval before prev. milking (min)
|526
|158
|527
|159
|}
</center>

=== Methods ===
The analysis started with the currently used regression formula which uses the effects: fat %, protein %, milk amount of sampling, interval before sampling, milk amount of the previous milking and interval before the previous milking (Peeters & Galesloot, 2002<ref name=":2" />). All these effects are considered to be linear. As an extra check of the data this regression formula was re-estimated and compared to the currently used regression formula. In order to estimate the regression formula first of all the 24-hour fat % was determined by using a weighted average of all milk samples for that cow on that herd test date.

Subsequently, a number of changes to the regression formula were tested for their effect on the accuracy of the 24-hour fat %. The changes that are tested are:

# non-linearity of the current effects;
# effect of time at sampling;
# effect of lactation stage;
# effect of parity;
# month of milk recording;

The effects were all tested in a similar way by plotting the residuals of the regression formula without the effect that is tested to the tested effect. Based on this plot a possible relation between residual and effect becomes clear and the best way of incorporating the effect is shown. The conclusion if an effect had a positive effect on the accuracy of the regression formula was based on the standard deviation of the difference between estimated and true 24-hour fat %. Also the correlation between the two fat %s and the b-factor (regression coefficient) of the linear regression between the two fat %s were considered.

=== Results ===
The regression coefficients of the re-estimated regression formula differed slightly from the estimates by Peeters & Galesloot (2002)<ref name=":1" />, probably due to the different dataset.

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %.
[[File:Imagefig1.png|center|thumb|''Figure 1a: Average residual per class for the variables sample fat %'']]
[[File:Imagefig1b.png|center|thumb|''Figure 1b: Sample protein %'' ]]
[[File:Imagefig1c.png|center|thumb|''Figure 1c : Interval before sampling'']]
[[File:Imagefig1d.png|center|thumb|''Figure 1d : Interval before previous milking'']]
[[File:Imagefig1e.png|center|thumb|''Figure 1e : Sample milk amount'']]
[[File:Imagefig1f.png|center|thumb|''Figure 1f: Milk amount before sampling'']]

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %. Of all variables, only fat % of the milk sample (Figure 1a) seemed to be linear. A 2nd order polynomial fitted the interval before the previous milking. The other variables, i.e. protein % of the milk sample, interval before sampling, milk amount of sample and milk amount of the previous milking were described by a 3rd order polynomial. For all variables except fat % of the sample higher order polynomials were found significant. This however was caused by the large amount of data and no longer a possible biological effect since it also had no effect on the accuracy of the estimation.

The effect of time of sampling showed a large amount of variability over time. Using a polynomial to fit the data was therefore difficult. Estimation of the effect by hourly intervals was a good alternative as is shown in Figure 2. Lactation stage had mainly an effect in the first 50 days of lactation as is shown by Figure 3. A 3rd order polynomial fitted the data properly.
[[File:Imagefig2.png|center|thumb|''Figure 2. Average residual per class for time of sampling (minutes after midnight).'']]
[[File:Imagefig33.png|center|thumb|''Figure 3. Average residual per class for lactation stage (days).'']]

The effects of parity and month of milk sampling were both considered as class variables. For parity the effects of parity 1 to 6 and 7 or higher were considered. Table 2 shows that mainly for the lower parities the estimated 24-hour fat % was overestimated. Also the months May to October, usually the pasture period, showed an overestimation of 24-hour fat %.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" |'''''Table 2. Effect of parity and month of sampling on estimated 24-hour fat % (*100).'''''
|-
|'''Parity'''
|'''Estimate'''
|'''Month of sampling'''
|'''Estimate'''
|-
|1
|<nowiki>-6.58</nowiki>
|January
|<nowiki>-0.24</nowiki>
|-
|2
|<nowiki>-3.56</nowiki>
|February
|<nowiki>-0.28</nowiki>
|-
|3
|<nowiki>-1.42</nowiki>
|June
|<nowiki>-0.54</nowiki>
|-
|4
|<nowiki>-0.48</nowiki>
|April
|<nowiki>-0.27</nowiki>
|-
|5
|<nowiki>-0.35</nowiki>
|May
|<nowiki>-2.07</nowiki>
|-
|6
|<nowiki>-0.35</nowiki>
|June
|<nowiki>-3.36</nowiki>
|-
|7+
|<nowiki>-0.00</nowiki>
|July
|<nowiki>-4.32</nowiki>
|-
|
|
|August
|<nowiki>-5.52</nowiki>
|-
|
|
|September
|<nowiki>-4.74</nowiki>
|-
|
|
|October
|<nowiki>-2.24</nowiki>
|-
|
|
|November
|<nowiki>-0.97</nowiki>
|-
|
|
|December
|<nowiki>-0.00</nowiki>
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" |'''''Table 3. Statistics of the difference between true and estimated 24-hour fat % for six regression formulas (current, re-estimated + five steps), each also including preceding steps.'''''
|-
|style="text-align: left;"|'''Regression'''
|'''Std.'''
|'''Min'''
|'''Max'''
|'''Cor'''
|'''b-factor'''
|-
|style="text-align: left;"|Current, re-estimated
|0.2856
|<nowiki>-1.840</nowiki>
|2.224
|0.898
|0.807
|-
|style="text-align: left;"|Non-linearity
|0.2820
|<nowiki>-1.890 </nowiki>
|2.198
|0.901
|0.812
|-
|style="text-align: left;"|Time of sampling
|0.2817
|<nowiki>-1.877 </nowiki>
|2.211
|0.901
|0.813
|-
|style="text-align: left;"|Lactation stage
|0.2803
|<nowiki>-1.883 </nowiki>
|2.196
|0.902
|0.814
|-
|style="text-align: left;"|Parity
|0.2794
|<nowiki>-1.887 </nowiki>
|2.179
|0.903
|0.816
|-
|style="text-align: left;"|Month of sampling
|0.2788
|<nowiki>-1.868 </nowiki>
|2.175
|0.903
|0.817
|}
</center>

Table 3 shows some statistics of the difference between the true and estimated 24-hour fat % based on dataset 2 (validation) of the different regression formulas. Each of the five changes to the regression formula had a (minor) positive effect on either the standard deviation of the difference between the true and estimated 24-hour fat % (Std.), the correlation (Cor) between the two fat %s, the b-factor of the linear regression between the two fat %s or a combination of the these. All changes together reduced the standard deviation with 2.4% from 0.2856 to 0.2788, increased the correlation from 0.898 to 0.903 and increased the b-factor from 0.807 to 0.817.

=== Conclusions ===
The regression formula to estimate the 24-hour fat % based on one milk sample was improved. Improvements were first of all considering non-linearity of the variables by using polynomials for protein % of the milk sample (3rd order), interval before sampling (3rd order), milk amount of sample (3rd order), milk amount of previous milking (3rd order) and interval before the previous milking (2nd order). Secondly, adding the effects of time of sampling (class variable), lactation stage (3rd order polynomial), parity (class variable) and month of sampling (class variable) gave a further reduction of the difference between true and estimated 24-hour fat %. The total reduction in standard deviation of the difference between true and estimated 24-hour fat % is 2.4% (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

</div>
</div>

== Appendix 3 - A unified Python implementation of standardized 305 day yield calculation methods ==
<div class="mw-collapsible mw-collapsed">
<div>
The ICAR guideline is translated into an open-source Python package that can serve as a reference implementation for 305-day yield calculation. In addition to implementing the methods described in the original guideline (with the exception of the multi-trait method, which will be added in future work), the package incorporates 14 lactation-curve models, including traditional parametric models, Bayesian fitting approaches, and an AI-based model. The package also provides tools to derive biologically relevant lactation characteristics such as time to peak, peak yield, cumulative yield, and persistency. The package is publicly available through PyPI and can be installed directly using pip install lactationcurve (van Leerdam et al., 2026). Extensive documentation was developed alongside the package to improve transparency and reproducibility [https://bovi-analytics.github.io/bovi/lactationcurve.html https://bovi-analytics.github.io/bovi/lactationcurve.html.]

Through a companioning website (https://tools.bovi-analytics.org<nowiki/>/), users can upload milk-recording data in CSV format, fit and visualize the implemented lactation-curve models, and compare different cumulative milk-yield methodologies on both test-day and fully daily-recorded lactations using metrics such as RMSE, Pearson correlation, MAPE, and MAE. Reference datasets are provided to allow organizations to benchmark their own calculations against alternative methodologies. In addition, downloadable PDF reports summarize the results through detailed statistics and scatterplots, both overall and stratified by parity.
</div>
</div>

Section 02 – Cattle Milk Recording

2026-07-22T17:55:08Z

Cmosconi: /* Procedure 1: Computing 24-hour Yields */

= Overview =
<div class="mw-collapsible mw-collapsed">
<div>
== Introduction ==
Information about milk production traits is very important for managing and breeding dairy herds. The milk recording process starts with the collection of animal identification, a calving date of milking cows, the amount of milk given and the date with time or time frame of a day. A milk sample may be taken. The obtained milk sample is analysed for milk constituents. The results of the analysis plus the data about milk yield and time of milking are stored in a database. Subsequently a number of parameters, cumulative yields and indices are calculated and stored in the database and, finally, reported to the farmer

This Section 2 of the ICAR Guidelines focuses on the milk recording process for dairy cattle.

== Scope ==
Figure 1 gives a pictorial summary of the main elements of this guideline.

In summary, this section of the ICAR Guidelines covers the milk recording process from the enrolment of a herd for milk recording, through to the delivery of information which a herd owner can use to assist in a range of decisions.
[[File:Scope of Section 2 - Dairy cattle milk recording..png|thumb|Figure 1. Scope of Section 2 -Dairy cattle milk recording.|center|524x524px]]

Not covered in this section are:
# Standards and guidelines for ICAR approval of milk recording devices. Please consult [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices|Section 11]] for this subject.
# Standards and guidelines for ICAR approval of ID devices. Please consult [[Section 10 – Identification Device Certification|Section 10]] for this subject.
# Standards and guidelines for preparation of milk samples and for quality assurance of milk analysis. Please consult [[Section 12 – Milk Analysis|Section 12]] for this subject.
# Standards and guidelines for in-line milk analysis on the farm. Please consult [[Section 13 – On-farm Milk Analysis|Section 13]] for this subject.

== Enrolment ==

Enrolment of new herds in the recording process should involve an agreement between the farmer and the recording organisation regarding technical and financial questions such as:

# General information about the recording programme itself, i.e.
#* Herd and cow identification.
#* Scope of recorded data, including database setup as required by the user.
#* Scheduling recording.
#* Data capture and processing.
#* Recording methods and intervals.
#* Milk measuring and meters.
#* Sampling and sample transport.
#* Reports (outcomes) and supporting decisions.
# Definition of supervision scheme and other quality assurance and plausibility checking steps.
# Fee structure and invoicing.
# Approval of technicians by milk recording organisations (MROs) so as to give them free access to farms for all recording and supervision actions.

In cases where the owner of the recorded cows or his employees carry out the recording itself, it is up to the organisation to decide upon, and provide for, any necessary training.

== Standard and Guidelines for Milk Recording ==
These standards and guidelines for milk recording are valid for all milking systems, including AMS where applicable.
====General Standards and Guidelines for milk recording====
#ICAR-approved (electronic) milk meters and sampling devices must be used on the recording day (see [https://wiki.icar.org/index.php/Section_11_%E2%80%93_Testing,_Approval_and_Checking_of_Measuring,_Recording_and_Sampling_Devices#Procedure_1:_Procedure_for_Application_for_Testing_of_Measuring,_Recording_and_Sampling_Devices_or_Sensor_Systems Procedure 1 of Section 11 - Guidelines for Testing, Approval and Checking of Milk Recording Devices]). The list of approved milk meters, jars and AMS and automatic milk sampler/tray combinations sampling devices can be found on the [https://www.icar.org/index.php/certifications/icar-certifications-for-milk-meters-for-cow-sheep-goats/ ICAR web page].
#Milk weights are recorded for each milking of the recording period. The measurement may be done using any of the ICAR approved recording devices, or by weighing. The minimum accuracy of the measurement is 0.2 kg.
#Where milk constituents are analysed, the equipment used must meet ICAR standards for accuracy. Please consult [[Section 12 – Milk Analysis|Sections 12]] and [[Section 13 – On-farm Milk Analysis|Section 13]] of the Guidelines for details.
#The accuracy of the equipment used for milk recording and sampling must be checked by an agency approved by the member organisations, on a regular and systematic basis using methods approved by ICAR. The list of methods is given in [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices#Procedure 6: Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices|Procedure 6 of Section 11]] - Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices.
#All analyses of the constituents of a milk sample must be carried out on the same milk sample.
#These samples should ideally represent the 24-hour milking period.
#If milk samples do not represent a 24-hour period, the results of milk analyses must be corrected to a 24-hour period by a method approved by ICAR (see [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]).
#In cases where the duration of recording deviates from 24 hours, the results must be converted into 24-hour yields. Only approved 24-hour yield calculation methods can be used. The appropriate methodology is described in [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]
#As date of recording, we recommend to use the date on which the last sample was taken. As alternative, the date of the first sample can be used.
#Calculation methods
##The quantities of milk and milk constituents shall be calculated according to one of the methods outlined in this section of the ICAR Guidelines (see [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Standard methods for calculating 24 hour yields]).
##Member organisations should keep the ICAR Secretariat informed about the calculation methods being used by the records processing operations in their organisation or country and shall be responsible for ensuring that the records are corrected and calculated as specified in this section of the ICAR Guidelines.
====Standards and Guidelines for milk recording using AMS====
This subsection covers systems where milk weights, milk quality or other traits of the cows are monitored constantly and automatically. This can be done in both automatic and manually operated milking systems.

Requirements:
*Animal identification is automatic and reliable. Farm transponders can also be used for automatic identification if they are linked to the cow’s official identification in farm software.
*All individual milkings must be recorded from all AMSs in the farm and transmitted to the recording database for calculation, interrupted milkings included.
*For official milk recording purposes, the data file obtained from electronic milk meters must contain the following: 1) Cow ID, 2) Milking time stamp, 3) Milk weight and 4) Sampling stamp to mark the milking where the sample comes from.
*All milkings within the recording period may be sampled, and in this case the samples should be analysed separately. Alternatively, a one-milking sample can be taken for each cow, followed by fat correction calculation.
*All cows in milk on the recording day have to be sampled. The sampling device must remain in operation until all cows are sampled. When the number of available sampling devices is smaller than the number of AMS units, sampling may need to be prolonged beyond one day to allow complete sampling of all cows. In that case, the sampling device has to be moved between AMS units.
*During sampling, the automatic sampler must be monitored to make sure there are vials left for the next cows.
*24-hour yield calculations must be carried out by a MRO, independently of the AMS manufacturer. This is done in order to guarantee harmonisation of calculation methods between the different brands of equipment and software.
*Data of all milkings over a given time period must be collected for the 24-hour milk yield calculation. A 96-hour data collection period is recommended.
Recommendations:
#Ideally, data of all milkings should be collected and used to compute lactation yield.
#Description of formats to exchange data recorded by an AMS can be requested from the manufacturer or the ICAR ADE data exchange standard for milking data can be used.
#In the case of milk recording method B (see [[Section 02 – Cattle Milk Recording#Recording|chapter 1.4 "Recording]]") with AMS, the milk recording organization should make sure that the farmer knows how to load or transfer data.
#Data can be extracted by: 1) manual operation by MRO Technician’s or Farmer (file extraction), 2) automated system and data transfer through an Application Programming Interface (API), 3) another data transfer and exchange system.
#Raw milk recording data from the AMS must be easily accessible for MRO data processing.
#For official milk recording purposes, the data file obtained from electronic milk meters may also contain the following: 1) Vial ID (this is obligatory with M sampling scheme), 2) Milking duration, 3) Milking speed, 4) Incomplete milking in automatic milking systems and 5) Other relevant data measured or reported by the equipment.
#Individual milkings should be tested for milk secretion rate in order to detect interrupted and unrecorded milkings, which in turn have an effect on the calculated 24-hour yields. If there is an interrupted milking or a milking that follows an interrupted milking at the beginning of the recording period, these two milkings must be excluded from the calculations. During the recording period they can be excluded but do not need to be.
#It is recommended to individually sample all milkings within the 24-hour recording period for 24-hour fat content calculation due to the high variability of milking frequency and milk fat content. In cases where sampling all milkings is not possible, please consult Chapter 2 of [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 - Computing 24-hour Yields] (for approved correction calculation methods).
#It is recommended to sample only milkings with a preceding interval longer than 4 hours.
====Authorisation to record====
It is recommended that professional milk recording technicians are trained and certified before they carry out recordings on their own. Ideally, such training includes a period of supervised work with a certified technician. Where such a certification system is in place, it is not allowed to record without an authorisation.

It is also recommended that frequent training is given to milk recording technicians on new technologies and equipment, safety instructions and data quality issues.

In B and C recording, farmers or their employees doing the practical recording need to be capable of operating the recording equipment correctly (e.g. milk meters, data capture tools) and are familiar with recording techniques.

It is recommended to have a conformation test from a certified recording agency and that frequent training take place.
====Cows to be recorded====
In a recorded herd, all milk-producing cows must be recorded. If a herd is divided into groups, all animals in the group have to be recorded on the same recording scheme. If different recording schemes are practiced on the farm all cows must be recorded according to the standards for recording and sampling intervals in table 3.

Acceptable reasons for missing data are discussed below, in 5.5. Missing results and/or abnormal intervals are reported [[Section 02 – Cattle Milk Recording#Missing results|here]].

===Identification (ID)===
====Herd ID====
Each herd in milk recording must be allocated a unique permanent identification number.
====Animal ID====
An official milk recording system must be based on a clearly identifiable and unique animal ID. It is recommended that one identification scheme for the whole country is used. Animal identification must also be in accordance with national and international regulation (e.g. EU member countries with EU legislation - 1760/2000 for cattle), and with relevant parts of currently valid ICAR Guidelines. The animal must be marked with an ICAR approved identification device or system. If the ID of imported animals is changed, the connection to the original ID must be maintained. Management numbers for cows can be used aside the official ID.
====Identification of the sample vial====
The sample, the milk weight and the cow ID must be linked at the milking.

Vials can be identified according to:
#Vial placement in the sampling unit.
#Cow or sample ID written on the vials.
#Barcoded vial with printed cow ID.
#Barcoded vial with cow ID registered at the milking.
#RFID vial with cow ID registered at the milking.
=====Sample identification without electronic equipment=====
Samples are identified according to their placement in the sampling unit. Additionally, sample or cow numbers can be written on the vials with a waterproof marker. If this marking is not done, there must be a sure and efficient way to identify sample No. 1 (e.g. different colour) and the sequence of other samples.

Each sampling unit must be connected to a list of samples where cow ID is given for each sample. Each transportation box also has to carry the relevant herd ID’s and, preferably, the sampling dates.
=====Barcoded vials=====
Samples are identified according to the barcode on the vial label.

If the label contains cow and/or herd ID, no electronic equipment is needed at the recording. The samples can be sent to the laboratory without accompanying sample lists or herd ID markings on the box.

If the label contains a random sample ID number, the cow ID must be connected with it on the farm. This is done with a barcode reader and computer programmes making the connection possible.
=====Vials with RFID=====
Samples are identified according to the RFID chip in the vial. This system requires the use of RFID readers and specific computer programmes creating a file where the cow and vial ID’s are connected.
=====Automatic sampling systems=====
In automatic milking systems (AMS), ICAR approved automatic samplers have to be used. Sample identification in these systems can be based on vial placement, barcode or RFID. The file with corresponding cow ID is in the management programme of the milking system. Data transfer is carried out with specific software and via a specific interface from the AMS to the MRO.
=====Sample ID in the laboratory=====
For impartiality and better quality, it is recommended that the samples are identified without cow ID and sent to the laboratory anonymously and the analysis results are merged afterwards in the data processing centre.
====Connection of the sample to milking and 24 h yield====
=====Sample and milk weight from the same milking=====
The ideal situation is that the sample and milk weight represent the same milking.
=====Sample from one milking, milk weight from two=====
A corrected analysis is routinely attached to the 24-hour yield.
=====Sample from one milking, milk weight from two or more, corrected by intervals=====
In this case, a 24-hour-yield is also combined with a one-milking sample, but the 24‑hour yield is obtained by correcting the recorded milkings according to the length of the preceding milking intervals. For example, if a cow has produced 20 kg milk in two milkings and the preceding intervals total 20 hours, her 24-hour yield is calculated as 20 kg * (24 h/20 h) = 24 kg. A corrected analysis is attached to this 24‑hour yield.
=====Sample from one milking or day, milk weight from several days=====
With electronic milk meters, it is possible to use the milk production from several days. This gives better accuracy of milk yield estimation; the highest accuracy with uncorrected milk weights is reached using a 4-day average. The problem is that the sample results become disconnected from the milk yield and a loss in fat and protein yield accuracy will occur. Ideally, fat and protein production should be connected to the recording day even in AMS.

In this case, there are three options to connect samples to the 24-hour yield:
#Milk weight is estimated from a longer measurement period but for fat and protein yield estimation only the milk yield on sampling day is used.
#Information only from the recording day for constituents in milk and milk yield estimation.
#Combination of multiple day milk yield with constituents from sampling. See ICAR procedures for using data from more than one day (Lazenby ''et al''., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>, estimation of fat and protein yield (Galesloot and Peeters , 2000)<ref name=":1">Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>.
The analysis data are merged with milk weights in the laboratory or data processing centre and the date of the analysis must be known.

=== Traits to be recorded ===

==== Definition of milking speed and box time ====

===== Introduction =====
Automated Milking Systems (AMS) do measure many traits. The definition of these traits might be different per brand of AMS. Data of these traits is often used by e.g. milk recording organisations, herdbooks or management software providers. When organisations store these data in their databases and use for certain services, it is important to know how these traits are defined.

These definitions could be used by milk recording organisations etc. to take into account differences between traits measured by different brands of AMS. These definitions could also be used by manufacturers of AMS to take into account for product development, to get more alignment in trait definitions between different brands of AMS.

Aim of this document is to propose a harmonized definition of some traits measured by AMS.

At this stage, the traits milking speed and box time are taken into account. Traits related to teat coordinates are described in Section 5 (Conformatoin Recording) of the ICAR guidelines.

==== Average milking speed ====
Definition = AverageMilkingSpeed (gr/min) = {TotalMilkYield / TotalMilkingTime}

* Total milk yield (kg) = Sum of all quarter level milk yields (kg)
* Total milking time = Last Take-off time (of any teat) - Begin of milk flow (of any teat)

Recommendations for manufacturers:

* Exclude any pre-treatment time from milking time.
* Provide take-off settings (threshold in gr/min at take-off, user-defined or default) and settings for the beginning of the measurement period, as milking time will be influenced by take-off settings and by the definition of the beginning of the milk flow.

Recommendations for data users:

* Don't report milking sessions with kick-off´s, interrupted and re-attached milkings because milking time will vary for these milkings.

==== Box time ====
Different types of box time:

* Milking
* Feed-only
* Pass-through
* Selection
* Training

Definition = {End box time - Begin box time} (HH:MM:SS)

* Begin box time = datetime of recognition of animal
* End box time = datetime when cow has exited the box (which might be different from opening of the gate), best to detect when cow has actually left the box

Additional data is needed to understand the status and completeness of the milking visit (Wethal and Heringstad, 2019). Registered issues during the milking are e.g.

* ff: at least 1 teat cup kicked off
* TeatNotFound: unable to find at least 1 of the teats for milking
* IncompleteMilking/FailedMilking: Minimum of 1 teat was registered as incompletely milked.
* The expected milk yield for a milking session depends on previous milkings. Settings like yield less than 80% of expectation for a teat, the milking session would be recorded as having an incompletely milked teat.
* Manual interaction like teat manually attached or milking finished manually.

Recommendations for manufacturers:

* Make the codes available that express if a milking was successful and the cause if the milking was not successful.
* Uniform names and definitions for interrupted, incomplete or failed milkings as well.

Recommendations for data users:

* Check the availability of a code that expresses if a milking was successful and the cause if the milking was not successful. The meaning of the code can be used to consider if the box time record has to be used for the intended purpose or not.
* To check if there is any extra box time due to feeding concentrates, e.g. through user specific settings such as 'PriorityFeeding'.

=== Traits to be recorded ===
In official milk recording, the following data have to be recorded, wherever available:

# Identification of each cow in the herd, even if they remain in the herd for a very short time.
# Birth date, sex, breed and parents of each animal when known.
# All services and embryo flushings and transfers: date, recipient, sire, dam of the embryo.
# All animal deaths and movements between farms and owners.
# Recording dates and locations.
# Milk yields for each cow and recording date.
# Fat content in milk for each cow and sampling date.

It is recommended to record also the following:

# Protein content in milk for each cow and sampling date.
# Milk somatic cell count for each cow and sampling date.
# Other results obtained from milk analysis.
# Milking duration and milking speed where possible.
# Milking times during recording.
# Recording methods and respective symbols used in records.
# Information about cow during the rearing period.

=== Recording method ===
The recording method for the herd consists of using five different symbols for:

# Responsibility for the practical recording.
# Sampling scheme.
# Recording interval.
# Sampling interval (if different from the above).
# Number of milkings per day (especially any deviation from 2x milking).

The symbols in Table 2 should be used:<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Symbols for milk recording schemes.''
|- style="background-color:#efefef; text-align:center;"

|'''Responsibility for recording'''
|'''Sampling scheme'''
|'''Recording interval (weeks)'''
|'''Sampling interval (weeks)'''
|'''Number of milkings per day'''
|-
| style="text-align:center;" | A
| style="text-align:center;" | P
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | B
| style="text-align:center;" | E
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | C
| style="text-align:center;" | Z
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" |
| style="text-align:center;" | T
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" |
| style="text-align:center;" | M
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:center;" | R x
|-
| style="text-align:center;" |
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | S x
|}
</center>

As an example: Recording method is CP36, 2x means that this is a recording where records/ samples are taken partly by the owner (farmer), and partly by a technician from the MRO, where the recording frequency is every 3 weeks, where the sampling frequency is every 6 weeks, and where the number of milkings per day is 2. If a national nomenclature system is used, it should be possible to transfer this system into ICAR nomenclature.

The reference milk recording method is by a representative of the recording organisation, measuring and sampling every four weeks, with proportional sampling and two milkings per day (AP44, 2x).

Recording other than by the reference method must be indicated using the appropriate symbols.

It is recommended that a limit is set for changing the recording method e.g. so that normally it is only possible to change the method twice per year.

It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

In the next sections the symbols are explained:
====Responsibility for the recording====
This symbol indicates who is responsible for measuring the milk yields and taking samples in the herd.
#Representative of the MRO (Method A; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Farmer or his/her representative (Method B; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Mixed responsibility (Method C; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
====ICAR Standards for sampling schemes====
=====Proportional sampling (P)=====
Samples and milk weights are taken at each milking during the recording day. The sampled amount corresponds to the milk yield of each milking. This is achieved by the use of a pipette in equal number of pipetting at each milking or of a specially designed tool which ensures proportional sampling to create one mixed sample. This is the default sampling scheme with no necessary correction to the analysis results, all other schemes must be reported.
=====Equal measure sampling (E)=====
Samples and milk weights are taken at each milking during the recording day. The amount of the sample is measured to be equal at each milking and mixed into one sample. The analysis results for fat should be corrected if one of the milking intervals is shorter than 10 or longer than 14 hours.
=====Multiple sampling (M)=====
Samples are taken at more than one milking during the recording day while milk weights are taken at each milking or over several days. Samples from different milkings are not mixed but they are kept in distinct vials so that each cow has at least two samples. The analysis results must be corrected to correspond to the 24-hour fat and protein yields. For example: a cow is milked 3x during 24 hours and 2 or 3 separate samples are taken, kept and analysed in different vials. This is the gold standard for AMS. It produces the most accurate results but is more expensive.
=====One-milking sampling with milk weights from more than one milking (Z)=====
Samples are taken from one milking during the recording day while milk weights are taken at each milking or over several days. The analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Alternated one-milking recording (T)=====
Samples and milk weights are taken during one milking, alternating between morning and evening milkings. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Constant one-milking recording (C)=====
Samples and milk weights are taken during one milking, constantly during morning or evening milking. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====In-line analysis recording (I)=====
Milk is not sampled but its constituents are continuously analysed by a stationary analyser.
====ICAR Standards for recording and sampling intervals====

<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Standards for recording and sampling intervals.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| rowspan="2" style="text-align:center;" |'''Recording or sampling interval (weeks)'''
| rowspan="2" style="text-align:center;" |'''Minimum number of recordings or samplings per year'''
| colspan="2" style="text-align:center;" |'''Interval between recordings or samplings (days)'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| rowspan="10" style="text-align:center;" |Reference method
| style="text-align:center;" |1
| style="text-align:center;" |44
| style="text-align:center;" |4
| style="text-align:center;" |10
|-
| style="text-align:center;" |2
| style="text-align:center;" |22
| style="text-align:center;" |10
| style="text-align:center;" |18
|-
| style="text-align:center;" |3
| style="text-align:center;" |15
| style="text-align:center;" |16
| style="text-align:center;" |26
|-
| style="text-align:center;" |4
| style="text-align:center;" |11
| style="text-align:center;" |22
| style="text-align:center;" |37
|-
| style="text-align:center;" |5
| style="text-align:center;" |9
| style="text-align:center;" |32
| style="text-align:center;" |46
|-
| style="text-align:center;" |6
| style="text-align:center;" |8
| style="text-align:center;" |38
| style="text-align:center;" |53
|-
| style="text-align:center;" |7
| style="text-align:center;" |7
| style="text-align:center;" |44
| style="text-align:center;" |60
|-
| style="text-align:center;" |8
| style="text-align:center;" |6
| style="text-align:center;" |50
| style="text-align:center;" |70
|-
| style="text-align:center;" |9
| style="text-align:center;" |5
| style="text-align:center;" |55
| style="text-align:center;" |75
|-
| style="text-align:center;" |Daily
| style="text-align:center;" |310
| style="text-align:center;" |1
| style="text-align:center;" |3
|}
</center>

====ICAR standards for number of milkings per day====

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 3. Symbols for number of milkings per day.''
|- style="background-color:#efefef; text-align:center;"
|'''Number of milkings per day'''
|'''Symbol'''
|-
| style="text-align:center;" | Once per day milking
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | Two milkings
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | Three milkings
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" | Four milkings
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" | Continuous milking (e.g. AMS)
| style="text-align:center;" | R x
|-
| style="text-align:center;" | Regular milkings not at the same times on each day (e.g. 10 milkings per week)
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" | Shown as the average number of milkings per day.
| style="text-align:center;" |
|-
| style="text-align:center;" | Animals that are both milked and suckled. (Number of times milked to prefix the S)
| style="text-align:center;" | S x
|}
</center>

Where a herd is dry for a period of the year, the minimum number of recordings should be adjusted proportionately to the production period.

Minimum number of herd recordings should be at least 85% of the normal number of recordings.

=== Missing results and/or abnormal intervals ===
{{anchor|Missing_results}}A recorded 24-hour yield is the best estimate of the yield and the constituents of the milk, weighed, sampled and recorded within 24 hours on the day of recording.
#When herds are normally milked at intervals such that the recording day is other than 24 hours, the yields shall be adjusted to a 24-hour interval using the following procedure (or other procedures approved by the ICAR):
#*Divide 24 by the interval, then multiply by the yield. For example:
#**For a 25 hour interval (24/25) x 35 kg = 33.6 kg
#**For a 20 hour interval (24/20) x 35 kg = 42.0 kg
#A recording is a set of daily test values for a given animal on a given day of recording, one or some or all of them can be missed (missing values)
#Missing values can be due to:
#*Out of range.
#*Sickness.
#*Disaster.
#*No sample analysis results.
#The number of the official and complete (milk, fat and protein) recordings in the lactation or other accumulated yield should be reported.
#Permitted range of the daily recorded values is given in Table 5. Outside of these ranges, the daily recorded<ref>'''Note:''' High fat breeds have breed average higher than 5.0 for fat %.</ref> value will be considered as a missing value.

<center>
{| class="wikitable"
! colspan="7" style="text-align:left;" | ''Table 5. Permitted range of the daily recorded values.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| colspan="2" style="text-align:center;" |'''Milk (kg)'''
| colspan="2" style="text-align:center;" |'''Fat %'''
| colspan="2" style="text-align:center;" |'''Protein %'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| style="text-align:center;" | Main Dairy Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 1.5
| style="text-align:center;" | 9.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 7.0
|-
| style="text-align:center;" | High Fat1 Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 2.0
| style="text-align:center;" | 12.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 9.0
|}
</center>1Note: High fat breeds have breed average higher than 5.0 for fat %The true daily recorded values collected from animals labelled by the farmer as sick, injured or under treatment must be used in the computation of the lactation record unless the milk yield is less than 50% of the previous milk yield or less than 60% of the predicted yield. In such a case, the whole set of daily recorded values may be considered as missing.

Estimates of the missing values of a daily recording can be computed by using interpolation procedures or by more sophisticated procedures approved by ICAR

== Samples ==

=== Representative sample ===
The milk sample has to represent the complete milking linked to it. This is achieved by mixing the milk thoroughly or pouring it into another vessel right before sampling.

Sampling scheme P requires using a pipette for making the sample proportional between different milkings.

With sampling scheme E, it is advisable to use a measuring cup to make sure the sample parts actually are equal.

Immediately after sampling, the vials have to be preserved, capped, shaken and marked. Samples should be stored cool and dark.

=== Transport ===
Samples should be transported for analysis to a laboratory as soon as possible after sampling.

The samples need to be packed for transport and handled during transport in a manner that guarantees that sample IDs are not compromised or mixed. It is also recommended to protect the packages from external interference.

The packing material must be clean and disposable or easy to clean.

During transportation, it is recommended that the temperature of the samples stays below +10°C.

== Database ==
Storing the recorded data in a milk recording database is an indispensable part of the recording. It is recommended to use the quickest possible means to store the data in the database in order to ensure up-to-date breeding values and management applications. Where computerised data capture is possible, it should not take more than five days after the recording to have the complete recording data set in the database.

The application of the Guidelines in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield], together with other parts of the Guidelines, ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

The guidelines on storage of data collected by the milk recording process are:

# For every recording, cow identification (ID), 24-hour milk yield or individual milk yields with a minimum of 0.2 kg (or the equivalent thereof) milk accuracy and recording date have to be stored.
# Where possible, it is advisable to store each milking separately. The data stored can include milk yield, time and date of milking, and milking scheme.
# Analysed results of the milk sample are stored, namely: sample ID, fat content (or percentage), sample status, sample type. Optional data can be stored on protein and/or lactose content, somatic cell count and additional analyses.
# Analysis results can be linked to one or more milkings of the cow.
# In case of storage or performance problems it might be necessary to remove old data of individual cow milkings from the database.
# Recording day information is the yield over 24 hours and should at least be kept in the database for the current lactation and the previous lactation.
# If recording day information is changed after batch processing it should be marked with a user-ID and time stamp.
# Yields are stored in kg or lbs or, in the case of fat and protein contents, in percent units.

The necessary additional information about how the results have been obtained include:

# Who did the recording (certified technician, farmer etc.).
# Herd and/or cow milking frequency.
# How many milkings were measured.
# How many milkings were sampled.
# Sampling scheme when sampling.
# Daily yield calculation method used.
# Recording and sampling intervals.
# It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

Basic checks for recording data:

# Farm (herd) ID: identified by a unique key.
# Animal ID: has to be unique in database.
# Format of animal ID: compliant to international standards of identification and registration.
# Recording date: less than or equal to today, greater than last recording date.
# Milk yield: stored with one decimal.
# 24 hour milk yield within range ( Table 5).
# Fat and protein content: e.g. within a range of +/- 3 standard deviation of population average (Table 5).
# Calving date: greater than birthday of cow (e.g. greater than birthday of cow + 20 months).
# Calving date: less than or equal to today.
# Sample analysis

This section of the ICAR Guidelines examines how observations are performed on farms and how data are collected, analysed and reported back to farmers. It forms an integral part with other sections of the ICAR Guidelines. It ensures that samples are analysed to the relevant degree of accuracy for the purposes of milk recording, breeding value prediction and other areas of usage. ICAR members operate in a range of situations, ranging from places with almost fully automated recording systems to areas with no roads and electricity. Therefore, the guidelines only demand standards that can be followed, irrespective of production situations and recommend more advanced options, where possible or required. Under the guidelines some practices might not be permitted while other practices are tolerated but not recommended.

== Yield calculations ==
This section covers 24-hour yields and accumulated yields for milk, fat, protein and somatic cells. It also describes the procedure for acceptance of new methods not previously mentioned in the guidelines.

The basic requirements for all calculation methods are that rounding shall only take place at the last step of the computation.

=== Lactation period ===

==== Commencement of the lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, is considered to commence is:

# The day that the cow calves (calving date), or
# In the absence of a calving date, the best estimate of the day that the cow commenced milk production.

A (valid) calving is defined as a parturition taking place:

# After the mid-point of the gestation period if a service has been recorded, or,
# After at least 75% of the normal gestation period has elapsed since the previous calving recorded if no service event has been recorded.

Any parturition falling outside the above definition shall be recorded as an abortion and shall not start a new lactation period.

For cows of dairy breeds the normal gestation length shall be deemed to be 280 days unless more specific breed information is available for use.

If the first recording is done on the calving date or within the first 4 days after calving, the milk yield and constituents at the first recording should not form part of the official lactation record, especially for automated milking systems (AMS) with multiple recorded days.

==== Completion of lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, has been completed is or:

# The day that the cow ceases to give milk (goes dry) or
# The day the cow gives less than 3.0 kg/day or 1.0 kg/milking in a recording (unless recorded sick) or
# When it is common practice not to record the dry-off date, the day of the midpoint between the last recording with the cow in milk and the first recording day with the animal dry may be assumed to be the dry-off date.

The lactation period ends on whichever date above occurs first.

Cows may be recorded as absent or sick on the recording day, without the lactation period being defined as terminated.

=== Production period ===
In the case where yield records are calculated on the basis of a period of production, usually a year, the record should be expressed as a ‘production period record‘ (symbol PP).

The production period begins the day after the end of the previous production period and ends as defined by the length (in days) of the production period.

=== Additional notes ===
For any ICAR method the interval between two consecutive recordings must routinely fulfil the value for the acceptable range on the herd level.

If the first recording occurs within 14 days from calving, then no adjustment is required to the first recorded value when computing the accumulated record. If the first recording occurs 15 to 95 days from calving, then an adjustment procedure may be applied.

If the 305th day of a lactation falls before the last recording, the interpolation method should be used also for the last period to compute the yields.

=== Standard methods for calculating 24 hour yields ===
The ICAR approved methods are presented in '''[https://www.icar.org/Guidelines/02-Procedure-1-Computing-24-Hour-Yield.pdf Procedure 1 of Section 2]'''. They include:

1. Methods for calculating daily yields from AM/PM milkings:

# Method of Delorenzo and Wiggans (1986)<ref>Delorenzo, M.A., and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. [https://www.journalofdairyscience.org/article/S0022-0302(86)80678-6/pdf J Dairy Sci 69; 2386]</ref>
# Method of Liu et al. (2019). Please note that in 2022 the method of Liu et al. (2000)<ref name=":0">Liu, Z., R. Reents, F. Reinhardt and K. Kuwan. 2000. Approaches to Estimating Daily Yield from Single Milk Testing Schemes and Use of a.m.-p.m. Records in Test-Day Model Genetic Evaluation in Dairy Cattle. [https://www.journalofdairyscience.org/article/S0022-0302(00)75161-7/pdf J. Dairy Sci. 83:2672-2682].</ref> has been updated to the method of Liu et al. (2019). We recommend to organisations that currently have implemented the method of Liu et al. (2000)<ref name=":0" /> to update to method of Liu et al. (2019).
# Method of Kyntäjä et al. (2021)<ref name=":3">1. Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. [https://www.icar.org/Documents/technical_series/ICAR-Technical-Series-no-25-Virtual-Meeting/Kyntaja.pdf ICAR Technical Series no. 25: 171-175.]</ref>

2. Methods to estimate 24h yield from Automatic Milking Systems:

# Using data on more than one day (Lazenby et al., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Using data on 1 day (Bouloc et al., 2002)<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Estimation of fat and protein yield (Galesloot and Peeters, 2000)<ref>Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>
# Sampling period (Hand et al., 2004<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D.F. 2004. Comparison of Protocols to Estimate 24 Hour Percent Fat and Protein. Presented at 34th ICAR session, Sousse, Tunisia, June, 2004. Proceedings of the 34th ICAR Meeting EAAP Publication No. 113:219-224</ref>; Bouloc et al., 2004)

3. Standard methods to estimate 24h yield from electronic milk meters:

# Estimation of 24-hour milk yield
# Using data on more than one day (Hand et al., 2006)<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. [https://doi.org/10.3168/jds.S0022-0302(06)72240-8 J. Dairy Sci. 89:1723-1726]</ref>
# Estimation of 24-hour fat and protein yield

=== Standard methods for calculating accumulated yields ===
The ICAR approved methods are presented in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_2_%E2%80%93_Computing_of_Accumulated_Lactation_Yield Procedure 2 of Section 2]. They include:

# Test Interval Method (TIM) (Sargent, 1968)<ref>Sargent, F.D., V.H. Lyton, and O.G. Wall, Jr . 1968. Test interval method of calculating Dairy Herd Improvement Association records. [https://doi.org/10.3168/jds.S0022-0302(68)86943-7 J. Dairy Sci. 51:170].</ref>
# Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987)<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. [https://doi.org/10.1016/0301-6226(87)90049-2 Livest. Prod. Sci. 17:l].</ref>
# Best prediction (VanRaden, 1997)<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. [https://doi.org/10.3168/jds.S0022-0302(97)76268-4 J. Dairy Sci. 80:3015-3022].</ref>
# Multiple-Trait Procedure (MTP) (Schaeffer and Jamrozik, 1996)<ref>Schaeffer, L.R. and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. [https://doi.org/10.3168/jds.S0022-0302(96)76578-5 J. Dairy Sci. 79:2044-2055.]</ref>

=== Procedure to approve new methods ===

# All parties interested in seeking approval for any new accumulated yield calculation method will notify the ICAR Secretariat and provide a description of the proposed method.
# These parties will provide a detailed report including statistical details, scientific references and other relevant data to the ICAR Dairy Cattle Milk Recording Working Group.
# The ICAR Dairy Cattle Milk Recording Working Group will then consider the proposal and recommend that it be conditionally approved, approved or rejected.
# The final steps will consist of approval by the General Assembly and publication in the guidelines. .

== Reporting ==
This subsection covers reports, data files, statistics and calculated key figures provided to farmers for breeding and management purposes.

It is recommended that farmers are given reports after each recording and at the end of the recording year or another longer recording period. These reports should contain data on both cow and herd level. In bigger herds, it is also advisable to present results by management groups or otherwise chosen cow groups within the herd. The reporting may be done on paper, through web pages and/or in the form of data files or electronic reports.

Where data files are distributed or direct access given to the results in the database, care must be taken that data ownership is clearly defined. This also includes defining who has access to data and how this access can be authorised.

ICAR members are advised to prepare annual statistics in a reasonable timeframe after closing the recording year. The minimum data requirements are what is needed for the ICAR [https://my.icar.org/stats/list Dairy Cattle Yearly Enquiry on-line database].

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 5. Examples of key figures for herd to be used by farmers and other users.''
|- style="background-color:#efefef; text-align:center;"
|style="text-align:left |'''Key figure'''
|style="text-align:left |'''Explanation'''
|-
| style="text-align:left;" | 12-month rolling average yield
| style="text-align:center;" | Total milk, fat and protein produced during the 365 (366) days preceding the recording divided by the average number of cows for the same period.
|-
| style="text-align:left;" | Average 305-day yield
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations finished during the reporting period divided with the number of finished 305-day lactations.
|-
| style="text-align:left;" | Average 305-day yield within a period
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations during the reporting period divided with the average number of cows on a 305-day lactation within the reporting period.
|-
| style="text-align:left;" | Average annual yield
| style="text-align:center;" | Total milk, fat and protein produced during the recording year divided by the average number of cows for the same recording year.
|-
| style="text-align:left;" | Average calving interval
| style="text-align:center;" | The average preceding intervals of all calvings second and more during the reporting period.
|-
| style="text-align:left;" | Average fat, protein or lactose contents in milk
| style="text-align:center;" | Total fat, protein and lactose yields divided by the total milk yield, usually expressed with two decimals.
|-
| style="text-align:left;" | Average lactation yield
| style="text-align:center;" | Total milk, fat and protein produced within lactations of any length finished during the reporting period divided with the number of finished lactations.
|-
| style="text-align:left;" | Average lactation yield within a period
| style="text-align:center;" | Total milk, fat and protein produced during the reporting period divided with the average number of cows in milk within the reporting period.
|-
| style="text-align:left;" | Average number of cows
| style="text-align:center;" | Average number of cows in the herd (or group) on a given day during the reporting period. Usually expressed with one decimal.
|-
| style="text-align:left;" | Average somatic cell count
| style="text-align:center;" | The average of all individual cow somatic cell counts weighted for individual milk yields.
|-
| style="text-align:left;" | Daily milk, fat and protein yields
| style="text-align:center;" | 1) Total daily milk, fat and protein yields divided by number of cows, or 2) Total daily milk, fat and protein yields divided by number of cows in milk.
|-
| style="text-align:left;" | Energy Corrected Milk (ECM)
| style="text-align:center;" | Calculated according to a national standard.
Example from the Nordic countries:

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + milk yield, kg * 0.7832)/3.14

or, if lactose has been analysed

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + lactose yield * 16.54 + milk yield, kg * 0.0207)/3.14.

From solids expressed as %:

ECM = [(fat content, % * 383 + protein content, % * 242 + 783.2)/3140]* milk yield, kg

or, if lactose has been analysed

ECM = [(fat content, % * 383 + protein content, % * 242 + lactose content, % * 165.4 + 20.7)/3140]* milk yield, kg.
|-
| style="text-align:left;" | Number of lactations
| style="text-align:center;" | Total number of finished lactations in the herd (or group) during the reporting period.
|-
| style="text-align:left;" | Reporting period
| style="text-align:center;" | The period presented in the given report. The most usual options are: one day, one recording interval, lactation, rolling 365 days, recording or calendar year, and the cow’s lifetime.
|}
</center>

== Decisions ==

As a result of the recording process and reports prepared on the basis of its results, decisions can be made on one or more of the following:

=== Short term impact: day-to-day management decisions taken on farms ===

# Decisions about bulk milk quality.
# Feeding decisions - daily diet based on group or individual performance.
# Pasture management decisions.
# Grouping decisions - placing cows in different management or feeding groups.
# Culling decisions - decisions on the sale or slaughter of cattle.
# Mating decisions.
# Decisions regarding programmes of certification for milk and milk products.
# Decisions based on data flow from MRO’s to farms and vice versa.

=== Medium-term impact ===

# Farmers’ decisions based on advisory services, veterinarians, independent experts and other services.
# Decisions about production planning on farms (herd development).

=== Long-term impact ===
# Breeding programme and selection decisions - breeding partners informed by genetic evaluation ([[Section 09 – Dairy Cattle Genetic Evaluation|Section 9)]] based on milk recording results.
# Decisions based on herd book and breeder association activities and deciding on business actions related to breeding animals, i.e. in some countries animal recording data are required for international trade with breeding animals.

=== Strategic decisions ===
# Research programmes concerning management, recording and breeding.
# Political decisions about possible subsidies in dairy cattle breeding at the governmental level and implementing measurements according to agriculture policy.

== Quality control ==
This Section together with other parts of the Guidelines ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

=== Bulk tank data comparison ===
It is a recommended practice to compare milk recording data with dairy deliveries and bulk tank milk contents. This can be done on the recording day or over a longer period of time. The calculation is done as follows:

# Comparison ratio = Total recorded milk yield, kg /Total milk produced, kg. This comparison is used where there is a reliable estimate of the farm use of milk.
# Quick comparison ratio = Total recorded milk yield, kg/ Total milk delivered, kg. This comparison is used where farm use of milk is not estimated.
# Content comparison = Recorded average fat / Bulk tank average fat
# Comparison ratio for fat = Total recorded fat yield, kg/ Total fat produced, kg
# Total recorded milk yield, kg = Ʃ (Individual milk yield, kg)
# Total milk delivered, kg = Total milk delivered, litres * milk density kg/litre
# Total milk produced, kg = (Total milk delivered, litres + Milk used or discarded on the farm, litres) * milk density kg/litre
# Total fat produced, kg = Total milk produced, kg x (Bulk tank fat percent/100)
# Recorded average fat = Ʃ [Individual milk yield kg x (Individual fat percent/100)]/Ʃ (Individual milk yield, kg)

The recommended acceptable range for comparison ratios is 0.95 - 1.05, and for quick comparison ratios 0.90 - 1.00, with due regard to herd size.

=== One day bulk tank data comparison ===
Milk yields and fat yields or contents are compared on the recording day. Comparing the contents is routinely possible where every delivery is sampled or by taking a bulk tank sample (see point [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Bulk_tank_data_comparison 1.10] above for how the comparison is done.)

=== Bulk tank data comparison over a longer period ===
Milk yields and fat yields or contents are compared over a longer period of time, e.g. 4 months or 12 months. This option requires a routine to obtain the applicable data from the dairies or milk buyers. Farm use of milk may be taken into account where applicable.

=== Bulk tank sample ===
Bulk tank samples can be used to verify the milk contents analysis obtained in milk recording. A sample is taken from a well-mixed bulk tank on the recording day. It must represent the milk of the whole 24-hour period. Bulk tank fat and protein contents are then compared to the weighted averages of the fat and protein percent obtained from milk recording. Normally, the difference between the values should not be more than 5%.

=== Supervised or repeated recording ===
Supervised recording is a tool designed to verify that individual cow records are reliable. It is based on repeating the herd recording as soon as possible after the original recording, and the obtained results are compared with the original recording. It is obligatory for ICAR Certificate of Quality (CoQ) holders to practice regular supervision, irrespective of recording methods used.

It is recommended that the supervised recording will follow immediately after the original recording, but for a good reason it can be postponed for up to 7 days.

The farmer and any other staff doing the original recording must not know that a supervised recording will follow. The technician who performs the supervised recording should not be the same person who did the original recording.

Usually supervised recording is done by recording the whole herd again, using the same sampling scheme and recording method (or a reference method) as in the previous recording. When herd size exceeds 200 cows, it is also allowed to do a supervised recording to selected, or randomised groups of animals in the herd.

Choosing the herds for supervised recording may be random or based on preselection. Traits for this preselection may include high yield, great increase in yield, presence of bull dams in the herd, and general suspicions about the correctness of herd results.

The traits compared in supervised recording must include milk and fat. Comparing protein is also recommended.

=== Supervision - example of comparison calculations ===

# Milk, fat and protein yields per cow are calculated for both the original and the supervised milking.
# Individual cow records where results between supervised recording and the original recording differ outside the norms might be excused where a good explanation can be given for exclusion (illness, heat, missed milking)
# Deviations (%) are calculated for each cow and yield constituent according to the formula: deviation = (supervised yield/unsupervised yield)*100-100
# Herd averages of the absolute values for each yield constituent are calculated.
# If the supervised recording occurs within 2 days of the original recording, the acceptable difference in herd averages are 7% for milk and protein and 9% for fat.
# If the supervised recording occurs between 3 and 7 days after the original recording, the acceptable difference of the aforementioned herd averages are 9% for milk and protein and 12% for fat.

The limits mentioned in these examples are typically applied by some of the member organisations, and are not meant to be understood as exact norms. Such norms should be laid down by each member organisation.

=== Evaluation of recording data ===
It is recommended that data quality is evaluated for each herd recording day. When such an evaluation is applied, the following features of the data have to be included:

# Person responsible for the recording.
# ICAR approval and calibration status of the recording equipment if owned by the farmer.
# Number of herd recordings per time period and/or recording interval.
# Number of herd samplings per time period and/or sampling interval.

The following features are also recommended to be included if possible:

# Deviation of milk and fat yields from dairy deliveries.
# Deviation of milk and fat yields from previous or predicted yields.
# Standard deviation of individual cow records.
# Number of recorded and/or sampled milkings within the recording day.
# Number of cows missed or not recorded in the recording.
</div>
</div>
= Procedures =
== Procedure 1: Computing 24-hour Yields ==
<div class="mw-collapsible mw-collapsed">
<div>
=== Methods to calculate 24-hour yield for milk yield and fat percentage from a single milking ===

==== Method of Delorenzo & Wiggans (1986)<ref>Delorenzo, M.A. and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. J. Dairy Sci. 69: 2386-2394.</ref> ====
Daily milk (DMY) and fat yield (DFY) estimates are based on measured yield and milking frequency. An adjustment factor accounts for differences in the average milking interval (expressed in decimal hours) between the preceding milking and the measured milking, and the time of day of the measured milking (started in a.m. or p.m.). For 2X milking, an additional adjustment is applied to milk yield for the interaction between milking interval and stage of lactation, with mid lactation (158 DIM) set to zero. Milking interval does not affect protein and solids non fat (SNF) percentages and so the percentages for the sampled milking are used for test-day estimates. Protein yield is calculated from the measured percentage and the adjusted milk yield.

The prediction of DMY and DFY from single milking on morning or evening in herds milked twice a day requires factors, that are the reciprocal of the proportion of total yield expected from single milkings in relation to the milking interval.

We propose to derive these coefficients (intercept, slope, etc.) for each country separately.

===== Adjustment of milking interval =====
The milking interval is the interval between milking time for the observed milking and the milking time preceding the observed milking. The milking interval is divided into 15-minutes classes. Factors for milk and fat yields may be calculated to each class using Equation 1:

''Equation 1. Factors for milk and fat yields.''
[[File:Equation 1.png|none|thumb|397x397px]]

===== Adjustment of lactation stage =====
Because the lactation stage of the cow has an influence on the effect of different milking intervals on milk production a second adjustment is made for every interval class through a covariate of days in milk as addition:

Covariate x (days in milk - 158)

===== Estimating sample day yields =====
Formulas for prediction sample day yields and percentages in herds with two milkings are:

''Equation 2. Equation for predicting 24-hour milk yield.''
[[File:Equation2.png|none|thumb|428x428px]]

''Equation 3. Equation for predicting 24-hour fat percentage.''
[[File:Equation3.png|none|thumb|431x431px]]

''Equation 4. Equation for predicting 24-hour fat yield.''
[[File:Equation4.png|none|thumb]]

''Equation 5. Equation for predicting 24-hour protein yield.''
[[File:Equation5.png|none|thumb|316x316px]]

===== Calculation examples =====

====== Practical Application ======
Two sets of factors are available for estimating DMY from a single milking, each for morning or evening milking sampling. The factors are calculated from the formula as described above and given in Table 1.
<center>
{| class="wikitable"
| colspan="5" align="left" |'''''Table 1. Factor of milk yield and covariate for herds milked twice a day.'''''
|- style="background-color:#efefef;"
| rowspan="2" align="center" |'''Length of milking interval in hours (minutes in decimal)'''
| colspan="2" align="center" |'''Morning milking'''
| colspan="2" align="center" |'''Evening milking'''
|- style="background-color:#efefef;"
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
|-
| align="center" |< 9.00
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.594
| align="center" |0.00378
|-
| align="center" |9.00-9.24
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.534
| align="center" |0.00485
|-
| align="center" |9.25-9.49
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.477
| align="center" |0.00486
|-
| align="center" |9.50-9.74
| align="center" |2.411
| align="center" |0.00716
| align="center" |2.423
| align="center" |0.00511
|-
| align="center" |9.75-9.99
| align="center" |2.359
| align="center" |0.00726
| align="center" |2.370
| align="center" |0.00473
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |10.00-10.24
| align="center" |2.310
| align="center" |0.00458
| align="center" |2.321
| align="center" |0.00337
|-
| align="center" |10.25-10.49
| align="center" |2.262
| align="center" |0.00399
| align="center" |2.273
| align="center" |0.00214
|-
| align="center" |10.50-10.74
| align="center" |2.217
| align="center" |0.00294
| align="center" |2.227
| align="center" |0.00000
|-
| align="center" |10.75-10.99
| align="center" |2.173
| align="center" |0.00223
| align="center" |2.183
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |11.00-11.24
| align="center" |2.131
| align="center" |0.00000
| align="center" |2.140
| align="center" |0.00000
|-
| align="center" |11.25-11.49
| align="center" |2.091
| align="center" |0.00000
| align="center" |2.099
| align="center" |0.00000
|-
| align="center" |11.50-11.74
| align="center" |2.052
| align="center" |0.00000
| align="center" |2.060
| align="center" |0.00000
|-
| align="center" |11.75-11.99
| align="center" |2.014
| align="center" |0.00000
| align="center" |2.022
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |12.00
| align="center" |2.000
| align="center" |0.00000
| align="center" |2.000
| align="center" |0.00000
|-
| align="center" |12.01-12.24
| align="center" |1.978
| align="center" |0.00000
| align="center" |1.986
| align="center" |0.00000
|-
| align="center" |12.25-12.49
| align="center" |1.943
| align="center" |0.00000
| align="center" |1.951
| align="center" |0.00000
|-
| align="center" |12.50-12.74
| align="center" |1.910
| align="center" |0.00000
| align="center" |1.917
| align="center" |0.00000
|-
| align="center" |12.75-12.99
| align="center" |1.877
| align="center" |0.00000
| align="center" |1.884
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |13.00-13.24
| align="center" |1.846
| align="center" |0.00000
| align="center" |1.852
| align="center" |-0.00190
|-
| align="center" |13.25-13.49
| align="center" |1.815
| align="center" |0.00000
| align="center" |1.822
| align="center" |-0.00231
|-
| align="center" |13.50-13.74
| align="center" |1.786
| align="center" |-0.00167
| align="center" |1.792
| align="center" |-0.00308
|-
| align="center" |13.75-13.99
| align="center" |1.757
| align="center" |-0.00258
| align="center" |1.763
| align="center" |-0.00339
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |14.00-14.24
| align="center" |1.730
| align="center" |-0.00347
| align="center" |1.736
| align="center" |-0.00509
|-
| align="center" |14.25-14.49
| align="center" |1.703
| align="center" |-0.00363
| align="center" |1.709
| align="center" |-0.00471
|-
| align="center" |14.50-14.74
| align="center" |1.677
| align="center" |-0.00332
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |14.75-14.99
| align="center" |1.652
| align="center" |-0.00316
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |≥ 15.00
| align="center" |1.628
| align="center" |-0.00235
| align="center" |1.683
| align="center" |-0.00454
|}
</center>

For estimating daily fat percentage there is only one table independent of morning or evening sampling – refer to Table 2.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" |'''''Table 2. Factor of fat percentage for herds milked twice a day.'''''
|- style="background-color:#efefef;"
|'''Length of milking'''

'''interval in hours'''
|'''Fat (percentage'''

'''factor)'''
|-
|< 9.00
|0.919
|-
|9.00-9.24
|0.927
|-
|9.25-9.49
|0.934
|-
|9.50-9.74
|0.941
|-
|9.75-9.99
|0.948
|-
|
|
|-
|10.00-10.24
|0.955
|-
|10.25-10.49
|0.961
|-
|10.50-10.74
|0.968
|-
|10.75-10.99
|0.974
|-
|
|
|-
|11.00-11.24
|0.980
|-
|11.25-11.49
|0.986
|-
|11.50-11.74
|0.992
|-
|11.75-11.99
|0.997
|-
|
|
|-
|12.00
|1.000
|-
|12.01-12.24
|1.003
|-
|12.25-12.49
|1.008
|-
|12.50-12.74
|1.013
|-
|12.75-12.99
|1.018
|-
|
|
|-
|13.00-13.24
|1.023
|-
|13.25-13.49
|1.028
|-
|13.50-13.74
|1.033
|-
|13.75-13.99
|1.037
|-
|
|
|-
|14.00-14.24
|1.042
|-
|14.25-14.49
|1.046
|-
|14.50-14.74
|1.050
|-
|14.75-14.99
|1.054
|-
|≥ 15.00
|1.058
|}
</center>

Milking-interval factors are calculated using Equation 1, where the intercept and slope are as in Table 3.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 3. Slope and intercept for milk yield and fat yield.'''''
|- style="background-color:#efefef;"
| rowspan="2" |'''Trait'''
| colspan="2" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started in a.m.'''
|'''For measured milking started in p.m.'''
|-
|Milk yield
|0.0654
|0.0634
|0.0363
|-
|Fat yield
|0.1965
|0.1939
|0.0254
|}
</center>
The milking interval has no significant influence on protein percentage. Therefore, the protein percentage of the sampled milking is used as the daily protein percentage.

====== Calculation of daily yields from morning milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Data for a cow from morning milking.'''''
|-
|Begin of recording:
|6:15
|(Morning milking)
|-
|Start of preceding milking:
|17:25
|
|-
|Length of milking interval:
|12 hours 50 minutes
|(Expressed as decimal 12.83)
|-
|Milk results at morning:
|12,0
|Milk-kg
|-
|
|4,12
|Fat-percentage
|-
|
|3,45
|Protein-percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 5. Factors for morning milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.877
|-
|The covariate is
|0
|-
|The factor for fat percentage from Table 2 is
|1.018
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 6. Example calculations for morning milking.'''''
|-
|The sample-day milk yield:
|1.877 x 12,0 kg + 0 x (120 - 158) = 22,5 kg
|-
|The sample-day fat percentage:
|1.018 x 4,12 = 4,19
|-
|The sample-day fat yield:
|22,5 kg x 0,0419 = 0,94 kg
|-
|The sample-day protein yield:
|22,5 kg x 0,0345 = 0,78 kg
|}
</center>

====== Calculation of daily yields from evening milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 7. Data for a cow from evening milking.'''''
|-
|Begin of recording:
|16:48
|Evening milking
|-
|Start of preceding milking:
|6:35
|
|-
|Length of milking interval:
|13 hours 47 minutes
|Expressed as decimal 13.78
|-
|Milk results at evening:
|14,0
|Milk kg
|-
|
|4,00
|Fat percentage
|-
|
|3,40
|Protein percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 8. Factors for evening milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.763
|-
|The covariate is
|<nowiki>-0,00339</nowiki>
|-
|The factor for fat percentage from Table 2 is
|1.037
|}
{| class="wikitable"
| colspan="2" |'''''Table 9. Example calculations for evening milking.'''''
|-
|The sample-day milk yield:
|1.763 x 14,0 kg - 0,00339 x (120 - 158) = 24,8 kg
|-
|The sample-day fat percentage:
|1.037 x 4,00 = 4,15
|-
|The sample-day fat yield:
|24,8 kg x 0,0415 = 1,03 kg
|-
|The sample-day protein yield:
|24,8 kg x 0,0340 = 0,84 kg
|}
</center>

====== Alternate recording of components and milk yield at both milkings ======
For this plan only the sample-day fat yield has to be calculated with regard to milking interval. The milk yield is the sum of evening and morning milk results.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 10. Example data for a cow from both milkings.'''''
|-
|Begin of recording evening:
|17:25
|
|-
|Milk results at evening:
|10:00
|Milk kg (only milking-yield)
|-
|Begin of recording morning:
|6:15
|
|-
|Milk results at morning:
|12:00
|Milk kg
|-
|
|4:20
|Fat percentage
|-
|
|3:50
|Protein percentage
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 11. Factor for fat percentage.'''''
|-
|Length of milking interval:
|12 hours 50 minutes (expressed

as decimal 12.83)
|-
|The factor for fat percentage from Table 2 is
|1.018.
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 12. Example calculation of daily yields.'''''
|-
|The sample-day milk yield:
|10,0 kg + 12,0 kg = 22,0 kg
|-
|The sample-day fat percentage:
|1.018 x 4,20 = 4,28
|-
|The sample-day fat yield:
|22,0 kg x 0,0428 = 0,94 kg
|-
|The sample-day protein yield:
|22,0 kg x 0,0350 = 0,77 kg
|}
</center>

====== Calculation for 3X Milking ======
For 3X herds, a single milking or two consecutive milkings may be weighed. The sample may be collected at one or both of these milkings. Stage of lactation × milking interval adjustments are not used for greater than 2× milking. These AM/PM factors for estimating daily yields in 3X herds should not be confused with factors that adjust 3X records to a 2X basis. Milking-interval factors are calculated using the same formula with the intercept and slope as in Table 13.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" align = "left" |'''''Table 13. Slope and intercept factors for 3X milking.'''''
|- style="background-color:#efefef;"
| rowspan="2" | '''Trait'''
| colspan="3" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started between 2 a.m. and 9:59 a.m.'''
|'''For measured milking started between 10 a.m. and 5:59 p.m.'''
|'''For measured milking started between 6:00 p.m. and 1:59 a.m.'''
|-
|Milk yield
|0.077
|0.068
|0.066
|0.0329
|-
|Fat yield
|0.186
|0.186
|0.182
|0.0186
|}
</center>
When two milkings are included for sampling, the intercepts and intervals for both milkings are included in determining a factor for calculated estimated milk yield that is applied to the total yield from both milkings as in Equation 6.

''Equation 6. Milking interval factor for 3X milking.''
[[File:Equation6.png|none|thumb|536x536px]]
Milk and fat percent factors are calculated separately based on the number of milkings weighed or sampled.

====== Calculation for 4X - 6X Milking ======
The intercept terms for calculating 3X factors (0.077, 0.068, and 0.066) are multiplied by the factor [3 / (milkings per day)] for use in calculating factors for milking frequencies greater than 3X.

==== Method of Liu et al. (2019) ====
A multiple regression method (MRM) is used for estimating 24-hour daily milk yield (DMY), daily fat yield (DFY) and daily protein yield (DPY) based on partial yields from either morning (AM) or evening (PM) milking. Fat percentage (DFP) or protein percentage (DPP) on a 24-hour daily basis are then derived using the estimated 24-hour daily yields. The MRM can be used as a reference method for estimating daily yields and component percentages.

The method of Liu et al. (2019) is an updated version of the method of Liu et al. (2000). The model is only used for farms with 2 time milkings during 24 hours.

The following formula is used to estimate DMY, DFY, DPY based on partial yields (PMY, PFY,PPY) from either morning (AM) or evening (PM) milking:

''Equation 7. Model for predicting 24-hour yield.''

''yijk = a + bijk * xijk''

where:

yijk is the estimated 24-hour daily yield (DMY, DFY or DPY);

xijk is AM or PM partial daily yield on a test day (PMY, PFY, or PPY).

Subscript '''''i''''' represents class of parity effect with 2 levels: first and higher parities.

Subscript '''''j''''' represents class of length of preceding milking interval with 8 levels for AM milking: < 720 minutes, < 740 minutes, < 760 minutes, < 780 minutes, < 800 minutes, < 820 minutes, < 840 minutes, >= 840 minutes and 8 levels for PM milking: < 600 minutes, < 620 minutes, < 640 minutes, < 660 minutes, < 680 minutes, < 700 minutes, < 720 minutes, >= 720 minutes.

Subscript '''''k''''' represents class of lactation stage with 7 classes: < 60 days, < 120 days, < 180 days, < 240 days, < 300 days, < 360 days, >= 360 days.

'''''a''''' is the estimated intercept for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

'''''b'''''ijk is the estimated slope for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

The factors for '''''a''''' and '''''b'''''ijk can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Appendix_1_-_Adjustment_factors_to_calculate_24-hour_yields_using_the_Liu_method Appendix 1].

For a given yield trait a total number of 112 formulae are to be estimated for calculating 24-hour daily yield based on partial yield from either AM or PM milking. Component percentage for fat (DFP) and protein (DPP), on a 24-hour basis is calculated by dividing estimated fat or protein yield by estimated daily milk yield:[[File:Imagefinal.png|center|thumb|339x339px]]

===== Calculation example with method of Liu et al. (2019) =====
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" align = "left" |'''''Table 14. Data from an evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="6" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="6" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="6" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow'''

'''ID'''
|'''Calving date'''
|'''Lactation number'''
| colspan="2" |'''Milk yield (kg)'''
|'''Fat content (%)'''
|'''Protein content (%)'''
|'''Fat yield (kg)'''
|'''Protein yield (kg)'''
|'''Index1'''
|-
|A
|01.01.2020
|1
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1132
|-
|B
|01.01.2020
|2
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1232
|-
|C
|27.03.2020
|1
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1131
|-
|D
|27.03.2020
|2
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1231
|-
|
|
|
|
|
|
|
|
|
|
|}
'''1''' Index is marked in the Appendix table.
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 15. Calculation of 24-hour daily yield and components for evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="3" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="3" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="3" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow ID'''
|'''DMY (kg)'''
|'''DFY (kg)'''
| colspan="2" |'''DPY (kg)'''
|'''DFP (%)'''
|'''DPP (%)'''
|-
|A
|3,47396+25,0

<nowiki>*</nowiki> 1,98268 = 53,0401 ≈ '''53,0'''
|0,2135+0,995

<nowiki>*</nowiki> 1,68050 = 1,8855975
| colspan="2" |0,10471+0,8325* 1,99092 = 1,7621509
|1,8855975 / 53,04096*100

≈ '''3,55'''
|1,7621509 / 53,04096*100

≈ '''3,32'''
|-
|B
|4,15080+25,0* 1,98520 = 53,7808 ≈ '''53,8'''
|0,3635+0,995

<nowiki>*</nowiki> 1,47515 = 1,8312743
| colspan="2" |0,13952+0,8325* 1,97074 = 1,7801611
|1,8312743 / 53,7808*100

≈ '''3,41'''
|1,7801611 / 53,7808*100

≈ '''3,31'''
|-
|C
|2,80244+33,1

<nowiki>*</nowiki> 2,02183 = 69,72501 ≈ '''69,7'''
|0,17663+1,3339 * 1,72438 = 2,4767805
| colspan="2" |0,11078+1,1122 * 1,96422 = 2,2953855
|2,4767805 / 69,725013*100

≈ '''3,55'''
|2,2953855 / 69,725013*100

≈ '''3,29'''
|-
|D
|3,85525+33,1 * 2,00429 = 70,19725 ≈ '''70,2'''
|0,27991+1,3339 * 1,62403 = 2,4462036
| colspan="2" |0,12863+1,1122* 1,98973 = 2,3416077
|2,4462036 / 70,7197249*100 ≈ '''3,48'''
|2,3416077 / 70,7197249*100 ≈ '''''3,34'''''
|-
|
|
|
|
|
|
|
|}
</center>
'''Note''' that intercepts and slopes of the applied regression formulae are underscored.

===== Fat correction for equal measure sampling =====
With Equal measure sampling, it is advisable to use Equation 8 (or the like) to correct fat contents:

Equation 8. Fat correction for equal measure sampling.

Fat, % = Analysed fat, % + 0.69 – 1.3 x (morning milk/ 24-hour milk)

The relation of morning milk to 24-hour milk is to be calculated to at least four decimals.

==== 1.1 Method of Kyntäjä & Nokka (2021)<ref name=":3" />: 24-hour correction factors for fat percentage ====
This method can be applied to calculate 24-hour correction factors for fat percentage, in case the milk recording is based on two milkings, with at least one known milk yield and one sample. A 24-hour recording day is assumed.

The conventional way to calculate correction factors is based on a data set where all milkings have been recorded and analysed separately. This approach requires a lot of effort and extra analysis, and is not cheap to organise. Organisations that have access to a large number of records may be able to use those data to calculate correction factors even if they have no extra analysis.

Requirements for the data set:

# The data set has to be large enough. Every single factor needs to be based on at least 10,000 or, even better, 100,000 observations.
# Each individual data set must contain at least one preceding milking interval, milk weight, and analysed sample. If it contains more milk weights, intervals etc. that is even better. It is also good to include breed, lactation number, days in milk and other data that may have an effect on the factors.

===== Calculation example of the method of Kyntäjä & Nokka (2021)<ref>Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. ICAR Technical Series no. 25: 171-175.</ref> =====

====== The accumulated data set ======
Since 2003, Finland had accumulated a data set of 7.5 million recordings with data on the time of the sampled and preceding milking as reported by the farmer, the lab analysis results, and the 24-hour milk yield. Grouped according to the preceding interval, the analysed fat content gives a nice sigmoid curve with the highest fat content found after a 540 to 630 minutes’ interval (9 to 10.5 hours) and the lowest at 810 to 930 minutes (13.5 to 15.5 hours).
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 16. Average analysed milk fat percentage by preceding interval class, 2003 – 2020.'''''
|- style="background-color:#efefef;"
|'''Interval before'''

'''Sampling (minutes)'''
|'''Number of samples'''
|'''Median interval in the class'''
|'''Average fat content analysed (%)'''
|-
|<510
|93,577
|495
|4.20
|-
|510-539
|19,523
|525
|4.70
|-
|540-569
|111,268
|555
|4.79
|-
|570-599
|253,807
|585
|4.83
|-
|600-629
|1,461,587
|615
|4.75
|-
|630-659
|919,968
|645
|4.66
|-
|660-689
|1,168,683
|675
|4.56
|-
|690-719
|223,877
|705
|4.42
|-
|720-749
|517,447
|735
|4.28
|-
|750-779
|212,428
|765
|4.16
|-
|780-809
|924,014
|795
|4.12
|-
|810-839
|698,463
|825
|4.09
|-
|840-869
|1,104,778
|855
|4.07
|-
|870-899
|154,561
|885
|4.05
|-
|900-929
|77,024
|915
|4.07
|-
|>929
|26,977
|945
|4.13
|}
</center>

The results were also divided into subgroups according to lactation number, phase of lactation, and breed. The effect of the preceding milk interval on milk fat seems to be bigger with older cows and in the beginning of lactation. It was also bigger with Ayrshire cows as compared with Holsteins. At this point, however, the decision was made not to take these factors into account when calculating new correction factors.

====== Calculation of new factors ======
The results above were turned into a simple set of correction factors, dependent solely on the preceding interval. In order to do this, two assumptions were made:

# A 24-hour recording day was assumed. This way, we can deduce the second milking interval from the one we know and mirror the fat percent for that milking.
# Milk secretion rate was assumed to be constant around the 24-hour period. This allows us to deduce the share of the 24-hour yield produced at each milking.

These assumptions allow us to create the new correction factors by mirroring the milk yield and milk fat content in the milking whose actual data we have not got. This way, we get the following formula:

Equation 9. Correction factor.
[[File:Equation9.png|none|thumb|545x545px]]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left" |'''''Table 17. Calculation of the mirrored milking and the correction factors'''''
|- style="background-color:#efefef;"
|'''Interval before sampling (minutes)'''
|'''Average fat in the sampled milking (%)'''
|'''Share of 24-hour milk in the sampled milking'''
|'''Mirrored interval (minutes)'''
|'''Average fat in the mirrored milking (%)'''
|'''Calculated 24-hour average fat(%)'''
|'''Correction factor'''
|-
|<510
|4.21
|0.34
|>929
|4.14
|4.16
|0.989
|-
|510-539
|4.77
|0.36
|900-929
|4.08
|4.33
|0.907
|-
|540-569
|4.82
|0.39
|870-899
|4.05
|4.35
|0.903
|-
|570-599
|4.84
|0.41
|840-869
|4.07
|4.38
|0.906
|-
|600-629
|4.76
|0.43
|810-839
|4.09
|4.37
|0.919
|-
|630-659
|4.66
|0.45
|780-809
|4.12
|4.36
|0.936
|-
|660-689
|4.56
|0.47
|750-779
|4.16
|4.35
|0.953
|-
|690-719
|4.43
|0.49
|720-749
|4.29
|4.36
|0.984
|-
|720-749
|4.29
|0.51
|690-719
|4.43
|4.36
|1.016
|-
|750-779
|4.16
|0.53
|660-689
|4.56
|4.35
|1.046
|-
|780-809
|4.12
|0.55
|630-659
|4.66
|4.36
|1.059
|-
|810-839
|4.09
|0.57
|600-629
|4.76
|4.37
|1.070
|-
|840-869
|4.07
|0.59
|570-599
|4.84
|4.38
|1.076
|-
|870-899
|4.05
|0.61
|540-569
|4.82
|4.35
|1.073
|-
|900-929
|4.08
|0.64
|510-539
|4.77
|4.33
|1.062
|-
|>929
|4.14
|0.66
|<510
|4.21
|4.16
|1.006
|}
</center>

=== Methods to calculate 24-hour yields in Automatic Milking Systems ===

==== General remarks about calculation of 24-hour milk yield ====
It is characteristic for AMS systems that individual cows set their own milking rhythm, thus making it largely irrelevant to use the traditional model of measuring milk yields and sampling at all milkings in the herd during the recording day. In order to determine how much an individual cow’s real 24-hour milk, fat and protein yield is, more complex calculations are required, especially with milk fat that varies considerably from milking to milking. For protein content and cell counts, no correction is needed for a one-milking sample.

The basic idea with calculating a 24-hour milk yield from AMS data is that milk yields per milking are converted into milk yield per time unit (minute or hour) during the preceding interval. This milk yield per time unit is then converted into milk yield in 24 hours. In order to do this, the data set must also contain time stamps for each milking.

How many milkings or how long a measurement period is used for creating 24-hour yields depends on the milk recording organisation. The fewer milkings are used the more random variance there will be in the individual cow milk yields. The absolute minimum is two milkings with preceding intervals, while a measuring period of 96 hours is recommended.

The sampled milking must always be inside the milk yield measurement period. For the calculation of fat and protein yields, it is recommended to use only those milk yields that are from the same period or day. With Z sampling, the 24-hour fat and protein yields may be calculated based on a shorter measurement period than what is used for calculating the 24-hour milk yields.

==== Calculation of milk yield using data of several days (Lazenby ''et al''., 2002<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Automatic Milking Systems (AMS). The average of most recent milk weights can be calculated using a number of preceding milkings or a number of preceding days. If number of milkings is used, the optimal estimate of the milking rate is obtained using an average of current milking together with the 12 most recent milkings back in time. The optimal estimate is the maximum value of the difference curve at which the correlation with the ‘true’ 24-hour milk yield is greatest and the variance across milkings is minimized. If number of days is used, the optimal estimate of the milking rate is obtained using an average of all milkings occurred in the last 96 hours (4 most recent days). In Table 18 the percent of maximum difference for various number of milkings and days is reported. The optimal estimate is independent from stage of lactation and parity.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 18. Percent maximum for different number of days and milkings.'''''
|- style="background-color:#efefef;"
|'''Days'''
|'''Percent Max.'''
|'''Current milking'''

'''+ most recent milkings'''
|'''Percent max.'''
|-
|1
|49.38
|10
|97.85
|-
|2
|77.26
|11
|99.08
|-
|3
|92.34
|12
|99.70
|-
|4
|98.91
|13
|99.81
|-
|5
|98.50
|14
|99.40
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table19.png|center|thumb|911x911px]]
Therefore, 24-hour yield estimation using most recent milkings (1+12) is computed using Equation 10.

''Equation 10. 24-hour yield estimation using 12 previous milkings from AMS.''
[[File:Equation10.png|none|thumb|527x527px]]
and, 24-hour yield estimation using all milkings occurred in the last 96 hours (most recent 4 days), all milking in the last 4 days are included is computed using Equation 11.

''Equation 11. 24 hours yield estimation using milkings from the last 96 hours from AMS''
[[File:Equation11.png|none|thumb|534x534px]]

===== Advantages and disadvantages of this method =====
In terms of Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between milk weights and contents may arise if contents are recorded on one day only. Moreover, some cows may begin or finish their lactation during the period of recording. In this case the computation of milk yield must be adapted. The number of data that need to be validated is higher (for instance, contents have short interval between two milkings).

==== Calculation of milk yield using data on 1 day (Bouloc ''et al''., 2002<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
When the number of milkings is reduced to milkings obtained during one day only, the accuracy of the estimation of the true performance is the same as classical milk recording methods with the same interval between two test days. For instance, Milk Yield estimated from all the milkings recorded during 24 hours, and with an interval between two test days of four weeks has the same accuracy as A4.

==== Calculation of fat and protein yield (Galesloot & Peeters, 2000<ref name=":1" />) ====
Calculation of fat and protein percent must be based on milk weights at time of sampling. The 24-hour protein percentage can be predicted by the protein percentage of the sample without adjustment. However, the 24-hour fat percentage is more difficult to predict, as levels of fat percent are inversely proportional to the amount of milk yield. It is important then to have a close connection between time of samples and actual milk yields.

The Peeters and Galesloot method is a multiple linear regression model for estimating 24-hour fat percent and yields from one-sampled milking during the AMS sampling period. Six different statistical models were tested. This method takes into account fat percent, protein percent, milk weight and milking interval of the sampled milking, milking interval and milk weight of the previous milking (simple model). Another model, based on six different classification of variables (Ca - Cf) such as, time of sampled milking, interval preceding the sampled milking, ratio of fat to protein percent, parity, lactation stage, can be applied (complex model).

===== Simple model =====
24-hour Fat% = b0 + b1* Fat%(n) + b2* Prot%(n) + b3* Int(n) + b4* Int(n-1) + b5* Milk(n) + b6* Milk (n-1) + e

b0= Intercept, b1 to b6 = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, e = Residual effect.

===== Complex model =====
24-hour Fat%i = b0i + b1i* Fat%(n) + b2i* Prot%(n) + b3i* Int(n) + b4i* Int(n-1) + b5i* Milk(n) + b6i* Milk(n-1) + ei

b0i = Intercept, b1i to b6i = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, ei = Residual effect

i = subclass of classification for class variables Cx for x = a, b, c, d, e, f

Ca = Day Time of sampled milking (h) 0-5.59, 6.00-11.59, 12.00-17.59, 18.00-23.59

Cb = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440

Cc = Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

Cd = Parity 1, 2, ≥ 3

Ce = Lactation stage 1-99, 100-199, ≥200

Cf = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440 and Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

The best prediction of 24-hour fat percent and 24-hour fat yields from this method, includes fat percent, protein percent, milk weight and milking interval of the sampled milking, milk weight and milking interval of the preceding milking and the interaction between milking interval, the ratio of fat to protein percent of the sampled milking (complex model corresponding to Cf classification).

The Peeters and Galesloot method has been updated by Roelofs et al. (2006)<ref>Peeters, R. and P. J. B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. J Dairy Sci. 85:682-688.</ref>. The Roelofs method is described in [[Section 02 – Cattle Milk Recording#Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme|Appendix 2]] of this Section.

N.B. This method has been developed by CRV. CRV has available a set of parameters, estimated with this method. For more information about costs and advice on application of this method, please contact CRV. ICAR has no benefit from the application of this method or any other method described in these guidelines.

==== Calculation example of 24-hour fat and protein yields with sampling scheme M ====
With this method, all milkings in a 24-hour recording period must be sampled. The obtained separate analysis results are then used to compute a 24-hour yield of milk solids, and a weighted average of their content.

Individual milkings (last 96 hours) and recording day contents:
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left" |'''''Table 20. Calculation of 24-hour fat and protein contents with sampling scheme M.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY/MM/DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat%'''
|'''Protein%'''
|-
|1
|2021/09/09
|20:45
|525
|13.7
|26.1
|
|
|-
|2
|2021/09/10
|5:30
|617
|16.0
|25.9
|
|
|-
|3
|2021/09/10
|15:47
|720
|18.7
|26.0
|
|
|-
|4
|2021/09/11
|3:25
|645
|16.8
|26.0
|
|
|-
|5
|2021/09/11
|14:10
|899
|18.3
|20.3
|
|
|-
|6
|2021/09/11
|23:27
|557
|14.6
|26.2
|
|
|-
|7
|2021/09/12
|10:51
|684
|17.4
|25.4
|4.53
|3.17
|-
|8
|2021/09/12
|19:44
|533
|14.1
|26.5
|4.92
|3.18
|-
|9
|2021/09/13
|1:35
|351
|9.9
|28.2
|5.92
|3.07
|}
</center>

For example, calculation of fat% on recording day:

24-hour Fat% = (9.9 kg milk x 5.92% fat + 14.1 kg milk x 4.92 % fat + 17.4 kg milk x 4.53 % fat) / (9.9 + 14.1 + 17.4) kg milk = 5.00 %

To calculate the 24-hour fat yield, the calculated 24-hour milk yield is multiplied by the fat content thus obtained (5.00 %).

The same method is used for protein, somatic cell count, urea, lactose and other milk constituents.

Estimation of milk contents: It is recommended to set the robot not to take samples if the preceding milking of the individual cow is not more than 4 hours earlier. If such milkings occur the milk sampled from them is not suitable for 24-hour fat calculation.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left"|'''''Table 21. Calculation of 24-hour fat and protein contents with sampling scheme M where one milking interval was shorter than 4 hours.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY-MM-DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat %'''
|'''Protein%'''
|-
|1
|2021/11/12
|20:05
|590
|15.4
|26.4
|
|
|-
|2
|2021/11/13
|6:31
|626
|16.3
|26.0
|
|
|-
|3
|2021/11/13
|17:12
|641
|17.1
|26.7
|
|
|-
|4
|2021/11/14
|4:40
|688
|17.5
|25.4
|
|
|-
|5
|2021/11/14
|15:11
|631
|16.4
|26.0
|
|
|-
|6
|2021/11/15
|2:25
|674
|16.5
|24.5
|
|
|-
|7
|2021/11/15
|9:47
|452
|10.8
|23.9
|
|
|-
|8
|2021/11/15
|18:30
|523
|13.6
|26.0
|4.71
|3.36
|-
|9
|2021/11/15
|21:15
|165
|3.1
|18.8
|5.161
|3.481
|-
|10
|2021/11/16
|7:49
|634
|16.5
|26.0
|4.47
|3.21
|}
1 Time between two consecutive milkings shorter than 4 hours, data not taken into account for calculation of milk contents.
</center>

Calculation of the fat content of milk during the recording day:

24-hour Fat% = (16.5 kg milk x 4.47 % fat + 13.6 kg milk x 4.71 % fat) / (16.5 kg + 13.6 kg) = 4.57 %

The same method is used for protein, somatic cells, urea, lactose and other milk constituents.

=== Methods to calculate 24-hour yields from electronic milk meters ===

==== Using data on more than one day (Hand ''et al''., 2006<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. J. Dairy Sci. 89:1723–1726.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Electronic Milk Meters. The average of most recent milk weights can be calculated using a number of preceding days. Table 22 reports the concordance correlations for a range of multiple-day averages. As soon as at least the 3 preceding days are used in the calculation, the concordance correlation reaches a high value of at least 0.981. There are no significant differences between 3, 4, 5, 6 and 7-day averages. The correlations are independent from stage of lactation and parity. Thus, 24-hour yields can be the average of from 3 to 7 daily milkings previous to the test day when fat and protein samples were taken.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 22. Concordance correlations for different multiple-day averages.'''''
|- style="background-color:#efefef;"
|'''Multiple-day average'''
|'''Concordance correlation'''
|-
|1
|0.957
|-
|2
|0.975
|-
|3
|0.981
|-
|4
|0.981
|-
|5
|0.982
|-
|6
|0.981
|-
|7
|0.981
|-
|10
|0.979
|-
|14
|0.977
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table20.png|center|thumb|923x923px]]

Therefore, 24-hour yield estimation averaging over 5 days is given by Equation 12.

''Equation 12. 24-hour yield estimation averaging over 5 days.''
[[File:Equation12.png|center|thumb|601x601px]]

===== Advantages and disadvantages of this method =====
Concerning Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between Milk weights and contents have been shown. The estimation bias increases proportionally to the number of days use to compute the 24-hour average. Thus, this method is recommended only if milk weight is the only variable of interest. If milk contents are of interest then the milk weight should be calculated using the milkings from the same day of sampling.

==== Estimation of 24-hour fat and protein yield ====
Fat and protein yields should be determined from the 24-hour yield on the day of sampling, and not the averaged value.

=== Calculation of daily fat percentage from single samples by Gerke et al., 2025 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Gerke.xlsx here]

Constant access to the automatic milking system (AMS) leads to varying milking frequency of cows and subsequently varying milking interval lengths (MI) and milk yield (MY) of single milkings. This influences milk production and can result in variable milk composition in individual milkings during the day. Therefore, the fat percentage from one sampled milking must be adjusted before it can be used as a daily value. The method described specifies the data required and the calculation procedure for deriving a corrected 24 h milk fat percentage from a single sample on test day (TD) in AMS herds.

==== Model specification ====
The multiple linear regression includes transformation, interaction, and polynomial parameters to model non-linearity and thereby improve prediction accuracy. Beside F% of a single milking (''m'') on TD, the model focused on lactation characteristics and milk recording data of up to 4 preceding milkings. With milking intervals ranging between 4 and 20 hours, the method can be applied to milk recording samples from cows with 2 or 3 milkings whose milking intervals lengths (MI) before sampling accumulate to less than 24 h.

The functional form of the model described below specifies the data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample:[[File:Image A.png|center|thumb|636x636px|'''Data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample''']]
</div>where:

DF% = estimated 24 h fat percentage on TD

''m'' = sampled milking on TD

''m-x'' = x milkings before the milking where the sample was taken (x: 1-3)

F% = fat percentage of the sampled milking ''m''

MY(''m'') = milk yield (kg) of ''m''

MI(''m'') = length of time interval (min) preceding the sampled milking ''m''

MY(''m''-x) = milk yields of the 1-3 preceding milkings of ''m''

MI(''m''-x) = milking interval length corresponding to MY(''m''-x)

DIM = days in milk on TD ranging between 5 and 330 d

Parity = parity class (e.g primiparous = 1 and multiparous = 0)

Daytime = time-of-day group of ''m'' (e.g. morning/noon/evening)

e = residual error

The method and its implementation are described in detail by Gerke et al. (2025).

==== Calculation and examples ====
The mathematical notation, with the corresponding regression coefficients in Table 1 for calculating the daily fat percentage (DF%):[[File:Calculating the daily fat percentage (DF%).jpg|center|Calculating the daily fat percentage (DF%)|thumb|511x511px]][[File:Calculating the daily fat percentage (DF%) 2.jpg|center|frame|'''Table 1. Coefficients for regression formula.''']]
</div>
[[File:Example data required for estimating 24 h fat percentage (DF%).jpg|alt=Example data required for estimating 24 h fat percentage (DF%)|center|frame|'''Table 2.''' '''Example data required for estimating 24 h fat percentage (DF%)''']]
Based on the data assembled on TD (Table 2), the corrected 24 h fat percentage (DF%) can be calculated using the mathematical formula und its corresponding coefficients listed in Table 1 as shown in the following examples:
[[File:Corrected 24 h fat percentage.jpg|alt=Corrected 24 h fat percentage|center|thumb|661x661px|'''Corrected 24 h fat percentage''']]

=== Reference ===
Gerke, J. S., Kammer, M., Werner, A., Köstler, R., Piepenburg, J., Mayerhofer, M., … Duda, J. (2025). Estimating daily fat percentage from single samples in herds with automatic milking system using a regression model. ''Livestock Science'', ''293'', 105649. doi: 10.1016/j.livsci.2025.105649

=== Calculation of daily fat percentage from single samples by Jenko et al., 2008, 2010 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Jenko.xlsx here]

This method estimates daily milk yield (DMY), daily fat yield (DFY), and daily protein yield (DPY) in the alternate one-milking recording (T) scheme. Daily fat percentage (DFP) and daily protein percentage (DPP) are then derived from the daily yield (DY) estimates. Utilizing this method allows us to remove the risk of underestimating high and overestimating low DY and contents.

The following formula is used to estimate the DY from the partial yield (PY) and the estimated PY/DY ratio (y):

DY=PYi/yi

where the subscript i is either morning (a.m.) or evening (p.m.).

The value of y is calculated based on the milking interval in minutes (MI), estimated intercept (µ) and regression coefficients (b1 and b2) for yield traits in a.m. or p.m. milking using the following equations for DMY and DPY:

'''Equation 1. Model for milk yield and protein yield.'''

yi = µ + b1 × MI

and for DFY

'''Equation 2. Model for fat yield.'''

yi = µ + b1 × MI + b2 × MI2

The intercept and regression coefficients can be either estimated from the data with records from both a.m. and p.m. milking or the estimates from Table 1 can be applied.

'''Table 1. Intercept and regression coefficients for calculation of daily yield.'''
{| class="wikitable"
|'''Daily yield'''
|'''Milking'''
|'''µ'''
|'''b1'''
|'''b2'''
|-
|DMY
|a.m.
|0,1081000000
|0,0005503000
|
|-
|
|p.m.
|0,0884200000
|0,0005683000
|
|-
|DPY
|a.m.
|0,1124000000
|0,0005419000
|
|-
|
|p.m.
|0,0966400000
|0,0005593000
|
|-
|DFY .
|a.m.
|0,5903000000
|<nowiki>-0,0005093000</nowiki>
|0,0000005377
|-
|
|p.m.
|0,1574000000
|0,0006705000
|<nowiki>-0,0000002744</nowiki>
|}
Finally, daily fat percentage (DFP) and daily protein percentage (DPP) are calculated from the estimated DY:

DFP=DFY/DMY × 100

DPP=DPY/DMY × 100

==== Calulation example with method of Jenko et al. (2008, 2010) ====
Example of the calculations of daily yields from morning milking and evening milking is presented in tables 3 and 4. Data from the Delorenzo and Wiggans method is used in the calculations (Table 2).

'''Table 2. Data for morning and evening milking.'''
{| class="wikitable"
|'''Milking'''
|'''a.m.'''
|'''p.m.'''
|-
|Beginning of recording
|06:15
|20:22
|-
|Start of preceding milking
|17:25
|06:35
|-
|Milking interval (min)
|770
|827
|-
|'''Milking results'''
|
|
|-
|Milk (kg)
|12,00
|14,00
|-
|Protein (%)
|3,45
|3,40
|-
|Fat (%)
|4,12
|4,00
|}

'''Table 3. Calculation of partial yield (PY) and calculation of y value.'''
{| class="wikitable"
|Trait
|Milking
|PY (%)
|PY (kg)
|y
|-
|Milk
|a.m.
|
|12,00
|0,1081000000 + 0,0005503000 x 770 = 0,531831
|-
|
|p.m.
|
|14,00
|0,0884200000 + 0,0005683000 x 827 = 0,558404
|-
|Protein
|a.m.
|3,45
|12,00 / 3,45 = 0,41
|0,1124000000 + 0,0005419000 x 770 = 0,529663
|-
|
|p.m.
|3,40
|14,00 / 3,40 = 0,48
|0,0966400000 + 0,0005593000 x 827 = 0,559181
|-
|Fat
|a.m.
|

4,12
|12,00 / 4,12 = 0,49
|0,5903000000 -0,0005093000 x 770 + 0,0000005377 x 7702 = 0,516941
|-
|
|p.m.
|

4,00
|12,00 / 4,00 = 0,56
|0,1574000000 +0,0006705000 x 827 - 0,0000002744 x 8272 = 0,524233
|}

'''Table 4. Calculation of daily yield (DY, kg) and daily components (DY, %).'''
{| class="wikitable"
|Trait
|DY
|Milking
|DY (kg)
|DY (%)
|-
|Milk
|DMY
|a.m.
|12,00 / 0,531831 = 22,56356
|
|-
|
|
|p.m.
|14,00 / 0,531831 = 25,07145
|
|-
|Protein
|DPY
|a.m.
|0,41 / 0,529663 = 0,781629
|(0,781629 / 22,56356) x 100 = 3,46
|-
|
|
|p.m.
|0,48 / 0,559181 = 0,851245
|(0,851245 / 25,07145) x 100 = 3,40
|-
|Fat
|DFY
|a.m.
|0,49 / 0,516941 = 0,956395
|(0,956395 / 22,56356) x 100 = 4,24
|-
|
|
|p.m.
|0,56 / 0,524233 = 1,068227
|(1,068227 / 25,07145) x 100 = 4,26
|}

==== References ====

* Jenko, J., Perpar, T., Logar, B., Sadar, M., Ivanovič, B., Jeretina, J., Verbič, J., Podgoršek, P. 2008. Comparison of different models for estimating daily yields from a.m./p.m. milkings in Slovenian dairy scheme. Presented at the 36th ICAR Session, Niagara Falls, New York, United States, June 16-20, 2008.
* Jenko, J., Perpar, T., Gorjanc G., Babnik, D. 2010. Evaluation of different approaches for the estimation of daily yield from single milk testing scheme in cattle, J. Dairy Res., 77 (2010), pp. 137-143; DOI: 10.1017/S0022029909990586

</div>
</div>

== Procedure 2 – Computing of Accumulated Lactation Yield ==
<div class="mw-collapsible mw-collapsed">
<div>
=== The Test Interval Method (TIM) (Sargent, 1968<ref>Sargent, F. D., V. H. Lyton, and 0. G. Wall, J r . 1968. Test interval method of calculating Dairy Herd Improvement Association records. J. Dairy Sci. 51:170.</ref>) ===
Test Interval Method is the reference method for calculating accumulated yields. Another adaptation of the method is the Centering Date Method where the yields from the preceding recording are used until the mid point of the recording interval and then substituted by the yields from the following recording.

The following equations are used to compute the lactation record for milk yield (MY), for fat (and protein) yield (FY), and for fat (and protein) percent (FP).
[[File:Equation1111.png|none|thumb|653x653px]]
Where:
M1, M2, Mn are the weights in kilograms, given to one decimal place, of the milk yielded in the 24 hours of the recording day.

F1, F2, Fn are the fat yields estimated by multiplying the milk yield and the fat percent (given to at least two decimal places) collected on the recording day.

I1, I2, In-1 are the intervals, in days, between recording dates.

I0 is the interval, in days, between the lactation period start date and the first recording date.

In is the interval, in days, between the last recording date and the end of the lactation period.

The equation applied for fat yield and percentage must be applied for any other milk components such as protein and lactose.

Details of how to apply the formulae are shown in Table 3 using the example data in Table 1, below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" align = "left" |'''''Table 1. Raw data used in example (TIM).'''''
|- style="background-color:#efefef;"
| colspan="6" align = "left"|'''Data:'''

'''Calving March 25'''
|- style="background-color:#efefef;"
|
|'''Date of'''

'''recording'''
|'''Number'''

'''of days'''
|'''Quantity of milk'''

'''weighed in kg'''
|'''Fat'''

'''percentage'''
|'''Fat'''

'''in grams'''
|-
|April
|8
|14
|28.2
|3.65
|1 029
|-
|May
|6
|28
|24.8
|3.45
|856
|-
|June
|5
|30
|26.6
|3.40
|904
|-
|July
|7
|32
|23.2
|3.55
|824
|-
|August
|2
|26
|20.2
|3.85
|778
|-
|August
|30
|28
|17.8
|4.05
|721
|-
|September
|25
|26
|13.2
|4.45
|587
|-
|October
|27
|32
|9.6
|4.65
|446
|-
|November
|22
|26
|5.8
|4.95
|287
|-
|December
|20
|28
|4.4
|5.25
|231
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left"|'''''Table 2. Lactation period summary (TIM).'''''
|-
|Beginning of lactation:
|March 26
|-
|End of lactation:
|January 3
|-
|Duration of lactation period:
|284 days
|-
|Number of testings (weighings):
|10
|}
</center>
<center>
{| class="wikitable"
| colspan="8" |'''''Table 3. Computations using Test Interval Method.'''''
|- style="background-color:#efefef;"
| colspan="3" rowspan="2" |'''Interval'''

'''both days included'''
|
| colspan="2" |'''Daily production'''
| colspan="2" |'''Sum'''
|- style="background-color:#efefef;"
|'''Days'''
|'''Kg milk'''
|'''Grams of fat'''
|'''Kg milk'''
|'''Kg fat'''
|-
|Mar 26
|<nowiki>-</nowiki>
|Apr 8
|14
|28.2
|1 029
|395
|14.410
|-
|Apr 9
|<nowiki>-</nowiki>
|May 6
|28
|(28.2+24.8)/2
|(1 029+856) /2
|742
|26.389
|-
|May 7
|<nowiki>-</nowiki>
|June 5
|30
|(24.8+26.6) /2
|(856+904) /2
|771
|26.400
|-
|June 6
|<nowiki>-</nowiki>
|July 7
|32
|(26.6+23.2) /2
|(904+824) /2
|797
|27.648
|-
|July 8
|<nowiki>-</nowiki>
|Aug. 2
|26
|(23.2+20.2) /2
|(824+778) /2
|564
|20.817
|-
|Aug. 3
|<nowiki>-</nowiki>
|Aug 30
|28
|(20.2+17.8) /2
|(778+721) /2
|532
|20.980
|-
|Aug 31
|<nowiki>-</nowiki>
|Sept. 25
|26
|(17.8+13.2) /2
|(721+587) /2
|403
|17.008
|-
|Sept. 26
|<nowiki>-</nowiki>
|Oct. 27
|32
|(13.2+9.6) /2
|(587+446) /2
|365
|16.541
|-
|Oct. 28
|<nowiki>-</nowiki>
|Nov. 22
|26
|(9.6+5.8) /2
|(446+287) /2
|200
|9.536
|-
|Nov. 23
|<nowiki>-</nowiki>
|Dec. 20
|28
|(5.8+4.4) /2
|(287+231) /2
|143
|7.253
|-
|Dec. 21
|<nowiki>-</nowiki>
|Jan. 3
|14
|4.4
|231
|62
|3.234
|-
|
|
|
|284
|
|
|4973
|190.216
|-
| colspan="8" |
|-
| colspan="8" |Total quantity of milk: 4 973. kg
|-
| colspan="8" |Total quantity of fat: 190 kg
|-
| colspan="8" |Average fat percentage (190.216 / 4973) x 100 = 3.82%
|}
</center>

=== Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. Livest. Prod. Sci. 17:l.</ref>) ===
With the method 'Interpolation using Standard Lactation Curves' missing test day yields and 305 day projections are predicted. The method makes use of separate standard lactation curves representing the expected course of the lactation, for a certain herd production level, age at calving and season of calving and yield trait. By interpolation using standard lactation curves, the fact that after calving milk yield generally increases and subsequently decreases is taken into account. The daily yields are predicted for fixed days of the lactation: day 0, 10, 30, 50 etc.

The cumulative yield is calculated as follows in :
[[File:Equation2222222.png|none|thumb|474x474px]]
where:

yi = the i-th daily yield;

INTi = the interval in days between the daily yields yi and yi+1;

''n'' = total number of daily yields (measured daily yields and predicted daily yields).

The next example illustrates the calculation of a record in progress. The cow was tested at day 35 and day 65 of the lactation. To determine the lactation yield, daily milk yields are determined for day 0, 10, 30 and 50 of the lactation, by means of the standard lactation curves. The daily yields are in Table 4.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Measured and derived daily yields, used to calculate the record in progress in the example (ISLC).'''''
|- style="background-color:#efefef;"
|'''Day of lactation'''
|'''Milk (kg)'''
|'''Note'''
|-
|0
|25.9
|Predicted
|-
|10
|27.8
|Predicted
|-
|30
|31.7
|Predicted
|-
|35
|31.8
|Measured
|-
|50
|32.9
|Interpolated using standard lactation curve
|-
|65
|33.0
|Measured
|}
</center>

Next, the record in progress can be calculated by means of the formula for a cumulative yield as follows:

[(10 - 1) * 25.9 + (10+1) * 27.8] / 2 +

[(20 - 1) * 27.8 + (20+1) * 31.7] / 2 +

[(5 - 1) * 31.7 + (5+1) * 31.8] / 2 +

[(15 - 1) * 31.8 + (15+1) * 32.9] / 2 +

[(15 - 1) * 32.9 + (15+1) * 33.0] / 2 = 2005.3 kg.

This corresponds to the surface below the line through the predicted and measured daily yields (see Figure 1).
[[File:Figure1.png|center|thumb|621x621px|''Figure 1. Example of calculation of record in progress.'']]

=== Best prediction (BP) (VanRaden, 1997<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. J. Dairy Sci. 80:3015-3022.</ref>) ===
Recorded milk weights are combined into a lactation record using standard selection index methods. Let vector y contain M1, M2, to Mn and let E('''y''') contain corresponding the expected values for each recorded day. The E(y) are obtained from standard lactation curves for the population or for the herd and should account for the cow's age and other environmental factors such as season, milking frequency, etc. The yields in '''y''' covary as a function of the recording interval between them (I). Diagonal elements in Var(y) are the population or herd variance for that recording day and off diagonals are obtained from autoregressive or similar functions such as Corr(M1, M2)=0.995I for first lactations or 0.992I for later lactations. Covariances of one observation with the lactation yield, for example Cov(M1, MY), are the sum of 305 individual covariances. E(MY) is the sum of 305 daily expected values. Lactation milk yield is then predicted as Equation 3:
[[File:Equation333333.png|none|thumb|640x640px]]
With best prediction, predicted milk yields have less variance than true milk yields. With TIM, estimated yields have more variance than true yields. The reason is that predicted yields are regressed toward the mean unless all 305 daily yields are observed. With best prediction, the predicted MY for a lactation without any observed yields is E(MY) which is the population or herd mean for a cow of that age and season. With TIM, the estimated MY is undefined if no daily yields are recorded.

Milk, fat, and protein yields can be processed separately using single-trait best prediction or jointly using multi-trait best prediction. Replacement of M1, M2, to Mn with F1, F2, to Fn or P1, P2, to Pn gives the single-trait predictions for fat or for protein. Multi-trait predictions require larger vectors and matrices but similar algebra. Products of trait correlations and autoregressive correlations, for example, may provide the needed covariances.

=== Multiple-Trait Procedure (MTP) (Schaeffer & Jamrozik, 1996<ref>Schaeffer, L.R., and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. J. Dairy Sci. 79:2044-2055.</ref>) ===
The Multiple-Trait Procedure predicts 305-d lactation yields for milk, fat, protein and SCS, incorporating information about standard lactation curves and covariances between milk, fat, and protein yields and SCS. Test day yields are weighted by their relative variances, and standard lactation curves of cows of similar breed, region, lactation number, age, and season of calving are used in the estimation of lactation curve parameters for each cow. The multiple-trait procedure can handle long intervals between test days, test days with milk only recorded, and can make 305-d predictions on the basis of just one test day record per cow. The procedure also lends itself to the calculation of peak yield, day of peak yield, yield persistency, and expected test-day yields, which could be useful management tools for a producer on a milk recording program.

The MTP method is based upon Wilmink's model in conjunction with an approach incorporating standard curve parameters for cows with the same production characteristics. Wilmink's function for one trait is given by Equation 4.

Equation 4. Wilmink function for one trait (MTP).

y = A + B''t'' ± C''exp'' (-0.05''t'') + ''e''

where y is yield on day t of lactation, A, B, and C are related to the shape of the lactation curve.

The parameters A, B, and C need to be estimated for each yield trait. The yield traits have high phenotypic correlations, and MTP would incorporate these correlations. Use of MTP would allow for the prediction of yields even if data were not available on each test day for a cow.

The vector of parameters to be estimated for one cow are designated:
[[File:Vectro.png|center|thumb]]
where M, F, and P represent milk, fat, and protein, respectively, and S represents somatic cell score. The vector c is to be estimated from the available test-day records. Let c0 represent the corresponding parameters estimated across all cows with the same production characteristics as the cow in question.

Let
[[File:Vector2.png|center|thumb]]

be the vector of yield traits and somatic cell scores on test ''k'' at day ''t'' of the lactation.

The incidence matrix, ''Xk'', is constructed as follows:
[[File:Vector3.png|center|thumb|558x558px]]

The MTP equations are:
[[File:Equation55555.png|none|thumb|560x560px]]
and ''n'' is the number of tests for that cow. ''Rk'' is a matrix of order 4 that contains the variances and covariances among the yields on ''kth'' test at day ''t'' of lactation. The elements of this matrix were derived from regression formulas based on fitting phenotypic variances and covariances of yields to models with ''t'' and ''t2'' as covariables. Thus, element ''ij'' of ''Rk'' would be determined by

rij(t) = ß0ij + ß1ij (t) + ß2ij (t2)

G is a 12 x 12 matrix containing variances and covariances among the parameters in '''ĉ''' and represents the cow to cow variation in these parameters, which includes genetic and permanent environmental effects, but ignores genetic covariances between cows. The parameters for '''''G''''' and '''''Rk''''' vary depending on the breed, but must be known. Initially, these matrices were allowed to vary by region of Canada in addition to breed, but this meant that there could exist two cows with identical production records on the same days in milk, but because one cow was in one region and the other cow was in another region, then the accuracy of their predictions would be different. This was considered to be too confusing for dairy producers, so that regional differences in variance-covariance matrices were ignored and one set of parameters would be used for all regions for a particular breed. Estimation of G is described later.

If a cow has a test, but only milk yield is reported, then

y’k(Mk 0 0 0)

and
[[File:And.png|center|thumb|540x540px]]

The inverse of '''''Rk''''' is the regular inverse of the nonzero submatrix within '''''Rk''''', ignoring the zero rows and columns. Thus, missing yields can be accommodated in MTP.

Accuracy of predicted 305-d lactation totals depends on the number of test-day records during the lactation and DIM associated with each test. Thus, any prediction procedure will require reliability figures to be reported with all predictions, especially if fewer tests at very irregular intervals are going to be frequent in milk recording. At the moment, an approximate procedure is applied that uses the inverse elements of '''(X’R-1X + G-1) -1.'''

==== 1.1 Example calculations ====
Four test day records on a 25 month old, Holstein cow calving in June from Ontario are given in the Table 5 below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 5. Example test day data for a cow (MTP).'''''
|- style="background-color:#efefef;"
|'''Test no.'''
|'''DIM=''t'''''
|'''Exp(-0.05''t'')'''
|'''Milk (kg)'''
|'''Fat (kg)'''
|'''Protein (kg)'''
|'''SCS'''
|-
|1
|15
|0.47237
|28.8
|
|
|3.130
|-
|2
|54
|0.06721
|29.2
|1.12
|0.87
|2.463
|-
|3
|188
|0.000083
|23.7
|0.97
|0.78
|2.157
|-
|4
|250
|0.0000037
|20.8
|
|
|2.619
|}
</center>

Notice that two tests do not have fat and protein yields, and that intervals between tests are irregular and large. The vector of standard curve parameters based on all available comparable cow, is
[[File:Vector4.png|center|thumb]]
The R^(-1)_k matrices for each test day need to be constructed. These matrices are derived from regression equations. The equations for Holsteins were:
<center>
{| class="wikitable" style="text-align: center;"
|''rMM(t) =''
|71.0752 - 0.281201''t'' + 0.0004977''t2''
|-
|''rMF(t) =''
|2.4365 - 0.013274''t'' + 0.0000302''t2''
|-
|''rMP(t) =''
|2.0504 - 0.008286''t'' + 0.0000163''t2''
|-
|''rMS(t) =''
|<nowiki>-1.7993 + 0.013209</nowiki>''t'' - 0.000056''t2''
|-
|''rFF(t) =''
|0.1312 - 0.000725''t'' + 0.000001586''t2''
|-
|''rFP(t) =''
|0.0739 - 0.000386''t'' + 0.000000926''t2''
|-
|''rFS(t) =''
|<nowiki>- 0.0386 + 0.000292</nowiki>''t'' - 0.000001796''t2''
|-
|''rPP(t) =''
|0.066 - 0.000267''t'' + 0.0000005636''t2''
|-
|''rPS(t) =''
|<nowiki>- 0.0404 + 0.000369</nowiki>''t'' - 0.000001743''t2''
|-
|''rSS(t) =''
|3.0404 - 0.000083''t'' - 0.000006105''t2''
|}
</center>

The inverses of the residual variance-covariance matrices for yields for the four test days are as follows:
<center>
{| class="wikitable" style="text-align: center;"
|
|0.0151259
|0
|0
|0.0080354
|-
|'''R^(-1)_1''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0080354
|0
|0
|0.3334553
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.1685584
|0.345947
|<nowiki>-4.851935</nowiki>
|0.0254775
|-
|'''R^(-1)_2''' = =
|<nowiki>-0.345947</nowiki>
|26.830915
|<nowiki>-17.40281</nowiki>
|<nowiki>-0.041445</nowiki>
|-
|
|<nowiki>-4.851935</nowiki>
|<nowiki>-17.40281</nowiki>
|187.18579
|<nowiki>-0.584885</nowiki>
|-
|
|0.0254775
|<nowiki>-0.041445</nowiki>
|<nowiki>-0.584885</nowiki>
|0.3365425
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.2620161
|0.1479068
|<nowiki>-7.943903</nowiki>
|0.0316069
|-
|'''R^(-1)_3''' = =
|0.1479068
|54.446977
|<nowiki>-56.01333</nowiki>
|0.3306741
|-
|
|<nowiki>-7.943903</nowiki>
|<nowiki>-56.01333</nowiki>
|317.9609
|<nowiki>-0.92601</nowiki>
|-
|
|0.0316069
|0.3306741
|<nowiki>-0.92601</nowiki>
|0.3654369
|}
{| class="wikitable" style="text-align: center;"
|

|0.0329465
|0
|0
|0.0251039
|-
|'''R^(-1)_4''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0251039
|0
|0
|0.3981981
|}

Inverse matrix G^(-1) of order 12 is the same for all cows of the same breed:

[[File:Left 6x6.jpg|center|thumb|600x600px|Inverse matrix G^(-1) of order 12]]

</center>
Note that many covariances between different parameters of the lactation curves have been set to zero. When all covariances were included, the prediction errors for individual cows were very large, possibly because the covariances were highly correlated to each other within and between traits. Including only covariances between the same parameter among traits gave much smaller prediction errors.

The elements of the MTP equations of order 12 for this cow are shown in partitioned format also:

'''X’R-1X ='''
<center>[[File:Elements of the MTP equations of order 12.jpg|center|thumb|600x600px|Elements of the MTP equations of order 12]]
</center>
[[File:Equation7.png|center|thumb|632x632px]]

The solution vector for this cow is
[[File:Equation6666.png|center|thumb]]

To predict 305-day yields, Y305
[[File:Equation7777.png|none|thumb|551x551px]]
Equation 6 is used separately for each trait (milk, fat, protein, and SCS). The results for this cow were 7456 kg milk, 301 kg fat, and 239 kg protein. The result for SCS is divided by 305 to give an average daily SCS of 2.477.
</div>
</div>

= Appendices =
== Appendix 1 - Adjustment factors to calculate 24-hour yields using the Liu method ==
<div class="mw-collapsible mw-collapsed">
<div>
In Table 6 the adjustment factors to calculate 24-hour yields, using the Liu method, can be found. The description of the Liu method can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2.]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" |'''''Table 1. Adjustment factors to calculate 24-hour yields using the Liu method. Milking time (MT) is either 1 (PM) or 2 (AM), i = parity class, j= milking interval class and k = stage of lactation class.'''''
|- style="background-color:#efefef;"
|'''MT'''
|'''i'''
|'''j'''
|'''k'''
| colspan="2" |'''Milk yield (DMY)'''
| colspan="2" |'''Fat yield (DFY)'''
| colspan="2" |'''Protein yield (DPY)'''
|-
| colspan="4" |
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|-
|1
|1
|1
|1
|5.29333
|1.83283
|0.30911
|1.43518
|0.18984
|1.77461
|-
|1
|1
|1
|2
|4.17676
|1.97447
|0.2803
|1.56914
|0.12246
|2.00568
|-
|1
|1
|1
|3
|4.26476
|1.95945
|0.18826
|1.82468
|0.12624
|2.0137
|-
|1
|1
|1
|4
|3.41282
|2.01814
|0.25025
|1.64707
|0.12519
|1.99629
|-
|1
|1
|1
|5
|1.79548
|2.22665
|0.06578
|2.09515
|0.05249
|2.24065
|-
|1
|1
|1
|6
|3.7751
|1.95508
|0.12854
|1.93892
|0.11936
|2.00979
|-
|1
|1
|1
|7
|1.544
|2.1478
|0.06425
|2.06779
|0.0569
|2.13851
|-
|1
|1
|2
|1
|5.8584
|1.79409
|0.33193
|1.42953
|0.20756
|1.7288
|-
|1
|1
|2
|2
|5.45524
|1.84258
|0.32877
|1.43235
|0.21332
|1.74001
|-
|1
|1
|2
|3
|4.64052
|1.86706
|0.27155
|1.57017
|0.16439
|1.84539
|-
|1
|1
|2
|4
|2.86835
|2.06209
|0.18647
|1.79403
|0.10803
|2.0193
|-
|1
|1
|2
|5
|2.11336
|2.12055
|0.10435
|1.97206
|0.07193
|2.10651
|-
|1
|1
|2
|6
|2.00673
|2.0636
|0.1386
|1.83336
|0.06892
|2.06532
|-
|1
|1
|2
|7
|1.71752
|2.11269
|0.06501
|2.0379
|0.05569
|2.12881
|-
|1
|1
|3
|1
|2.80244
|2.02183
|0.17663
|1.72438
|0.11078
|1.96422
|-
|1
|1
|3
|2
|3.47396
|1.98268
|0.2135
|1.6805
|0.10471
|1.99092
|-
|1
|1
|3
|3
|2.81702
|2.04348
|0.20754
|1.71868
|0.1127
|1.98403
|-
|1
|1
|3
|4
|3.1989
|1.998
|0.21578
|1.6991
|0.10802
|1.99517
|-
|1
|1
|3
|5
|2.47055
|2.04826
|0.15418
|1.83151
|0.07492
|2.07547
|-
|1
|1
|3
|6
|1.923
|2.07728
|0.11783
|1.89678
|0.06457
|2.08391
|-
|1
|1
|3
|7
|1.85264
|2.0873
|0.13047
|1.86711
|0.071
|2.06917
|-
|1
|1
|4
|1
|2.75042
|1.96631
|0.24794
|1.61741
|0.09248
|1.95376
|-
|1
|1
|4
|2
|2.97505
|1.96711
|0.20029
|1.71842
|0.09381
|1.97081
|-
|1
|1
|4
|3
|2.33365
|2.02986
|0.17021
|1.79996
|0.07631
|2.03167
|-
|1
|1
|4
|4
|3.41505
|1.94107
|0.1845
|1.76799
|0.10989
|1.95456
|-
|1
|1
|4
|5
|2.67488
|1.97797
|0.13433
|1.85893
|0.09432
|1.97755
|-
|1
|1
|4
|6
|1.89907
|2.04841
|0.08715
|1.96251
|0.07132
|2.04225
|-
|1
|1
|4
|7
|1.80326
|2.03554
|0.1251
|1.86477
|0.06072
|2.04747
|-
|1
|1
|5
|1
|2.76763
|1.92863
|0.15754
|1.72474
|0.10187
|1.88749
|-
|1
|1
|5
|2
|3.36896
|1.92048
|0.2236
|1.64149
|0.12369
|1.8823
|-
|1
|1
|5
|3
|2.22763
|2.00452
|0.17614
|1.7474
|0.08019
|1.9782
|-
|1
|1
|5
|4
|2.44625
|1.97049
|0.17217
|1.74753
|0.0889
|1.94647
|-
|1
|1
|5
|5
|2.379
|1.97307
|0.15965
|1.76134
|0.0896
|1.94575
|-
|1
|1
|5
|6
|1.62948
|2.02491
|0.11021
|1.85546
|0.0852
|1.94593
|-
|1
|1
|5
|7
|1.45651
|2.0254
|0.07479
|1.92789
|0.05846
|2.00196
|-
|1
|1
|6
|1
|2.01088
|1.9497
|0.16548
|1.68143
|0.101
|1.85846
|-
|1
|1
|6
|2
|2.96605
|1.93064
|0.25841
|1.52566
|0.12097
|1.86061
|-
|1
|1
|6
|3
|2.2281
|1.96085
|0.19036
|1.69013
|0.08032
|1.9375
|-
|1
|1
|6
|4
|2.39473
|1.952
|0.17854
|1.72423
|0.06863
|1.97582
|-
|1
|1
|6
|5
|2.37955
|1.94127
|0.19579
|1.66419
|0.08447
|1.93156
|-
|1
|1
|6
|6
|0.36203
|2.12393
|0.14291
|1.75822
|0.03845
|2.04562
|-
|1
|1
|6
|7
|1.5702
|1.96794
|0.1336
|1.76796
|0.06449
|1.94829
|-
|1
|1
|7
|1
|3.93654
|1.82772
|0.2359
|1.61894
|0.15032
|1.76054
|-
|1
|1
|7
|2
|4.39662
|1.81581
|0.24969
|1.5881
|0.16909
|1.74794
|-
|1
|1
|7
|3
|3.78325
|1.82778
|0.19228
|1.71802
|0.12368
|1.8268
|-
|1
|1
|7
|4
|3.39116
|1.86302
|0.1969
|1.71838
|0.12282
|1.848
|-
|1
|1
|7
|5
|3.20111
|1.83255
|0.09893
|1.86309
|0.1044
|1.84257
|-
|1
|1
|7
|6
|3.75639
|1.78665
|0.25205
|1.56174
|0.14105
|1.76802
|-
|1
|1
|7
|7
|1.42153
|1.95649
|0.09226
|1.85882
|0.04636
|1.96245
|-
|1
|1
|8
|1
|2.3454
|1.90436
|0.14321
|1.77423
|0.10703
|1.82306
|-
|1
|1
|8
|2
|3.97557
|1.82746
|0.26651
|1.58374
|0.15298
|1.76385
|-
|1
|1
|8
|3
|4.26939
|1.80503
|0.22918
|1.64925
|0.12924
|1.81061
|-
|1
|1
|8
|4
|2.90779
|1.89861
|0.18578
|1.73968
|0.13948
|1.79679
|-
|1
|1
|8
|5
|2.8265
|1.87632
|0.19374
|1.67929
|0.12377
|1.80944
|-
|1
|1
|8
|6
|2.26312
|1.87397
|0.09917
|1.82528
|0.08819
|1.84453
|-
|1
|1
|8
|7
|0.31382
|2.04402
|0.05049
|1.95773
|0.02612
|1.99012
|-
|1
|2
|1
|1
|4.63752
|1.99615
|0.31102
|1.58962
|0.16637
|1.96686
|-
|1
|2
|1
|2
|5.56226
|1.91521
|0.26761
|1.64342
|0.16973
|1.94145
|-
|1
|2
|1
|3
|4.51983
|1.96962
|0.26221
|1.65088
|0.12245
|2.03857
|-
|1
|2
|1
|4
|4.51563
|1.93033
|0.18468
|1.80715
|0.15252
|1.94807
|-
|1
|2
|1
|5
|2.60334
|2.07338
|0.16011
|1.81257
|0.09892
|2.05493
|-
|1
|2
|1
|6
|2.86068
|1.98457
|0.15381
|1.79197
|0.08619
|2.04046
|-
|1
|2
|1
|7
|1.6596
|2.11753
|0.13089
|1.83687
|0.09908
|1.96479
|-
|1
|2
|2
|1
|3.94656
|2.03607
|0.23716
|1.6988
|0.19559
|1.88765
|-
|1
|2
|2
|2
|4.20525
|1.98621
|0.3553
|1.46663
|0.1657
|1.92175
|-
|1
|2
|2
|3
|3.31729
|2.04589
|0.29682
|1.57761
|0.12491
|2.00945
|-
|1
|2
|2
|4
|1.95977
|2.13926
|0.16059
|1.79846
|0.06713
|2.12835
|-
|1
|2
|2
|5
|1.49014
|2.14889
|0.10057
|1.90772
|0.05279
|2.14047
|-
|1
|2
|2
|6
|0.82235
|2.22517
|0.07573
|1.94963
|0.04014
|2.17549
|-
|1
|2
|2
|7
|1.53608
|2.08972
|0.11472
|1.81148
|0.0676
|2.03957
|-
|1
|2
|3
|1
|3.85525
|2.00429
|0.27991
|1.62403
|0.12863
|1.98973
|-
|1
|2
|3
|2
|4.1508
|1.9852
|0.3635
|1.47515
|0.13952
|1.97074
|-
|1
|2
|3
|3
|3.31493
|2.02332
|0.31131
|1.55183
|0.11703
|2.00696
|-
|1
|2
|3
|4
|2.47354
|2.0652
|0.20828
|1.71637
|0.09402
|2.04147
|-
|1
|2
|3
|5
|1.68517
|2.08809
|0.14418
|1.80246
|0.06917
|2.05808
|-
|1
|2
|3
|6
|1.316
|2.12714
|0.11206
|1.87179
|0.04723
|2.12486
|-
|1
|2
|3
|7
|0.4841
|2.20538
|0.04633
|2.02915
|0.02369
|2.18113
|-
|1
|2
|4
|1
|2.82623
|2.01819
|0.25826
|1.69268
|0.11251
|1.97665
|-
|1
|2
|4
|2
|3.24039
|1.9811
|0.36283
|1.50648
|0.11719
|1.96246
|-
|1
|2
|4
|3
|2.4545
|2.03386
|0.19627
|1.75339
|0.09698
|2.00807
|-
|1
|2
|4
|4
|2.46446
|2.01626
|0.17827
|1.76414
|0.08026
|2.02912
|-
|1
|2
|4
|5
|2.11339
|2.00724
|0.14884
|1.77964
|0.07749
|2.00585
|-
|1
|2
|4
|6
|1.51141
|2.04563
|0.11559
|1.82474
|0.06194
|2.02586
|-
|1
|2
|4
|7
|0.95936
|2.09963
|0.07044
|1.95281
|0.03645
|2.0993
|-
|1
|2
|5
|1
|3.36561
|1.97323
|0.2649
|1.65361
|0.13019
|1.92402
|-
|1
|2
|5
|2
|3.66222
|1.95479
|0.35065
|1.51028
|0.14652
|1.89882
|-
|1
|2
|5
|3
|3.20442
|1.96165
|0.28676
|1.58823
|0.12031
|1.93028
|-
|1
|2
|5
|4
|1.78673
|2.0426
|0.17183
|1.75198
|0.0678
|2.02025
|-
|1
|2
|5
|5
|1.61868
|2.01988
|0.11914
|1.80878
|0.06624
|1.99283
|-
|1
|2
|5
|6
|1.30123
|2.02218
|0.10515
|1.80653
|0.05345
|2.00292
|-
|1
|2
|5
|7
|0.65695
|2.08269
|0.06835
|1.89102
|0.0332
|2.0525
|-
|1
|2
|6
|1
|2.3773
|1.9669
|0.24867
|1.6336
|0.08319
|1.94741
|-
|1
|2
|6
|2
|2.82556
|1.95506
|0.31731
|1.51798
|0.12008
|1.89324
|-
|1
|2
|6
|3
|2.7235
|1.94883
|0.30621
|1.5177
|0.09365
|1.93764
|-
|1
|2
|6
|4
|1.77727
|1.98273
|0.17989
|1.69341
|0.07314
|1.95161
|-
|1
|2
|6
|5
|0.81041
|2.05295
|0.13961
|1.74391
|0.04468
|2.01091
|-
|1
|2
|6
|6
|0.72188
|2.0465
|0.09874
|1.79927
|0.03137
|2.03309
|-
|1
|2
|6
|7
|1.21598
|1.97942
|0.07065
|1.87211
|0.04484
|1.98491
|-
|1
|2
|7
|1
|3.55054
|1.89128
|0.27402
|1.61031
|0.10827
|1.89085
|-
|1
|2
|7
|2
|5.0062
|1.81574
|0.3119
|1.54857
|0.18009
|1.76865
|-
|1
|2
|7
|3
|3.95204
|1.84947
|0.30465
|1.53907
|0.16048
|1.789
|-
|1
|2
|7
|4
|2.36233
|1.9168
|0.18751
|1.70412
|0.09531
|1.88355
|-
|1
|2
|7
|5
|1.48851
|1.94443
|0.09973
|1.81041
|0.05904
|1.92497
|-
|1
|2
|7
|6
|1.22525
|1.94454
|0.06617
|1.87082
|0.05516
|1.91259
|-
|1
|2
|7
|7
|1.13847
|1.93756
|0.08109
|1.83388
|0.04706
|1.93165
|-
|1
|2
|8
|1
|4.09874
|1.87708
|0.20312
|1.73434
|0.15506
|1.83083
|-
|1
|2
|8
|2
|4.66403
|1.84302
|0.31808
|1.56093
|0.18049
|1.78288
|-
|1
|2
|8
|3
|3.24375
|1.89351
|0.2827
|1.59546
|0.13583
|1.83427
|-
|1
|2
|8
|4
|2.24175
|1.92084
|0.17795
|1.72611
|0.09636
|1.87438
|-
|1
|2
|8
|5
|1.63783
|1.93625
|0.1225
|1.78642
|0.0659
|1.90934
|-
|1
|2
|8
|6
|2.01753
|1.89095
|0.13742
|1.74752
|0.08289
|1.86553
|-
|1
|2
|8
|7
|0.97568
|1.97215
|0.05926
|1.88807
|0.04057
|1.95672
|-
|2
|1
|1
|1
|3.44076
|1.73133
|0.27759
|1.55037
|0.13323
|1.68913
|-
|2
|1
|1
|2
|4.99596
|1.64527
|0.2322
|1.58033
|0.17533
|1.62422
|-
|2
|1
|1
|3
|3.83372
|1.68144
|0.25087
|1.52033
|0.14525
|1.66706
|-
|2
|1
|1
|4
|3.87034
|1.68102
|0.20979
|1.60153
|0.13627
|1.68885
|-
|2
|1
|1
|5
|1.76134
|1.80424
|0.15241
|1.70485
|0.06231
|1.81524
|-
|2
|1
|1
|6
|0.79304
|1.89072
|0.09906
|1.80312
|0.03277
|1.89435
|-
|2
|1
|1
|7
|1.43535
|1.80614
|0.0593
|1.81589
|0.0407
|1.85002
|-
|2
|1
|2
|1
|3.72284
|1.68499
|0.19226
|1.66567
|0.1237
|1.66453
|-
|2
|1
|2
|2
|4.42667
|1.66508
|0.24314
|1.55652
|0.14361
|1.66251
|-
|2
|1
|2
|3
|2.7019
|1.75871
|0.32717
|1.38452
|0.11056
|1.72312
|-
|2
|1
|2
|4
|2.41538
|1.75937
|0.14575
|1.68355
|0.09038
|1.74138
|-
|2
|1
|2
|5
|1.65412
|1.81649
|0.13926
|1.70623
|0.0597
|1.81378
|-
|2
|1
|2
|6
|2.0843
|1.7735
|0.21052
|1.57508
|0.07244
|1.78566
|-
|2
|1
|2
|7
|1.43238
|1.80651
|0.08031
|1.78712
|0.05269
|1.81727
|-
|2
|1
|3
|1
|2.45314
|1.77068
|0.18152
|1.73443
|0.07657
|1.78025
|-
|2
|1
|3
|2
|3.01217
|1.70966
|0.19388
|1.66175
|0.05624
|1.80606
|-
|2
|1
|3
|3
|2.09997
|1.74945
|0.14493
|1.68277
|0.05446
|1.7922
|-
|2
|1
|3
|4
|2.36683
|1.71741
|0.12244
|1.71407
|0.06775
|1.75721
|-
|2
|1
|3
|5
|1.56776
|1.75755
|0.08776
|1.76946
|0.04244
|1.79675
|-
|2
|1
|3
|6
|1.63824
|1.75452
|0.09422
|1.76794
|0.04181
|1.80604
|-
|2
|1
|3
|7
|0.74114
|1.83421
|0.08039
|1.78306
|0.02347
|1.85596
|-
|2
|1
|4
|1
|1.47047
|1.78588
|0.17271
|1.69379
|0.06511
|1.74985
|-
|2
|1
|4
|2
|2.22168
|1.72985
|0.20701
|1.59429
|0.08178
|1.71455
|-
|2
|1
|4
|3
|2.50108
|1.69618
|0.16828
|1.61962
|0.08598
|1.70516
|-
|2
|1
|4
|4
|1.97141
|1.7202
|0.1446
|1.66357
|0.06856
|1.73201
|-
|2
|1
|4
|5
|1.17054
|1.75879
|0.1172
|1.69234
|0.04624
|1.75806
|-
|2
|1
|4
|6
|1.74755
|1.70968
|0.12562
|1.67603
|0.0629
|1.72333
|-
|2
|1
|4
|7
|0.52482
|1.80155
|0.07345
|1.75615
|0.02671
|1.79288
|-
|2
|1
|5
|1
|1.76464
|1.76219
|0.24301
|1.59094
|0.07156
|1.73136
|-
|2
|1
|5
|2
|1.99594
|1.73438
|0.1984
|1.5954
|0.06489
|1.73449
|-
|2
|1
|5
|3
|1.8804
|1.72362
|0.13019
|1.67977
|0.06783
|1.71916
|-
|2
|1
|5
|4
|1.83337
|1.71477
|0.11197
|1.70244
|0.05764
|1.73194
|-
|2
|1
|5
|5
|1.49752
|1.72615
|0.13128
|1.65461
|0.04656
|1.7433
|-
|2
|1
|5
|6
|1.3042
|1.7305
|0.07173
|1.75315
|0.04482
|1.7399
|-
|2
|1
|5
|7
|2.00868
|1.67669
|0.12298
|1.64761
|0.09175
|1.64669
|-
|2
|1
|6
|1
|0.84993
|1.75972
|0.12918
|1.74026
|0.0328
|1.74802
|-
|2
|1
|6
|2
|1.93666
|1.67406
|0.16606
|1.59943
|0.04535
|1.7106
|-
|2
|1
|6
|3
|2.12115
|1.64964
|0.19988
|1.50821
|0.05229
|1.68986
|-
|2
|1
|6
|4
|0.68831
|1.73901
|0.09674
|1.6838
|0.01696
|1.75787
|-
|2
|1
|6
|5
|1.13081
|1.69479
|0.06413
|1.72559
|0.04936
|1.67757
|-
|2
|1
|6
|6
|0.5893
|1.72537
|0.02598
|1.80138
|0.01591
|1.74082
|-
|2
|1
|6
|7
|0.72519
|1.71955
|0.03157
|1.78405
|0.02889
|1.71972
|-
|2
|1
|7
|1
|1.85937
|1.66064
|0.2416
|1.49676
|0.06807
|1.63599
|-
|2
|1
|7
|2
|1.8527
|1.64892
|0.2374
|1.43845
|0.06336
|1.6431
|-
|2
|1
|7
|3
|1.56905
|1.66084
|0.15434
|1.55598
|0.04336
|1.68109
|-
|2
|1
|7
|4
|0.74968
|1.69857
|0.13496
|1.56636
|0.02871
|1.6933
|-
|2
|1
|7
|5
|1.08222
|1.65925
|0.10847
|1.613
|0.03305
|1.67829
|-
|2
|1
|7
|6
|1.1124
|1.68059
|0.14267
|1.57525
|0.04416
|1.6776
|-
|2
|1
|7
|7
|0.88031
|1.6751
|0.10534
|1.60483
|0.04216
|1.66444
|-
|2
|1
|8
|1
|0.62802
|1.72402
|0.19225
|1.54631
|0.03247
|1.69368
|-
|2
|1
|8
|2
|0.83902
|1.68303
|0.15492
|1.53421
|0.05922
|1.61411
|-
|2
|1
|8
|3
|1.33727
|1.63407
|0.19835
|1.43309
|0.05874
|1.61141
|-
|2
|1
|8
|4
|1.06381
|1.64762
|0.11026
|1.58762
|0.04019
|1.64574
|-
|2
|1
|8
|5
|1.13714
|1.61716
|0.13322
|1.53166
|0.05648
|1.59149
|-
|2
|1
|8
|6
|1.19134
|1.60463
|0.11089
|1.54864
|0.06258
|1.56912
|-
|2
|1
|8
|7
|1.58872
|1.60204
|0.066
|1.64659
|0.04748
|1.63282
|-
|2
|2
|1
|1
|3.46775
|1.78609
|0.28956
|1.68515
|0.15003
|1.72171
|-
|2
|2
|1
|2
|5.69879
|1.67614
|0.3725
|1.5045
|0.19774
|1.64659
|-
|2
|2
|1
|3
|5.18985
|1.66571
|0.40124
|1.40574
|0.17828
|1.65793
|-
|2
|2
|1
|4
|3.43435
|1.74182
|0.20332
|1.66994
|0.11075
|1.76221
|-
|2
|2
|1
|5
|2.48643
|1.76219
|0.13714
|1.7396
|0.09636
|1.75624
|-
|2
|2
|1
|6
|1.41151
|1.82292
|0.15415
|1.6725
|0.06549
|1.80013
|-
|2
|2
|1
|7
|0.9096
|1.8409
|0.08811
|1.7823
|0.03467
|1.85275
|-
|2
|2
|2
|1
|1.85358
|1.83615
|0.28355
|1.64765
|0.06055
|1.83138
|-
|2
|2
|2
|2
|3.81188
|1.74978
|0.25972
|1.62799
|0.11238
|1.7646
|-
|2
|2
|2
|3
|3.16717
|1.76679
|0.29832
|1.53409
|0.09407
|1.78959
|-
|2
|2
|2
|4
|2.33664
|1.78934
|0.22694
|1.60101
|0.07273
|1.80371
|-
|2
|2
|2
|5
|2.01675
|1.79303
|0.10664
|1.79792
|0.06062
|1.8184
|-
|2
|2
|2
|6
|1.80809
|1.80081
|0.13659
|1.70935
|0.07335
|1.79213
|-
|2
|2
|2
|7
|1.01661
|1.8295
|0.0548
|1.84688
|0.03414
|1.84213
|-
|2
|2
|3
|1
|2.01474
|1.8142
|0.21867
|1.74325
|0.05359
|1.83088
|-
|2
|2
|3
|2
|3.53989
|1.71985
|0.28196
|1.60868
|0.10823
|1.73763
|-
|2
|2
|3
|3
|3.38412
|1.69907
|0.27409
|1.56164
|0.11042
|1.71397
|-
|2
|2
|3
|4
|2.2171
|1.74622
|0.16076
|1.70107
|0.07372
|1.75906
|-
|2
|2
|3
|5
|1.11799
|1.80944
|0.11087
|1.75678
|0.03792
|1.81891
|-
|2
|2
|3
|6
|1.40464
|1.76033
|0.10048
|1.72933
|0.05342
|1.75745
|-
|2
|2
|3
|7
|0.11328
|1.8972
|0.04052
|1.87101
|0.00787
|1.88753
|-
|2
|2
|4
|1
|2.59777
|1.74476
|0.28154
|1.66509
|0.10763
|1.71072
|-
|2
|2
|4
|2
|3.53853
|1.69511
|0.38311
|1.46839
|0.13243
|1.66523
|-
|2
|2
|4
|3
|2.80538
|1.70587
|0.26686
|1.55787
|0.1126
|1.68024
|-
|2
|2
|4
|4
|2.18191
|1.72068
|0.18333
|1.65612
|0.085
|1.71029
|-
|2
|2
|4
|5
|1.23383
|1.7716
|0.12824
|1.71179
|0.04845
|1.76628
|-
|2
|2
|4
|6
|0.85652
|1.79279
|0.0763
|1.79314
|0.03563
|1.78528
|-
|2
|2
|4
|7
|0.97995
|1.77178
|0.0797
|1.7577
|0.03846
|1.77043
|-
|2
|2
|5
|1
|2.47016
|1.74985
|0.32061
|1.60073
|0.10455
|1.71058
|-
|2
|2
|5
|2
|3.76194
|1.68979
|0.32787
|1.54675
|0.11781
|1.69109
|-
|2
|2
|5
|3
|2.61421
|1.70766
|0.20307
|1.64866
|0.08315
|1.71378
|-
|2
|2
|5
|4
|1.6809
|1.74028
|0.16795
|1.66491
|0.06202
|1.73305
|-
|2
|2
|5
|5
|1.31241
|1.75722
|0.14383
|1.68302
|0.05338
|1.74562
|-
|2
|2
|5
|6
|1.66563
|1.71781
|0.12721
|1.69231
|0.06147
|1.72101
|-
|2
|2
|5
|7
|0.87471
|1.74991
|0.07882
|1.71706
|0.04173
|1.73246
|-
|2
|2
|6
|1
|1.70055
|1.72832
|0.20839
|1.67759
|0.06001
|1.71779
|-
|2
|2
|6
|2
|3.20558
|1.65143
|0.33676
|1.47797
|0.09642
|1.6546
|-
|2
|2
|6
|3
|1.5827
|1.71538
|0.19719
|1.62038
|0.05324
|1.71254
|-
|2
|2
|6
|4
|1.7692
|1.69473
|0.14854
|1.66225
|0.05758
|1.69946
|-
|2
|2
|6
|5
|1.33003
|1.70542
|0.10726
|1.69398
|0.04565
|1.7096
|-
|2
|2
|6
|6
|1.01266
|1.71155
|0.09376
|1.70285
|0.04005
|1.70822
|-
|2
|2
|6
|7
|0.9856
|1.70091
|0.06454
|1.73063
|0.0394
|1.69796
|-
|2
|2
|7
|1
|2.02441
|1.67788
|0.30435
|1.5407
|0.08673
|1.63673
|-
|2
|2
|7
|2
|1.43949
|1.71143
|0.30098
|1.47963
|0.06527
|1.67295
|-
|2
|2
|7
|3
|1.68946
|1.66442
|0.24777
|1.47116
|0.06594
|1.64834
|-
|2
|2
|7
|4
|1.10967
|1.68591
|0.15663
|1.60109
|0.04949
|1.67069
|-
|2
|2
|7
|5
|0.77866
|1.70882
|0.11248
|1.64389
|0.03402
|1.70215
|-
|2
|2
|7
|6
|0.67502
|1.69719
|0.10289
|1.62419
|0.03507
|1.67744
|-
|2
|2
|7
|7
|0.65216
|1.70336
|0.05545
|1.73388
|0.02233
|1.72102
|-
|2
|2
|8
|1
|1.33877
|1.67358
|0.18369
|1.64385
|0.06055
|1.63818
|-
|2
|2
|8
|2
|0.71697
|1.71038
|0.25461
|1.49037
|0.04798
|1.66397
|-
|2
|2
|8
|3
|2.13197
|1.62429
|0.2393
|1.47673
|0.08136
|1.6065
|-
|2
|2
|8
|4
|1.16932
|1.66188
|0.13759
|1.60108
|0.0463
|1.64856
|-
|2
|2
|8
|5
|1.48369
|1.62387
|0.12547
|1.58988
|0.06919
|1.5925
|-
|2
|2
|8
|6
|1.18879
|1.65442
|0.10031
|1.62813
|0.07392
|1.58846
|-
|2
|2
|8
|7
|0.58052
|1.68546
|0.02696
|1.7382
|0.01982
|1.70519
|}
</center>
</div>
</div>

== Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme ==
<div class="mw-collapsible mw-collapsed">
<div>
=== Abstract ===
Based on comments on imprecision of the estimation method for 24-hour fat % in AM/PM milk recording schemes the regression formula was extended and re-estimated. Non-linearity for the existing effects of protein % of the milk sample, interval before sampling, milk amount of sample, milk amount of previous milking and interval before the previous milking was incorporated by using polynomials. Extensions were made by adding the effects of time of sampling, parity and month of sampling as class variables and lactation stage as polynomial. In total a reduction of the standard deviation of the difference between true and estimated 24-hour fat % of 2.4% was reached (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

'''''Keywords''''': estimation, fat %, AM/PM.

=== Introduction ===
The AM/PM milk recording routine is based on only one morning (a.m.) or evening (p.m.) milk sample which are collected in an alternating way. A condition to take part in this AM/PM milk recording in The Netherlands is that on farm electronic milk measurements (EMM) are available. EMM-data consists of time of milking and milk quantity of every milking. Based on one milk sample and the EMM-data the 24-hour fat % is estimated (Peeters & Galesloot, 2002<ref name=":2">Peeters, R. and P. Galesloot, 2002.Estimating daily fat yield from a single milking on test day for herds with a robotic milking system. J. Dairy Sci. 85, 682-688.</ref>). Also for farms with an automatic milking system (AMS) this estimation is used when only one milk sample is available for analysis on milk composition.

Based on comments from farmers on fluctuations in 24-hour fat % preliminary research was conducted. This showed that the current estimation caused an underestimation of 24-hour fat % based on an a.m.-sample of 0.09% while the estimate based on a p.m.-sample was overestimated by 0.05%. Possible causes for this fluctuation are differences in milk-fat synthesis between day- and night-time as was shown by Gilbert et al. (1972) <ref>Gilbert, G.R., G.L. Hargrove and M. Kroger, 1972. Diurnal variations in milk yield, fat yield, milk fat % and milk protein % by the test interval method. J. Dairy Sci. 56, 409-410.</ref>and Lee & Wardorp (1984)<ref>Lee, A.J. and Wardorp, 1984. Predicting daily milk yield, fat percent, and protein percent from morning or afternoon tests. J. Dairy Sci. 67, 351-360.</ref>. Other factors of imprecision in the current estimation can be caused by lactation stage and parity, two factors that are accounted for in the method of Liu et al. (2000)<ref>Liu, Z., R. Reents, F. Reinhardt and K Kuwan, 2000. Approaches to estimating daily yield from single milk testing schemes and use of a.m.-p.m. records in test-day model genetic evaluation in dairy cattle. J. Dairy Sci. 83, 2672-2682.</ref>.

The objective of this research is to re-estimate the regression formula which is used to estimate the 24-hour fat %s in AM/PM milk recording and AMS recordings with only one sample. By testing for non-linearity of current effects and introducing new explanatory variables the aim is to increase the accuracy of the estimated 24-hour fat %.

=== Material and Methods ===
The data needed for the objective had to meet a number of criteria. The most important criteria were that the data comprised:

* differences in interval between milking times;
* different milking times;
* multiple samples per cow per herd test date;
* milking time and quantity of all milkings;

Only data of farms that use an AMS met all of these criteria. Therefore the research was conducted on data of all farms that used an AMS from January 20th 2001 until July 1st 2004. Records with only one sample per herd test date were excluded from the analysis.

In order to estimate as well as validate the new regression formula the each herd test date was assigned at random into two separate datasets. Dataset 1 was used for estimation and contained 371.528 samplings on 50.591 cows on 537 farms. Dataset 2 was used for validation and contained 371.885 milkings on 50.643 cows on 538 farms. Some characteristics of variables of both datasets are presented in Table 1.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" |'''''Table 1. Characteristics of variables in dataset 1 (estimation) and dataset 2 (validation).'''''
|-
| rowspan="2" |'''Variable'''
| colspan="2" |'''Dataset 1 (estimation)'''
| colspan="2" |'''Dataset 2 (validation)'''
|-
|'''Mean'''
|'''Std'''
|'''Mean'''
|'''Std'''
|-
|Sample milk amount (kg)
|10.1
|3.1
|10.1
|3.1
|-
|Sample fat (%)
|4.40
|0.76
|4.41
|0.76
|-
|Sample protein (%)
|3.49
|0.35
|3.49
|0.35
|-
|Time at sampling
|12.29
|7.24
|12.31
|7.24
|-
|Interval before sample (min)
|520
|154
|521
|155
|-
|Interval before prev. milking (min)
|526
|158
|527
|159
|}
</center>

=== Methods ===
The analysis started with the currently used regression formula which uses the effects: fat %, protein %, milk amount of sampling, interval before sampling, milk amount of the previous milking and interval before the previous milking (Peeters & Galesloot, 2002<ref name=":2" />). All these effects are considered to be linear. As an extra check of the data this regression formula was re-estimated and compared to the currently used regression formula. In order to estimate the regression formula first of all the 24-hour fat % was determined by using a weighted average of all milk samples for that cow on that herd test date.

Subsequently, a number of changes to the regression formula were tested for their effect on the accuracy of the 24-hour fat %. The changes that are tested are:

# non-linearity of the current effects;
# effect of time at sampling;
# effect of lactation stage;
# effect of parity;
# month of milk recording;

The effects were all tested in a similar way by plotting the residuals of the regression formula without the effect that is tested to the tested effect. Based on this plot a possible relation between residual and effect becomes clear and the best way of incorporating the effect is shown. The conclusion if an effect had a positive effect on the accuracy of the regression formula was based on the standard deviation of the difference between estimated and true 24-hour fat %. Also the correlation between the two fat %s and the b-factor (regression coefficient) of the linear regression between the two fat %s were considered.

=== Results ===
The regression coefficients of the re-estimated regression formula differed slightly from the estimates by Peeters & Galesloot (2002)<ref name=":1" />, probably due to the different dataset.

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %.
[[File:Imagefig1.png|center|thumb|''Figure 1a: Average residual per class for the variables sample fat %'']]
[[File:Imagefig1b.png|center|thumb|''Figure 1b: Sample protein %'' ]]
[[File:Imagefig1c.png|center|thumb|''Figure 1c : Interval before sampling'']]
[[File:Imagefig1d.png|center|thumb|''Figure 1d : Interval before previous milking'']]
[[File:Imagefig1e.png|center|thumb|''Figure 1e : Sample milk amount'']]
[[File:Imagefig1f.png|center|thumb|''Figure 1f: Milk amount before sampling'']]

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %. Of all variables, only fat % of the milk sample (Figure 1a) seemed to be linear. A 2nd order polynomial fitted the interval before the previous milking. The other variables, i.e. protein % of the milk sample, interval before sampling, milk amount of sample and milk amount of the previous milking were described by a 3rd order polynomial. For all variables except fat % of the sample higher order polynomials were found significant. This however was caused by the large amount of data and no longer a possible biological effect since it also had no effect on the accuracy of the estimation.

The effect of time of sampling showed a large amount of variability over time. Using a polynomial to fit the data was therefore difficult. Estimation of the effect by hourly intervals was a good alternative as is shown in Figure 2. Lactation stage had mainly an effect in the first 50 days of lactation as is shown by Figure 3. A 3rd order polynomial fitted the data properly.
[[File:Imagefig2.png|center|thumb|''Figure 2. Average residual per class for time of sampling (minutes after midnight).'']]
[[File:Imagefig33.png|center|thumb|''Figure 3. Average residual per class for lactation stage (days).'']]

The effects of parity and month of milk sampling were both considered as class variables. For parity the effects of parity 1 to 6 and 7 or higher were considered. Table 2 shows that mainly for the lower parities the estimated 24-hour fat % was overestimated. Also the months May to October, usually the pasture period, showed an overestimation of 24-hour fat %.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" |'''''Table 2. Effect of parity and month of sampling on estimated 24-hour fat % (*100).'''''
|-
|'''Parity'''
|'''Estimate'''
|'''Month of sampling'''
|'''Estimate'''
|-
|1
|<nowiki>-6.58</nowiki>
|January
|<nowiki>-0.24</nowiki>
|-
|2
|<nowiki>-3.56</nowiki>
|February
|<nowiki>-0.28</nowiki>
|-
|3
|<nowiki>-1.42</nowiki>
|June
|<nowiki>-0.54</nowiki>
|-
|4
|<nowiki>-0.48</nowiki>
|April
|<nowiki>-0.27</nowiki>
|-
|5
|<nowiki>-0.35</nowiki>
|May
|<nowiki>-2.07</nowiki>
|-
|6
|<nowiki>-0.35</nowiki>
|June
|<nowiki>-3.36</nowiki>
|-
|7+
|<nowiki>-0.00</nowiki>
|July
|<nowiki>-4.32</nowiki>
|-
|
|
|August
|<nowiki>-5.52</nowiki>
|-
|
|
|September
|<nowiki>-4.74</nowiki>
|-
|
|
|October
|<nowiki>-2.24</nowiki>
|-
|
|
|November
|<nowiki>-0.97</nowiki>
|-
|
|
|December
|<nowiki>-0.00</nowiki>
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" |'''''Table 3. Statistics of the difference between true and estimated 24-hour fat % for six regression formulas (current, re-estimated + five steps), each also including preceding steps.'''''
|-
|style="text-align: left;"|'''Regression'''
|'''Std.'''
|'''Min'''
|'''Max'''
|'''Cor'''
|'''b-factor'''
|-
|style="text-align: left;"|Current, re-estimated
|0.2856
|<nowiki>-1.840</nowiki>
|2.224
|0.898
|0.807
|-
|style="text-align: left;"|Non-linearity
|0.2820
|<nowiki>-1.890 </nowiki>
|2.198
|0.901
|0.812
|-
|style="text-align: left;"|Time of sampling
|0.2817
|<nowiki>-1.877 </nowiki>
|2.211
|0.901
|0.813
|-
|style="text-align: left;"|Lactation stage
|0.2803
|<nowiki>-1.883 </nowiki>
|2.196
|0.902
|0.814
|-
|style="text-align: left;"|Parity
|0.2794
|<nowiki>-1.887 </nowiki>
|2.179
|0.903
|0.816
|-
|style="text-align: left;"|Month of sampling
|0.2788
|<nowiki>-1.868 </nowiki>
|2.175
|0.903
|0.817
|}
</center>

Table 3 shows some statistics of the difference between the true and estimated 24-hour fat % based on dataset 2 (validation) of the different regression formulas. Each of the five changes to the regression formula had a (minor) positive effect on either the standard deviation of the difference between the true and estimated 24-hour fat % (Std.), the correlation (Cor) between the two fat %s, the b-factor of the linear regression between the two fat %s or a combination of the these. All changes together reduced the standard deviation with 2.4% from 0.2856 to 0.2788, increased the correlation from 0.898 to 0.903 and increased the b-factor from 0.807 to 0.817.

=== Conclusions ===
The regression formula to estimate the 24-hour fat % based on one milk sample was improved. Improvements were first of all considering non-linearity of the variables by using polynomials for protein % of the milk sample (3rd order), interval before sampling (3rd order), milk amount of sample (3rd order), milk amount of previous milking (3rd order) and interval before the previous milking (2nd order). Secondly, adding the effects of time of sampling (class variable), lactation stage (3rd order polynomial), parity (class variable) and month of sampling (class variable) gave a further reduction of the difference between true and estimated 24-hour fat %. The total reduction in standard deviation of the difference between true and estimated 24-hour fat % is 2.4% (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

== Appendix 3 - A unified Python implementation of standardized 305 day yield calculation methods ==
The ICAR guideline is translated into an open-source Python package that can serve as a reference implementation for 305-day yield calculation. In addition to implementing the methods described in the original guideline (with the exception of the multi-trait method, which will be added in future work), the package incorporates 14 lactation-curve models, including traditional parametric models, Bayesian fitting approaches, and an AI-based model. The package also provides tools to derive biologically relevant lactation characteristics such as time to peak, peak yield, cumulative yield, and persistency. The package is publicly available through PyPI and can be installed directly using pip install lactationcurve (van Leerdam et al., 2026). Extensive documentation was developed alongside the package to improve transparency and reproducibility [https://bovi-analytics.github.io/bovi/lactationcurve.html https://bovi-analytics.github.io/bovi/lactationcurve.html.]

Through a companioning website (https://tools.bovi-analytics.org<nowiki/>/), users can upload milk-recording data in CSV format, fit and visualize the implemented lactation-curve models, and compare different cumulative milk-yield methodologies on both test-day and fully daily-recorded lactations using metrics such as RMSE, Pearson correlation, MAPE, and MAE. Reference datasets are provided to allow organizations to benchmark their own calculations against alternative methodologies. In addition, downloadable PDF reports summarize the results through detailed statistics and scatterplots, both overall and stratified by parity.
</div>
</div>

Section 02 – Cattle Milk Recording

2026-07-22T17:53:23Z

Cmosconi: /* Procedure 1: Computing 24-hour Yields */

= Overview =
<div class="mw-collapsible mw-collapsed">
<div>
== Introduction ==
Information about milk production traits is very important for managing and breeding dairy herds. The milk recording process starts with the collection of animal identification, a calving date of milking cows, the amount of milk given and the date with time or time frame of a day. A milk sample may be taken. The obtained milk sample is analysed for milk constituents. The results of the analysis plus the data about milk yield and time of milking are stored in a database. Subsequently a number of parameters, cumulative yields and indices are calculated and stored in the database and, finally, reported to the farmer

This Section 2 of the ICAR Guidelines focuses on the milk recording process for dairy cattle.

== Scope ==
Figure 1 gives a pictorial summary of the main elements of this guideline.

In summary, this section of the ICAR Guidelines covers the milk recording process from the enrolment of a herd for milk recording, through to the delivery of information which a herd owner can use to assist in a range of decisions.
[[File:Scope of Section 2 - Dairy cattle milk recording..png|thumb|Figure 1. Scope of Section 2 -Dairy cattle milk recording.|center|524x524px]]

Not covered in this section are:
# Standards and guidelines for ICAR approval of milk recording devices. Please consult [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices|Section 11]] for this subject.
# Standards and guidelines for ICAR approval of ID devices. Please consult [[Section 10 – Identification Device Certification|Section 10]] for this subject.
# Standards and guidelines for preparation of milk samples and for quality assurance of milk analysis. Please consult [[Section 12 – Milk Analysis|Section 12]] for this subject.
# Standards and guidelines for in-line milk analysis on the farm. Please consult [[Section 13 – On-farm Milk Analysis|Section 13]] for this subject.

== Enrolment ==

Enrolment of new herds in the recording process should involve an agreement between the farmer and the recording organisation regarding technical and financial questions such as:

# General information about the recording programme itself, i.e.
#* Herd and cow identification.
#* Scope of recorded data, including database setup as required by the user.
#* Scheduling recording.
#* Data capture and processing.
#* Recording methods and intervals.
#* Milk measuring and meters.
#* Sampling and sample transport.
#* Reports (outcomes) and supporting decisions.
# Definition of supervision scheme and other quality assurance and plausibility checking steps.
# Fee structure and invoicing.
# Approval of technicians by milk recording organisations (MROs) so as to give them free access to farms for all recording and supervision actions.

In cases where the owner of the recorded cows or his employees carry out the recording itself, it is up to the organisation to decide upon, and provide for, any necessary training.

== Standard and Guidelines for Milk Recording ==
These standards and guidelines for milk recording are valid for all milking systems, including AMS where applicable.
====General Standards and Guidelines for milk recording====
#ICAR-approved (electronic) milk meters and sampling devices must be used on the recording day (see [https://wiki.icar.org/index.php/Section_11_%E2%80%93_Testing,_Approval_and_Checking_of_Measuring,_Recording_and_Sampling_Devices#Procedure_1:_Procedure_for_Application_for_Testing_of_Measuring,_Recording_and_Sampling_Devices_or_Sensor_Systems Procedure 1 of Section 11 - Guidelines for Testing, Approval and Checking of Milk Recording Devices]). The list of approved milk meters, jars and AMS and automatic milk sampler/tray combinations sampling devices can be found on the [https://www.icar.org/index.php/certifications/icar-certifications-for-milk-meters-for-cow-sheep-goats/ ICAR web page].
#Milk weights are recorded for each milking of the recording period. The measurement may be done using any of the ICAR approved recording devices, or by weighing. The minimum accuracy of the measurement is 0.2 kg.
#Where milk constituents are analysed, the equipment used must meet ICAR standards for accuracy. Please consult [[Section 12 – Milk Analysis|Sections 12]] and [[Section 13 – On-farm Milk Analysis|Section 13]] of the Guidelines for details.
#The accuracy of the equipment used for milk recording and sampling must be checked by an agency approved by the member organisations, on a regular and systematic basis using methods approved by ICAR. The list of methods is given in [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices#Procedure 6: Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices|Procedure 6 of Section 11]] - Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices.
#All analyses of the constituents of a milk sample must be carried out on the same milk sample.
#These samples should ideally represent the 24-hour milking period.
#If milk samples do not represent a 24-hour period, the results of milk analyses must be corrected to a 24-hour period by a method approved by ICAR (see [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]).
#In cases where the duration of recording deviates from 24 hours, the results must be converted into 24-hour yields. Only approved 24-hour yield calculation methods can be used. The appropriate methodology is described in [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]
#As date of recording, we recommend to use the date on which the last sample was taken. As alternative, the date of the first sample can be used.
#Calculation methods
##The quantities of milk and milk constituents shall be calculated according to one of the methods outlined in this section of the ICAR Guidelines (see [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Standard methods for calculating 24 hour yields]).
##Member organisations should keep the ICAR Secretariat informed about the calculation methods being used by the records processing operations in their organisation or country and shall be responsible for ensuring that the records are corrected and calculated as specified in this section of the ICAR Guidelines.
====Standards and Guidelines for milk recording using AMS====
This subsection covers systems where milk weights, milk quality or other traits of the cows are monitored constantly and automatically. This can be done in both automatic and manually operated milking systems.

Requirements:
*Animal identification is automatic and reliable. Farm transponders can also be used for automatic identification if they are linked to the cow’s official identification in farm software.
*All individual milkings must be recorded from all AMSs in the farm and transmitted to the recording database for calculation, interrupted milkings included.
*For official milk recording purposes, the data file obtained from electronic milk meters must contain the following: 1) Cow ID, 2) Milking time stamp, 3) Milk weight and 4) Sampling stamp to mark the milking where the sample comes from.
*All milkings within the recording period may be sampled, and in this case the samples should be analysed separately. Alternatively, a one-milking sample can be taken for each cow, followed by fat correction calculation.
*All cows in milk on the recording day have to be sampled. The sampling device must remain in operation until all cows are sampled. When the number of available sampling devices is smaller than the number of AMS units, sampling may need to be prolonged beyond one day to allow complete sampling of all cows. In that case, the sampling device has to be moved between AMS units.
*During sampling, the automatic sampler must be monitored to make sure there are vials left for the next cows.
*24-hour yield calculations must be carried out by a MRO, independently of the AMS manufacturer. This is done in order to guarantee harmonisation of calculation methods between the different brands of equipment and software.
*Data of all milkings over a given time period must be collected for the 24-hour milk yield calculation. A 96-hour data collection period is recommended.
Recommendations:
#Ideally, data of all milkings should be collected and used to compute lactation yield.
#Description of formats to exchange data recorded by an AMS can be requested from the manufacturer or the ICAR ADE data exchange standard for milking data can be used.
#In the case of milk recording method B (see [[Section 02 – Cattle Milk Recording#Recording|chapter 1.4 "Recording]]") with AMS, the milk recording organization should make sure that the farmer knows how to load or transfer data.
#Data can be extracted by: 1) manual operation by MRO Technician’s or Farmer (file extraction), 2) automated system and data transfer through an Application Programming Interface (API), 3) another data transfer and exchange system.
#Raw milk recording data from the AMS must be easily accessible for MRO data processing.
#For official milk recording purposes, the data file obtained from electronic milk meters may also contain the following: 1) Vial ID (this is obligatory with M sampling scheme), 2) Milking duration, 3) Milking speed, 4) Incomplete milking in automatic milking systems and 5) Other relevant data measured or reported by the equipment.
#Individual milkings should be tested for milk secretion rate in order to detect interrupted and unrecorded milkings, which in turn have an effect on the calculated 24-hour yields. If there is an interrupted milking or a milking that follows an interrupted milking at the beginning of the recording period, these two milkings must be excluded from the calculations. During the recording period they can be excluded but do not need to be.
#It is recommended to individually sample all milkings within the 24-hour recording period for 24-hour fat content calculation due to the high variability of milking frequency and milk fat content. In cases where sampling all milkings is not possible, please consult Chapter 2 of [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 - Computing 24-hour Yields] (for approved correction calculation methods).
#It is recommended to sample only milkings with a preceding interval longer than 4 hours.
====Authorisation to record====
It is recommended that professional milk recording technicians are trained and certified before they carry out recordings on their own. Ideally, such training includes a period of supervised work with a certified technician. Where such a certification system is in place, it is not allowed to record without an authorisation.

It is also recommended that frequent training is given to milk recording technicians on new technologies and equipment, safety instructions and data quality issues.

In B and C recording, farmers or their employees doing the practical recording need to be capable of operating the recording equipment correctly (e.g. milk meters, data capture tools) and are familiar with recording techniques.

It is recommended to have a conformation test from a certified recording agency and that frequent training take place.
====Cows to be recorded====
In a recorded herd, all milk-producing cows must be recorded. If a herd is divided into groups, all animals in the group have to be recorded on the same recording scheme. If different recording schemes are practiced on the farm all cows must be recorded according to the standards for recording and sampling intervals in table 3.

Acceptable reasons for missing data are discussed below, in 5.5. Missing results and/or abnormal intervals are reported [[Section 02 – Cattle Milk Recording#Missing results|here]].

===Identification (ID)===
====Herd ID====
Each herd in milk recording must be allocated a unique permanent identification number.
====Animal ID====
An official milk recording system must be based on a clearly identifiable and unique animal ID. It is recommended that one identification scheme for the whole country is used. Animal identification must also be in accordance with national and international regulation (e.g. EU member countries with EU legislation - 1760/2000 for cattle), and with relevant parts of currently valid ICAR Guidelines. The animal must be marked with an ICAR approved identification device or system. If the ID of imported animals is changed, the connection to the original ID must be maintained. Management numbers for cows can be used aside the official ID.
====Identification of the sample vial====
The sample, the milk weight and the cow ID must be linked at the milking.

Vials can be identified according to:
#Vial placement in the sampling unit.
#Cow or sample ID written on the vials.
#Barcoded vial with printed cow ID.
#Barcoded vial with cow ID registered at the milking.
#RFID vial with cow ID registered at the milking.
=====Sample identification without electronic equipment=====
Samples are identified according to their placement in the sampling unit. Additionally, sample or cow numbers can be written on the vials with a waterproof marker. If this marking is not done, there must be a sure and efficient way to identify sample No. 1 (e.g. different colour) and the sequence of other samples.

Each sampling unit must be connected to a list of samples where cow ID is given for each sample. Each transportation box also has to carry the relevant herd ID’s and, preferably, the sampling dates.
=====Barcoded vials=====
Samples are identified according to the barcode on the vial label.

If the label contains cow and/or herd ID, no electronic equipment is needed at the recording. The samples can be sent to the laboratory without accompanying sample lists or herd ID markings on the box.

If the label contains a random sample ID number, the cow ID must be connected with it on the farm. This is done with a barcode reader and computer programmes making the connection possible.
=====Vials with RFID=====
Samples are identified according to the RFID chip in the vial. This system requires the use of RFID readers and specific computer programmes creating a file where the cow and vial ID’s are connected.
=====Automatic sampling systems=====
In automatic milking systems (AMS), ICAR approved automatic samplers have to be used. Sample identification in these systems can be based on vial placement, barcode or RFID. The file with corresponding cow ID is in the management programme of the milking system. Data transfer is carried out with specific software and via a specific interface from the AMS to the MRO.
=====Sample ID in the laboratory=====
For impartiality and better quality, it is recommended that the samples are identified without cow ID and sent to the laboratory anonymously and the analysis results are merged afterwards in the data processing centre.
====Connection of the sample to milking and 24 h yield====
=====Sample and milk weight from the same milking=====
The ideal situation is that the sample and milk weight represent the same milking.
=====Sample from one milking, milk weight from two=====
A corrected analysis is routinely attached to the 24-hour yield.
=====Sample from one milking, milk weight from two or more, corrected by intervals=====
In this case, a 24-hour-yield is also combined with a one-milking sample, but the 24‑hour yield is obtained by correcting the recorded milkings according to the length of the preceding milking intervals. For example, if a cow has produced 20 kg milk in two milkings and the preceding intervals total 20 hours, her 24-hour yield is calculated as 20 kg * (24 h/20 h) = 24 kg. A corrected analysis is attached to this 24‑hour yield.
=====Sample from one milking or day, milk weight from several days=====
With electronic milk meters, it is possible to use the milk production from several days. This gives better accuracy of milk yield estimation; the highest accuracy with uncorrected milk weights is reached using a 4-day average. The problem is that the sample results become disconnected from the milk yield and a loss in fat and protein yield accuracy will occur. Ideally, fat and protein production should be connected to the recording day even in AMS.

In this case, there are three options to connect samples to the 24-hour yield:
#Milk weight is estimated from a longer measurement period but for fat and protein yield estimation only the milk yield on sampling day is used.
#Information only from the recording day for constituents in milk and milk yield estimation.
#Combination of multiple day milk yield with constituents from sampling. See ICAR procedures for using data from more than one day (Lazenby ''et al''., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>, estimation of fat and protein yield (Galesloot and Peeters , 2000)<ref name=":1">Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>.
The analysis data are merged with milk weights in the laboratory or data processing centre and the date of the analysis must be known.

=== Traits to be recorded ===

==== Definition of milking speed and box time ====

===== Introduction =====
Automated Milking Systems (AMS) do measure many traits. The definition of these traits might be different per brand of AMS. Data of these traits is often used by e.g. milk recording organisations, herdbooks or management software providers. When organisations store these data in their databases and use for certain services, it is important to know how these traits are defined.

These definitions could be used by milk recording organisations etc. to take into account differences between traits measured by different brands of AMS. These definitions could also be used by manufacturers of AMS to take into account for product development, to get more alignment in trait definitions between different brands of AMS.

Aim of this document is to propose a harmonized definition of some traits measured by AMS.

At this stage, the traits milking speed and box time are taken into account. Traits related to teat coordinates are described in Section 5 (Conformatoin Recording) of the ICAR guidelines.

==== Average milking speed ====
Definition = AverageMilkingSpeed (gr/min) = {TotalMilkYield / TotalMilkingTime}

* Total milk yield (kg) = Sum of all quarter level milk yields (kg)
* Total milking time = Last Take-off time (of any teat) - Begin of milk flow (of any teat)

Recommendations for manufacturers:

* Exclude any pre-treatment time from milking time.
* Provide take-off settings (threshold in gr/min at take-off, user-defined or default) and settings for the beginning of the measurement period, as milking time will be influenced by take-off settings and by the definition of the beginning of the milk flow.

Recommendations for data users:

* Don't report milking sessions with kick-off´s, interrupted and re-attached milkings because milking time will vary for these milkings.

==== Box time ====
Different types of box time:

* Milking
* Feed-only
* Pass-through
* Selection
* Training

Definition = {End box time - Begin box time} (HH:MM:SS)

* Begin box time = datetime of recognition of animal
* End box time = datetime when cow has exited the box (which might be different from opening of the gate), best to detect when cow has actually left the box

Additional data is needed to understand the status and completeness of the milking visit (Wethal and Heringstad, 2019). Registered issues during the milking are e.g.

* ff: at least 1 teat cup kicked off
* TeatNotFound: unable to find at least 1 of the teats for milking
* IncompleteMilking/FailedMilking: Minimum of 1 teat was registered as incompletely milked.
* The expected milk yield for a milking session depends on previous milkings. Settings like yield less than 80% of expectation for a teat, the milking session would be recorded as having an incompletely milked teat.
* Manual interaction like teat manually attached or milking finished manually.

Recommendations for manufacturers:

* Make the codes available that express if a milking was successful and the cause if the milking was not successful.
* Uniform names and definitions for interrupted, incomplete or failed milkings as well.

Recommendations for data users:

* Check the availability of a code that expresses if a milking was successful and the cause if the milking was not successful. The meaning of the code can be used to consider if the box time record has to be used for the intended purpose or not.
* To check if there is any extra box time due to feeding concentrates, e.g. through user specific settings such as 'PriorityFeeding'.

=== Traits to be recorded ===
In official milk recording, the following data have to be recorded, wherever available:

# Identification of each cow in the herd, even if they remain in the herd for a very short time.
# Birth date, sex, breed and parents of each animal when known.
# All services and embryo flushings and transfers: date, recipient, sire, dam of the embryo.
# All animal deaths and movements between farms and owners.
# Recording dates and locations.
# Milk yields for each cow and recording date.
# Fat content in milk for each cow and sampling date.

It is recommended to record also the following:

# Protein content in milk for each cow and sampling date.
# Milk somatic cell count for each cow and sampling date.
# Other results obtained from milk analysis.
# Milking duration and milking speed where possible.
# Milking times during recording.
# Recording methods and respective symbols used in records.
# Information about cow during the rearing period.

=== Recording method ===
The recording method for the herd consists of using five different symbols for:

# Responsibility for the practical recording.
# Sampling scheme.
# Recording interval.
# Sampling interval (if different from the above).
# Number of milkings per day (especially any deviation from 2x milking).

The symbols in Table 2 should be used:<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Symbols for milk recording schemes.''
|- style="background-color:#efefef; text-align:center;"

|'''Responsibility for recording'''
|'''Sampling scheme'''
|'''Recording interval (weeks)'''
|'''Sampling interval (weeks)'''
|'''Number of milkings per day'''
|-
| style="text-align:center;" | A
| style="text-align:center;" | P
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | B
| style="text-align:center;" | E
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | C
| style="text-align:center;" | Z
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" |
| style="text-align:center;" | T
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" |
| style="text-align:center;" | M
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:center;" | R x
|-
| style="text-align:center;" |
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | S x
|}
</center>

As an example: Recording method is CP36, 2x means that this is a recording where records/ samples are taken partly by the owner (farmer), and partly by a technician from the MRO, where the recording frequency is every 3 weeks, where the sampling frequency is every 6 weeks, and where the number of milkings per day is 2. If a national nomenclature system is used, it should be possible to transfer this system into ICAR nomenclature.

The reference milk recording method is by a representative of the recording organisation, measuring and sampling every four weeks, with proportional sampling and two milkings per day (AP44, 2x).

Recording other than by the reference method must be indicated using the appropriate symbols.

It is recommended that a limit is set for changing the recording method e.g. so that normally it is only possible to change the method twice per year.

It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

In the next sections the symbols are explained:
====Responsibility for the recording====
This symbol indicates who is responsible for measuring the milk yields and taking samples in the herd.
#Representative of the MRO (Method A; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Farmer or his/her representative (Method B; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Mixed responsibility (Method C; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
====ICAR Standards for sampling schemes====
=====Proportional sampling (P)=====
Samples and milk weights are taken at each milking during the recording day. The sampled amount corresponds to the milk yield of each milking. This is achieved by the use of a pipette in equal number of pipetting at each milking or of a specially designed tool which ensures proportional sampling to create one mixed sample. This is the default sampling scheme with no necessary correction to the analysis results, all other schemes must be reported.
=====Equal measure sampling (E)=====
Samples and milk weights are taken at each milking during the recording day. The amount of the sample is measured to be equal at each milking and mixed into one sample. The analysis results for fat should be corrected if one of the milking intervals is shorter than 10 or longer than 14 hours.
=====Multiple sampling (M)=====
Samples are taken at more than one milking during the recording day while milk weights are taken at each milking or over several days. Samples from different milkings are not mixed but they are kept in distinct vials so that each cow has at least two samples. The analysis results must be corrected to correspond to the 24-hour fat and protein yields. For example: a cow is milked 3x during 24 hours and 2 or 3 separate samples are taken, kept and analysed in different vials. This is the gold standard for AMS. It produces the most accurate results but is more expensive.
=====One-milking sampling with milk weights from more than one milking (Z)=====
Samples are taken from one milking during the recording day while milk weights are taken at each milking or over several days. The analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Alternated one-milking recording (T)=====
Samples and milk weights are taken during one milking, alternating between morning and evening milkings. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Constant one-milking recording (C)=====
Samples and milk weights are taken during one milking, constantly during morning or evening milking. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====In-line analysis recording (I)=====
Milk is not sampled but its constituents are continuously analysed by a stationary analyser.
====ICAR Standards for recording and sampling intervals====

<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Standards for recording and sampling intervals.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| rowspan="2" style="text-align:center;" |'''Recording or sampling interval (weeks)'''
| rowspan="2" style="text-align:center;" |'''Minimum number of recordings or samplings per year'''
| colspan="2" style="text-align:center;" |'''Interval between recordings or samplings (days)'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| rowspan="10" style="text-align:center;" |Reference method
| style="text-align:center;" |1
| style="text-align:center;" |44
| style="text-align:center;" |4
| style="text-align:center;" |10
|-
| style="text-align:center;" |2
| style="text-align:center;" |22
| style="text-align:center;" |10
| style="text-align:center;" |18
|-
| style="text-align:center;" |3
| style="text-align:center;" |15
| style="text-align:center;" |16
| style="text-align:center;" |26
|-
| style="text-align:center;" |4
| style="text-align:center;" |11
| style="text-align:center;" |22
| style="text-align:center;" |37
|-
| style="text-align:center;" |5
| style="text-align:center;" |9
| style="text-align:center;" |32
| style="text-align:center;" |46
|-
| style="text-align:center;" |6
| style="text-align:center;" |8
| style="text-align:center;" |38
| style="text-align:center;" |53
|-
| style="text-align:center;" |7
| style="text-align:center;" |7
| style="text-align:center;" |44
| style="text-align:center;" |60
|-
| style="text-align:center;" |8
| style="text-align:center;" |6
| style="text-align:center;" |50
| style="text-align:center;" |70
|-
| style="text-align:center;" |9
| style="text-align:center;" |5
| style="text-align:center;" |55
| style="text-align:center;" |75
|-
| style="text-align:center;" |Daily
| style="text-align:center;" |310
| style="text-align:center;" |1
| style="text-align:center;" |3
|}
</center>

====ICAR standards for number of milkings per day====

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 3. Symbols for number of milkings per day.''
|- style="background-color:#efefef; text-align:center;"
|'''Number of milkings per day'''
|'''Symbol'''
|-
| style="text-align:center;" | Once per day milking
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | Two milkings
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | Three milkings
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" | Four milkings
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" | Continuous milking (e.g. AMS)
| style="text-align:center;" | R x
|-
| style="text-align:center;" | Regular milkings not at the same times on each day (e.g. 10 milkings per week)
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" | Shown as the average number of milkings per day.
| style="text-align:center;" |
|-
| style="text-align:center;" | Animals that are both milked and suckled. (Number of times milked to prefix the S)
| style="text-align:center;" | S x
|}
</center>

Where a herd is dry for a period of the year, the minimum number of recordings should be adjusted proportionately to the production period.

Minimum number of herd recordings should be at least 85% of the normal number of recordings.

=== Missing results and/or abnormal intervals ===
{{anchor|Missing_results}}A recorded 24-hour yield is the best estimate of the yield and the constituents of the milk, weighed, sampled and recorded within 24 hours on the day of recording.
#When herds are normally milked at intervals such that the recording day is other than 24 hours, the yields shall be adjusted to a 24-hour interval using the following procedure (or other procedures approved by the ICAR):
#*Divide 24 by the interval, then multiply by the yield. For example:
#**For a 25 hour interval (24/25) x 35 kg = 33.6 kg
#**For a 20 hour interval (24/20) x 35 kg = 42.0 kg
#A recording is a set of daily test values for a given animal on a given day of recording, one or some or all of them can be missed (missing values)
#Missing values can be due to:
#*Out of range.
#*Sickness.
#*Disaster.
#*No sample analysis results.
#The number of the official and complete (milk, fat and protein) recordings in the lactation or other accumulated yield should be reported.
#Permitted range of the daily recorded values is given in Table 5. Outside of these ranges, the daily recorded<ref>'''Note:''' High fat breeds have breed average higher than 5.0 for fat %.</ref> value will be considered as a missing value.

<center>
{| class="wikitable"
! colspan="7" style="text-align:left;" | ''Table 5. Permitted range of the daily recorded values.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| colspan="2" style="text-align:center;" |'''Milk (kg)'''
| colspan="2" style="text-align:center;" |'''Fat %'''
| colspan="2" style="text-align:center;" |'''Protein %'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| style="text-align:center;" | Main Dairy Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 1.5
| style="text-align:center;" | 9.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 7.0
|-
| style="text-align:center;" | High Fat1 Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 2.0
| style="text-align:center;" | 12.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 9.0
|}
</center>1Note: High fat breeds have breed average higher than 5.0 for fat %The true daily recorded values collected from animals labelled by the farmer as sick, injured or under treatment must be used in the computation of the lactation record unless the milk yield is less than 50% of the previous milk yield or less than 60% of the predicted yield. In such a case, the whole set of daily recorded values may be considered as missing.

Estimates of the missing values of a daily recording can be computed by using interpolation procedures or by more sophisticated procedures approved by ICAR

== Samples ==

=== Representative sample ===
The milk sample has to represent the complete milking linked to it. This is achieved by mixing the milk thoroughly or pouring it into another vessel right before sampling.

Sampling scheme P requires using a pipette for making the sample proportional between different milkings.

With sampling scheme E, it is advisable to use a measuring cup to make sure the sample parts actually are equal.

Immediately after sampling, the vials have to be preserved, capped, shaken and marked. Samples should be stored cool and dark.

=== Transport ===
Samples should be transported for analysis to a laboratory as soon as possible after sampling.

The samples need to be packed for transport and handled during transport in a manner that guarantees that sample IDs are not compromised or mixed. It is also recommended to protect the packages from external interference.

The packing material must be clean and disposable or easy to clean.

During transportation, it is recommended that the temperature of the samples stays below +10°C.

== Database ==
Storing the recorded data in a milk recording database is an indispensable part of the recording. It is recommended to use the quickest possible means to store the data in the database in order to ensure up-to-date breeding values and management applications. Where computerised data capture is possible, it should not take more than five days after the recording to have the complete recording data set in the database.

The application of the Guidelines in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield], together with other parts of the Guidelines, ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

The guidelines on storage of data collected by the milk recording process are:

# For every recording, cow identification (ID), 24-hour milk yield or individual milk yields with a minimum of 0.2 kg (or the equivalent thereof) milk accuracy and recording date have to be stored.
# Where possible, it is advisable to store each milking separately. The data stored can include milk yield, time and date of milking, and milking scheme.
# Analysed results of the milk sample are stored, namely: sample ID, fat content (or percentage), sample status, sample type. Optional data can be stored on protein and/or lactose content, somatic cell count and additional analyses.
# Analysis results can be linked to one or more milkings of the cow.
# In case of storage or performance problems it might be necessary to remove old data of individual cow milkings from the database.
# Recording day information is the yield over 24 hours and should at least be kept in the database for the current lactation and the previous lactation.
# If recording day information is changed after batch processing it should be marked with a user-ID and time stamp.
# Yields are stored in kg or lbs or, in the case of fat and protein contents, in percent units.

The necessary additional information about how the results have been obtained include:

# Who did the recording (certified technician, farmer etc.).
# Herd and/or cow milking frequency.
# How many milkings were measured.
# How many milkings were sampled.
# Sampling scheme when sampling.
# Daily yield calculation method used.
# Recording and sampling intervals.
# It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

Basic checks for recording data:

# Farm (herd) ID: identified by a unique key.
# Animal ID: has to be unique in database.
# Format of animal ID: compliant to international standards of identification and registration.
# Recording date: less than or equal to today, greater than last recording date.
# Milk yield: stored with one decimal.
# 24 hour milk yield within range ( Table 5).
# Fat and protein content: e.g. within a range of +/- 3 standard deviation of population average (Table 5).
# Calving date: greater than birthday of cow (e.g. greater than birthday of cow + 20 months).
# Calving date: less than or equal to today.
# Sample analysis

This section of the ICAR Guidelines examines how observations are performed on farms and how data are collected, analysed and reported back to farmers. It forms an integral part with other sections of the ICAR Guidelines. It ensures that samples are analysed to the relevant degree of accuracy for the purposes of milk recording, breeding value prediction and other areas of usage. ICAR members operate in a range of situations, ranging from places with almost fully automated recording systems to areas with no roads and electricity. Therefore, the guidelines only demand standards that can be followed, irrespective of production situations and recommend more advanced options, where possible or required. Under the guidelines some practices might not be permitted while other practices are tolerated but not recommended.

== Yield calculations ==
This section covers 24-hour yields and accumulated yields for milk, fat, protein and somatic cells. It also describes the procedure for acceptance of new methods not previously mentioned in the guidelines.

The basic requirements for all calculation methods are that rounding shall only take place at the last step of the computation.

=== Lactation period ===

==== Commencement of the lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, is considered to commence is:

# The day that the cow calves (calving date), or
# In the absence of a calving date, the best estimate of the day that the cow commenced milk production.

A (valid) calving is defined as a parturition taking place:

# After the mid-point of the gestation period if a service has been recorded, or,
# After at least 75% of the normal gestation period has elapsed since the previous calving recorded if no service event has been recorded.

Any parturition falling outside the above definition shall be recorded as an abortion and shall not start a new lactation period.

For cows of dairy breeds the normal gestation length shall be deemed to be 280 days unless more specific breed information is available for use.

If the first recording is done on the calving date or within the first 4 days after calving, the milk yield and constituents at the first recording should not form part of the official lactation record, especially for automated milking systems (AMS) with multiple recorded days.

==== Completion of lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, has been completed is or:

# The day that the cow ceases to give milk (goes dry) or
# The day the cow gives less than 3.0 kg/day or 1.0 kg/milking in a recording (unless recorded sick) or
# When it is common practice not to record the dry-off date, the day of the midpoint between the last recording with the cow in milk and the first recording day with the animal dry may be assumed to be the dry-off date.

The lactation period ends on whichever date above occurs first.

Cows may be recorded as absent or sick on the recording day, without the lactation period being defined as terminated.

=== Production period ===
In the case where yield records are calculated on the basis of a period of production, usually a year, the record should be expressed as a ‘production period record‘ (symbol PP).

The production period begins the day after the end of the previous production period and ends as defined by the length (in days) of the production period.

=== Additional notes ===
For any ICAR method the interval between two consecutive recordings must routinely fulfil the value for the acceptable range on the herd level.

If the first recording occurs within 14 days from calving, then no adjustment is required to the first recorded value when computing the accumulated record. If the first recording occurs 15 to 95 days from calving, then an adjustment procedure may be applied.

If the 305th day of a lactation falls before the last recording, the interpolation method should be used also for the last period to compute the yields.

=== Standard methods for calculating 24 hour yields ===
The ICAR approved methods are presented in '''[https://www.icar.org/Guidelines/02-Procedure-1-Computing-24-Hour-Yield.pdf Procedure 1 of Section 2]'''. They include:

1. Methods for calculating daily yields from AM/PM milkings:

# Method of Delorenzo and Wiggans (1986)<ref>Delorenzo, M.A., and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. [https://www.journalofdairyscience.org/article/S0022-0302(86)80678-6/pdf J Dairy Sci 69; 2386]</ref>
# Method of Liu et al. (2019). Please note that in 2022 the method of Liu et al. (2000)<ref name=":0">Liu, Z., R. Reents, F. Reinhardt and K. Kuwan. 2000. Approaches to Estimating Daily Yield from Single Milk Testing Schemes and Use of a.m.-p.m. Records in Test-Day Model Genetic Evaluation in Dairy Cattle. [https://www.journalofdairyscience.org/article/S0022-0302(00)75161-7/pdf J. Dairy Sci. 83:2672-2682].</ref> has been updated to the method of Liu et al. (2019). We recommend to organisations that currently have implemented the method of Liu et al. (2000)<ref name=":0" /> to update to method of Liu et al. (2019).
# Method of Kyntäjä et al. (2021)<ref name=":3">1. Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. [https://www.icar.org/Documents/technical_series/ICAR-Technical-Series-no-25-Virtual-Meeting/Kyntaja.pdf ICAR Technical Series no. 25: 171-175.]</ref>

2. Methods to estimate 24h yield from Automatic Milking Systems:

# Using data on more than one day (Lazenby et al., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Using data on 1 day (Bouloc et al., 2002)<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Estimation of fat and protein yield (Galesloot and Peeters, 2000)<ref>Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>
# Sampling period (Hand et al., 2004<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D.F. 2004. Comparison of Protocols to Estimate 24 Hour Percent Fat and Protein. Presented at 34th ICAR session, Sousse, Tunisia, June, 2004. Proceedings of the 34th ICAR Meeting EAAP Publication No. 113:219-224</ref>; Bouloc et al., 2004)

3. Standard methods to estimate 24h yield from electronic milk meters:

# Estimation of 24-hour milk yield
# Using data on more than one day (Hand et al., 2006)<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. [https://doi.org/10.3168/jds.S0022-0302(06)72240-8 J. Dairy Sci. 89:1723-1726]</ref>
# Estimation of 24-hour fat and protein yield

=== Standard methods for calculating accumulated yields ===
The ICAR approved methods are presented in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_2_%E2%80%93_Computing_of_Accumulated_Lactation_Yield Procedure 2 of Section 2]. They include:

# Test Interval Method (TIM) (Sargent, 1968)<ref>Sargent, F.D., V.H. Lyton, and O.G. Wall, Jr . 1968. Test interval method of calculating Dairy Herd Improvement Association records. [https://doi.org/10.3168/jds.S0022-0302(68)86943-7 J. Dairy Sci. 51:170].</ref>
# Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987)<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. [https://doi.org/10.1016/0301-6226(87)90049-2 Livest. Prod. Sci. 17:l].</ref>
# Best prediction (VanRaden, 1997)<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. [https://doi.org/10.3168/jds.S0022-0302(97)76268-4 J. Dairy Sci. 80:3015-3022].</ref>
# Multiple-Trait Procedure (MTP) (Schaeffer and Jamrozik, 1996)<ref>Schaeffer, L.R. and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. [https://doi.org/10.3168/jds.S0022-0302(96)76578-5 J. Dairy Sci. 79:2044-2055.]</ref>

=== Procedure to approve new methods ===

# All parties interested in seeking approval for any new accumulated yield calculation method will notify the ICAR Secretariat and provide a description of the proposed method.
# These parties will provide a detailed report including statistical details, scientific references and other relevant data to the ICAR Dairy Cattle Milk Recording Working Group.
# The ICAR Dairy Cattle Milk Recording Working Group will then consider the proposal and recommend that it be conditionally approved, approved or rejected.
# The final steps will consist of approval by the General Assembly and publication in the guidelines. .

== Reporting ==
This subsection covers reports, data files, statistics and calculated key figures provided to farmers for breeding and management purposes.

It is recommended that farmers are given reports after each recording and at the end of the recording year or another longer recording period. These reports should contain data on both cow and herd level. In bigger herds, it is also advisable to present results by management groups or otherwise chosen cow groups within the herd. The reporting may be done on paper, through web pages and/or in the form of data files or electronic reports.

Where data files are distributed or direct access given to the results in the database, care must be taken that data ownership is clearly defined. This also includes defining who has access to data and how this access can be authorised.

ICAR members are advised to prepare annual statistics in a reasonable timeframe after closing the recording year. The minimum data requirements are what is needed for the ICAR [https://my.icar.org/stats/list Dairy Cattle Yearly Enquiry on-line database].

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 5. Examples of key figures for herd to be used by farmers and other users.''
|- style="background-color:#efefef; text-align:center;"
|style="text-align:left |'''Key figure'''
|style="text-align:left |'''Explanation'''
|-
| style="text-align:left;" | 12-month rolling average yield
| style="text-align:center;" | Total milk, fat and protein produced during the 365 (366) days preceding the recording divided by the average number of cows for the same period.
|-
| style="text-align:left;" | Average 305-day yield
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations finished during the reporting period divided with the number of finished 305-day lactations.
|-
| style="text-align:left;" | Average 305-day yield within a period
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations during the reporting period divided with the average number of cows on a 305-day lactation within the reporting period.
|-
| style="text-align:left;" | Average annual yield
| style="text-align:center;" | Total milk, fat and protein produced during the recording year divided by the average number of cows for the same recording year.
|-
| style="text-align:left;" | Average calving interval
| style="text-align:center;" | The average preceding intervals of all calvings second and more during the reporting period.
|-
| style="text-align:left;" | Average fat, protein or lactose contents in milk
| style="text-align:center;" | Total fat, protein and lactose yields divided by the total milk yield, usually expressed with two decimals.
|-
| style="text-align:left;" | Average lactation yield
| style="text-align:center;" | Total milk, fat and protein produced within lactations of any length finished during the reporting period divided with the number of finished lactations.
|-
| style="text-align:left;" | Average lactation yield within a period
| style="text-align:center;" | Total milk, fat and protein produced during the reporting period divided with the average number of cows in milk within the reporting period.
|-
| style="text-align:left;" | Average number of cows
| style="text-align:center;" | Average number of cows in the herd (or group) on a given day during the reporting period. Usually expressed with one decimal.
|-
| style="text-align:left;" | Average somatic cell count
| style="text-align:center;" | The average of all individual cow somatic cell counts weighted for individual milk yields.
|-
| style="text-align:left;" | Daily milk, fat and protein yields
| style="text-align:center;" | 1) Total daily milk, fat and protein yields divided by number of cows, or 2) Total daily milk, fat and protein yields divided by number of cows in milk.
|-
| style="text-align:left;" | Energy Corrected Milk (ECM)
| style="text-align:center;" | Calculated according to a national standard.
Example from the Nordic countries:

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + milk yield, kg * 0.7832)/3.14

or, if lactose has been analysed

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + lactose yield * 16.54 + milk yield, kg * 0.0207)/3.14.

From solids expressed as %:

ECM = [(fat content, % * 383 + protein content, % * 242 + 783.2)/3140]* milk yield, kg

or, if lactose has been analysed

ECM = [(fat content, % * 383 + protein content, % * 242 + lactose content, % * 165.4 + 20.7)/3140]* milk yield, kg.
|-
| style="text-align:left;" | Number of lactations
| style="text-align:center;" | Total number of finished lactations in the herd (or group) during the reporting period.
|-
| style="text-align:left;" | Reporting period
| style="text-align:center;" | The period presented in the given report. The most usual options are: one day, one recording interval, lactation, rolling 365 days, recording or calendar year, and the cow’s lifetime.
|}
</center>

== Decisions ==

As a result of the recording process and reports prepared on the basis of its results, decisions can be made on one or more of the following:

=== Short term impact: day-to-day management decisions taken on farms ===

# Decisions about bulk milk quality.
# Feeding decisions - daily diet based on group or individual performance.
# Pasture management decisions.
# Grouping decisions - placing cows in different management or feeding groups.
# Culling decisions - decisions on the sale or slaughter of cattle.
# Mating decisions.
# Decisions regarding programmes of certification for milk and milk products.
# Decisions based on data flow from MRO’s to farms and vice versa.

=== Medium-term impact ===

# Farmers’ decisions based on advisory services, veterinarians, independent experts and other services.
# Decisions about production planning on farms (herd development).

=== Long-term impact ===
# Breeding programme and selection decisions - breeding partners informed by genetic evaluation ([[Section 09 – Dairy Cattle Genetic Evaluation|Section 9)]] based on milk recording results.
# Decisions based on herd book and breeder association activities and deciding on business actions related to breeding animals, i.e. in some countries animal recording data are required for international trade with breeding animals.

=== Strategic decisions ===
# Research programmes concerning management, recording and breeding.
# Political decisions about possible subsidies in dairy cattle breeding at the governmental level and implementing measurements according to agriculture policy.

== Quality control ==
This Section together with other parts of the Guidelines ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

=== Bulk tank data comparison ===
It is a recommended practice to compare milk recording data with dairy deliveries and bulk tank milk contents. This can be done on the recording day or over a longer period of time. The calculation is done as follows:

# Comparison ratio = Total recorded milk yield, kg /Total milk produced, kg. This comparison is used where there is a reliable estimate of the farm use of milk.
# Quick comparison ratio = Total recorded milk yield, kg/ Total milk delivered, kg. This comparison is used where farm use of milk is not estimated.
# Content comparison = Recorded average fat / Bulk tank average fat
# Comparison ratio for fat = Total recorded fat yield, kg/ Total fat produced, kg
# Total recorded milk yield, kg = Ʃ (Individual milk yield, kg)
# Total milk delivered, kg = Total milk delivered, litres * milk density kg/litre
# Total milk produced, kg = (Total milk delivered, litres + Milk used or discarded on the farm, litres) * milk density kg/litre
# Total fat produced, kg = Total milk produced, kg x (Bulk tank fat percent/100)
# Recorded average fat = Ʃ [Individual milk yield kg x (Individual fat percent/100)]/Ʃ (Individual milk yield, kg)

The recommended acceptable range for comparison ratios is 0.95 - 1.05, and for quick comparison ratios 0.90 - 1.00, with due regard to herd size.

=== One day bulk tank data comparison ===
Milk yields and fat yields or contents are compared on the recording day. Comparing the contents is routinely possible where every delivery is sampled or by taking a bulk tank sample (see point [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Bulk_tank_data_comparison 1.10] above for how the comparison is done.)

=== Bulk tank data comparison over a longer period ===
Milk yields and fat yields or contents are compared over a longer period of time, e.g. 4 months or 12 months. This option requires a routine to obtain the applicable data from the dairies or milk buyers. Farm use of milk may be taken into account where applicable.

=== Bulk tank sample ===
Bulk tank samples can be used to verify the milk contents analysis obtained in milk recording. A sample is taken from a well-mixed bulk tank on the recording day. It must represent the milk of the whole 24-hour period. Bulk tank fat and protein contents are then compared to the weighted averages of the fat and protein percent obtained from milk recording. Normally, the difference between the values should not be more than 5%.

=== Supervised or repeated recording ===
Supervised recording is a tool designed to verify that individual cow records are reliable. It is based on repeating the herd recording as soon as possible after the original recording, and the obtained results are compared with the original recording. It is obligatory for ICAR Certificate of Quality (CoQ) holders to practice regular supervision, irrespective of recording methods used.

It is recommended that the supervised recording will follow immediately after the original recording, but for a good reason it can be postponed for up to 7 days.

The farmer and any other staff doing the original recording must not know that a supervised recording will follow. The technician who performs the supervised recording should not be the same person who did the original recording.

Usually supervised recording is done by recording the whole herd again, using the same sampling scheme and recording method (or a reference method) as in the previous recording. When herd size exceeds 200 cows, it is also allowed to do a supervised recording to selected, or randomised groups of animals in the herd.

Choosing the herds for supervised recording may be random or based on preselection. Traits for this preselection may include high yield, great increase in yield, presence of bull dams in the herd, and general suspicions about the correctness of herd results.

The traits compared in supervised recording must include milk and fat. Comparing protein is also recommended.

=== Supervision - example of comparison calculations ===

# Milk, fat and protein yields per cow are calculated for both the original and the supervised milking.
# Individual cow records where results between supervised recording and the original recording differ outside the norms might be excused where a good explanation can be given for exclusion (illness, heat, missed milking)
# Deviations (%) are calculated for each cow and yield constituent according to the formula: deviation = (supervised yield/unsupervised yield)*100-100
# Herd averages of the absolute values for each yield constituent are calculated.
# If the supervised recording occurs within 2 days of the original recording, the acceptable difference in herd averages are 7% for milk and protein and 9% for fat.
# If the supervised recording occurs between 3 and 7 days after the original recording, the acceptable difference of the aforementioned herd averages are 9% for milk and protein and 12% for fat.

The limits mentioned in these examples are typically applied by some of the member organisations, and are not meant to be understood as exact norms. Such norms should be laid down by each member organisation.

=== Evaluation of recording data ===
It is recommended that data quality is evaluated for each herd recording day. When such an evaluation is applied, the following features of the data have to be included:

# Person responsible for the recording.
# ICAR approval and calibration status of the recording equipment if owned by the farmer.
# Number of herd recordings per time period and/or recording interval.
# Number of herd samplings per time period and/or sampling interval.

The following features are also recommended to be included if possible:

# Deviation of milk and fat yields from dairy deliveries.
# Deviation of milk and fat yields from previous or predicted yields.
# Standard deviation of individual cow records.
# Number of recorded and/or sampled milkings within the recording day.
# Number of cows missed or not recorded in the recording.
</div>
</div>
= Procedures =
== Procedure 1: Computing 24-hour Yields ==
<div class="mw-collapsible mw-collapsed">
<div>
=== Methods to calculate 24-hour yield for milk yield and fat percentage from a single milking ===

==== Method of Delorenzo & Wiggans (1986)<ref>Delorenzo, M.A. and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. J. Dairy Sci. 69: 2386-2394.</ref> ====
Daily milk (DMY) and fat yield (DFY) estimates are based on measured yield and milking frequency. An adjustment factor accounts for differences in the average milking interval (expressed in decimal hours) between the preceding milking and the measured milking, and the time of day of the measured milking (started in a.m. or p.m.). For 2X milking, an additional adjustment is applied to milk yield for the interaction between milking interval and stage of lactation, with mid lactation (158 DIM) set to zero. Milking interval does not affect protein and solids non fat (SNF) percentages and so the percentages for the sampled milking are used for test-day estimates. Protein yield is calculated from the measured percentage and the adjusted milk yield.

The prediction of DMY and DFY from single milking on morning or evening in herds milked twice a day requires factors, that are the reciprocal of the proportion of total yield expected from single milkings in relation to the milking interval.

We propose to derive these coefficients (intercept, slope, etc.) for each country separately.

===== Adjustment of milking interval =====
The milking interval is the interval between milking time for the observed milking and the milking time preceding the observed milking. The milking interval is divided into 15-minutes classes. Factors for milk and fat yields may be calculated to each class using Equation 1:

''Equation 1. Factors for milk and fat yields.''
[[File:Equation 1.png|none|thumb|397x397px]]

===== Adjustment of lactation stage =====
Because the lactation stage of the cow has an influence on the effect of different milking intervals on milk production a second adjustment is made for every interval class through a covariate of days in milk as addition:

Covariate x (days in milk - 158)

===== Estimating sample day yields =====
Formulas for prediction sample day yields and percentages in herds with two milkings are:

''Equation 2. Equation for predicting 24-hour milk yield.''
[[File:Equation2.png|none|thumb|428x428px]]

''Equation 3. Equation for predicting 24-hour fat percentage.''
[[File:Equation3.png|none|thumb|431x431px]]

''Equation 4. Equation for predicting 24-hour fat yield.''
[[File:Equation4.png|none|thumb]]

''Equation 5. Equation for predicting 24-hour protein yield.''
[[File:Equation5.png|none|thumb|316x316px]]

===== Calculation examples =====

====== Practical Application ======
Two sets of factors are available for estimating DMY from a single milking, each for morning or evening milking sampling. The factors are calculated from the formula as described above and given in Table 1.
<center>
{| class="wikitable"
| colspan="5" align="left" |'''''Table 1. Factor of milk yield and covariate for herds milked twice a day.'''''
|- style="background-color:#efefef;"
| rowspan="2" align="center" |'''Length of milking interval in hours (minutes in decimal)'''
| colspan="2" align="center" |'''Morning milking'''
| colspan="2" align="center" |'''Evening milking'''
|- style="background-color:#efefef;"
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
|-
| align="center" |< 9.00
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.594
| align="center" |0.00378
|-
| align="center" |9.00-9.24
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.534
| align="center" |0.00485
|-
| align="center" |9.25-9.49
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.477
| align="center" |0.00486
|-
| align="center" |9.50-9.74
| align="center" |2.411
| align="center" |0.00716
| align="center" |2.423
| align="center" |0.00511
|-
| align="center" |9.75-9.99
| align="center" |2.359
| align="center" |0.00726
| align="center" |2.370
| align="center" |0.00473
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |10.00-10.24
| align="center" |2.310
| align="center" |0.00458
| align="center" |2.321
| align="center" |0.00337
|-
| align="center" |10.25-10.49
| align="center" |2.262
| align="center" |0.00399
| align="center" |2.273
| align="center" |0.00214
|-
| align="center" |10.50-10.74
| align="center" |2.217
| align="center" |0.00294
| align="center" |2.227
| align="center" |0.00000
|-
| align="center" |10.75-10.99
| align="center" |2.173
| align="center" |0.00223
| align="center" |2.183
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |11.00-11.24
| align="center" |2.131
| align="center" |0.00000
| align="center" |2.140
| align="center" |0.00000
|-
| align="center" |11.25-11.49
| align="center" |2.091
| align="center" |0.00000
| align="center" |2.099
| align="center" |0.00000
|-
| align="center" |11.50-11.74
| align="center" |2.052
| align="center" |0.00000
| align="center" |2.060
| align="center" |0.00000
|-
| align="center" |11.75-11.99
| align="center" |2.014
| align="center" |0.00000
| align="center" |2.022
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |12.00
| align="center" |2.000
| align="center" |0.00000
| align="center" |2.000
| align="center" |0.00000
|-
| align="center" |12.01-12.24
| align="center" |1.978
| align="center" |0.00000
| align="center" |1.986
| align="center" |0.00000
|-
| align="center" |12.25-12.49
| align="center" |1.943
| align="center" |0.00000
| align="center" |1.951
| align="center" |0.00000
|-
| align="center" |12.50-12.74
| align="center" |1.910
| align="center" |0.00000
| align="center" |1.917
| align="center" |0.00000
|-
| align="center" |12.75-12.99
| align="center" |1.877
| align="center" |0.00000
| align="center" |1.884
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |13.00-13.24
| align="center" |1.846
| align="center" |0.00000
| align="center" |1.852
| align="center" |-0.00190
|-
| align="center" |13.25-13.49
| align="center" |1.815
| align="center" |0.00000
| align="center" |1.822
| align="center" |-0.00231
|-
| align="center" |13.50-13.74
| align="center" |1.786
| align="center" |-0.00167
| align="center" |1.792
| align="center" |-0.00308
|-
| align="center" |13.75-13.99
| align="center" |1.757
| align="center" |-0.00258
| align="center" |1.763
| align="center" |-0.00339
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |14.00-14.24
| align="center" |1.730
| align="center" |-0.00347
| align="center" |1.736
| align="center" |-0.00509
|-
| align="center" |14.25-14.49
| align="center" |1.703
| align="center" |-0.00363
| align="center" |1.709
| align="center" |-0.00471
|-
| align="center" |14.50-14.74
| align="center" |1.677
| align="center" |-0.00332
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |14.75-14.99
| align="center" |1.652
| align="center" |-0.00316
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |≥ 15.00
| align="center" |1.628
| align="center" |-0.00235
| align="center" |1.683
| align="center" |-0.00454
|}
</center>

For estimating daily fat percentage there is only one table independent of morning or evening sampling – refer to Table 2.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" |'''''Table 2. Factor of fat percentage for herds milked twice a day.'''''
|- style="background-color:#efefef;"
|'''Length of milking'''

'''interval in hours'''
|'''Fat (percentage'''

'''factor)'''
|-
|< 9.00
|0.919
|-
|9.00-9.24
|0.927
|-
|9.25-9.49
|0.934
|-
|9.50-9.74
|0.941
|-
|9.75-9.99
|0.948
|-
|
|
|-
|10.00-10.24
|0.955
|-
|10.25-10.49
|0.961
|-
|10.50-10.74
|0.968
|-
|10.75-10.99
|0.974
|-
|
|
|-
|11.00-11.24
|0.980
|-
|11.25-11.49
|0.986
|-
|11.50-11.74
|0.992
|-
|11.75-11.99
|0.997
|-
|
|
|-
|12.00
|1.000
|-
|12.01-12.24
|1.003
|-
|12.25-12.49
|1.008
|-
|12.50-12.74
|1.013
|-
|12.75-12.99
|1.018
|-
|
|
|-
|13.00-13.24
|1.023
|-
|13.25-13.49
|1.028
|-
|13.50-13.74
|1.033
|-
|13.75-13.99
|1.037
|-
|
|
|-
|14.00-14.24
|1.042
|-
|14.25-14.49
|1.046
|-
|14.50-14.74
|1.050
|-
|14.75-14.99
|1.054
|-
|≥ 15.00
|1.058
|}
</center>

Milking-interval factors are calculated using Equation 1, where the intercept and slope are as in Table 3.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 3. Slope and intercept for milk yield and fat yield.'''''
|- style="background-color:#efefef;"
| rowspan="2" |'''Trait'''
| colspan="2" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started in a.m.'''
|'''For measured milking started in p.m.'''
|-
|Milk yield
|0.0654
|0.0634
|0.0363
|-
|Fat yield
|0.1965
|0.1939
|0.0254
|}
</center>
The milking interval has no significant influence on protein percentage. Therefore, the protein percentage of the sampled milking is used as the daily protein percentage.

====== Calculation of daily yields from morning milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Data for a cow from morning milking.'''''
|-
|Begin of recording:
|6:15
|(Morning milking)
|-
|Start of preceding milking:
|17:25
|
|-
|Length of milking interval:
|12 hours 50 minutes
|(Expressed as decimal 12.83)
|-
|Milk results at morning:
|12,0
|Milk-kg
|-
|
|4,12
|Fat-percentage
|-
|
|3,45
|Protein-percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 5. Factors for morning milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.877
|-
|The covariate is
|0
|-
|The factor for fat percentage from Table 2 is
|1.018
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 6. Example calculations for morning milking.'''''
|-
|The sample-day milk yield:
|1.877 x 12,0 kg + 0 x (120 - 158) = 22,5 kg
|-
|The sample-day fat percentage:
|1.018 x 4,12 = 4,19
|-
|The sample-day fat yield:
|22,5 kg x 0,0419 = 0,94 kg
|-
|The sample-day protein yield:
|22,5 kg x 0,0345 = 0,78 kg
|}
</center>

====== Calculation of daily yields from evening milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 7. Data for a cow from evening milking.'''''
|-
|Begin of recording:
|16:48
|Evening milking
|-
|Start of preceding milking:
|6:35
|
|-
|Length of milking interval:
|13 hours 47 minutes
|Expressed as decimal 13.78
|-
|Milk results at evening:
|14,0
|Milk kg
|-
|
|4,00
|Fat percentage
|-
|
|3,40
|Protein percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 8. Factors for evening milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.763
|-
|The covariate is
|<nowiki>-0,00339</nowiki>
|-
|The factor for fat percentage from Table 2 is
|1.037
|}
{| class="wikitable"
| colspan="2" |'''''Table 9. Example calculations for evening milking.'''''
|-
|The sample-day milk yield:
|1.763 x 14,0 kg - 0,00339 x (120 - 158) = 24,8 kg
|-
|The sample-day fat percentage:
|1.037 x 4,00 = 4,15
|-
|The sample-day fat yield:
|24,8 kg x 0,0415 = 1,03 kg
|-
|The sample-day protein yield:
|24,8 kg x 0,0340 = 0,84 kg
|}
</center>

====== Alternate recording of components and milk yield at both milkings ======
For this plan only the sample-day fat yield has to be calculated with regard to milking interval. The milk yield is the sum of evening and morning milk results.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 10. Example data for a cow from both milkings.'''''
|-
|Begin of recording evening:
|17:25
|
|-
|Milk results at evening:
|10:00
|Milk kg (only milking-yield)
|-
|Begin of recording morning:
|6:15
|
|-
|Milk results at morning:
|12:00
|Milk kg
|-
|
|4:20
|Fat percentage
|-
|
|3:50
|Protein percentage
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 11. Factor for fat percentage.'''''
|-
|Length of milking interval:
|12 hours 50 minutes (expressed

as decimal 12.83)
|-
|The factor for fat percentage from Table 2 is
|1.018.
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 12. Example calculation of daily yields.'''''
|-
|The sample-day milk yield:
|10,0 kg + 12,0 kg = 22,0 kg
|-
|The sample-day fat percentage:
|1.018 x 4,20 = 4,28
|-
|The sample-day fat yield:
|22,0 kg x 0,0428 = 0,94 kg
|-
|The sample-day protein yield:
|22,0 kg x 0,0350 = 0,77 kg
|}
</center>

====== Calculation for 3X Milking ======
For 3X herds, a single milking or two consecutive milkings may be weighed. The sample may be collected at one or both of these milkings. Stage of lactation × milking interval adjustments are not used for greater than 2× milking. These AM/PM factors for estimating daily yields in 3X herds should not be confused with factors that adjust 3X records to a 2X basis. Milking-interval factors are calculated using the same formula with the intercept and slope as in Table 13.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" align = "left" |'''''Table 13. Slope and intercept factors for 3X milking.'''''
|- style="background-color:#efefef;"
| rowspan="2" | '''Trait'''
| colspan="3" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started between 2 a.m. and 9:59 a.m.'''
|'''For measured milking started between 10 a.m. and 5:59 p.m.'''
|'''For measured milking started between 6:00 p.m. and 1:59 a.m.'''
|-
|Milk yield
|0.077
|0.068
|0.066
|0.0329
|-
|Fat yield
|0.186
|0.186
|0.182
|0.0186
|}
</center>
When two milkings are included for sampling, the intercepts and intervals for both milkings are included in determining a factor for calculated estimated milk yield that is applied to the total yield from both milkings as in Equation 6.

''Equation 6. Milking interval factor for 3X milking.''
[[File:Equation6.png|none|thumb|536x536px]]
Milk and fat percent factors are calculated separately based on the number of milkings weighed or sampled.

====== Calculation for 4X - 6X Milking ======
The intercept terms for calculating 3X factors (0.077, 0.068, and 0.066) are multiplied by the factor [3 / (milkings per day)] for use in calculating factors for milking frequencies greater than 3X.

==== Method of Liu et al. (2019) ====
A multiple regression method (MRM) is used for estimating 24-hour daily milk yield (DMY), daily fat yield (DFY) and daily protein yield (DPY) based on partial yields from either morning (AM) or evening (PM) milking. Fat percentage (DFP) or protein percentage (DPP) on a 24-hour daily basis are then derived using the estimated 24-hour daily yields. The MRM can be used as a reference method for estimating daily yields and component percentages.

The method of Liu et al. (2019) is an updated version of the method of Liu et al. (2000). The model is only used for farms with 2 time milkings during 24 hours.

The following formula is used to estimate DMY, DFY, DPY based on partial yields (PMY, PFY,PPY) from either morning (AM) or evening (PM) milking:

''Equation 7. Model for predicting 24-hour yield.''

''yijk = a + bijk * xijk''

where:

yijk is the estimated 24-hour daily yield (DMY, DFY or DPY);

xijk is AM or PM partial daily yield on a test day (PMY, PFY, or PPY).

Subscript '''''i''''' represents class of parity effect with 2 levels: first and higher parities.

Subscript '''''j''''' represents class of length of preceding milking interval with 8 levels for AM milking: < 720 minutes, < 740 minutes, < 760 minutes, < 780 minutes, < 800 minutes, < 820 minutes, < 840 minutes, >= 840 minutes and 8 levels for PM milking: < 600 minutes, < 620 minutes, < 640 minutes, < 660 minutes, < 680 minutes, < 700 minutes, < 720 minutes, >= 720 minutes.

Subscript '''''k''''' represents class of lactation stage with 7 classes: < 60 days, < 120 days, < 180 days, < 240 days, < 300 days, < 360 days, >= 360 days.

'''''a''''' is the estimated intercept for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

'''''b'''''ijk is the estimated slope for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

The factors for '''''a''''' and '''''b'''''ijk can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Appendix_1_-_Adjustment_factors_to_calculate_24-hour_yields_using_the_Liu_method Appendix 1].

For a given yield trait a total number of 112 formulae are to be estimated for calculating 24-hour daily yield based on partial yield from either AM or PM milking. Component percentage for fat (DFP) and protein (DPP), on a 24-hour basis is calculated by dividing estimated fat or protein yield by estimated daily milk yield:[[File:Imagefinal.png|center|thumb|339x339px]]

===== Calculation example with method of Liu et al. (2019) =====
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" align = "left" |'''''Table 14. Data from an evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="6" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="6" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="6" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow'''

'''ID'''
|'''Calving date'''
|'''Lactation number'''
| colspan="2" |'''Milk yield (kg)'''
|'''Fat content (%)'''
|'''Protein content (%)'''
|'''Fat yield (kg)'''
|'''Protein yield (kg)'''
|'''Index1'''
|-
|A
|01.01.2020
|1
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1132
|-
|B
|01.01.2020
|2
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1232
|-
|C
|27.03.2020
|1
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1131
|-
|D
|27.03.2020
|2
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1231
|-
|
|
|
|
|
|
|
|
|
|
|}
'''1''' Index is marked in the Appendix table.
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 15. Calculation of 24-hour daily yield and components for evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="3" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="3" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="3" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow ID'''
|'''DMY (kg)'''
|'''DFY (kg)'''
| colspan="2" |'''DPY (kg)'''
|'''DFP (%)'''
|'''DPP (%)'''
|-
|A
|3,47396+25,0

<nowiki>*</nowiki> 1,98268 = 53,0401 ≈ '''53,0'''
|0,2135+0,995

<nowiki>*</nowiki> 1,68050 = 1,8855975
| colspan="2" |0,10471+0,8325* 1,99092 = 1,7621509
|1,8855975 / 53,04096*100

≈ '''3,55'''
|1,7621509 / 53,04096*100

≈ '''3,32'''
|-
|B
|4,15080+25,0* 1,98520 = 53,7808 ≈ '''53,8'''
|0,3635+0,995

<nowiki>*</nowiki> 1,47515 = 1,8312743
| colspan="2" |0,13952+0,8325* 1,97074 = 1,7801611
|1,8312743 / 53,7808*100

≈ '''3,41'''
|1,7801611 / 53,7808*100

≈ '''3,31'''
|-
|C
|2,80244+33,1

<nowiki>*</nowiki> 2,02183 = 69,72501 ≈ '''69,7'''
|0,17663+1,3339 * 1,72438 = 2,4767805
| colspan="2" |0,11078+1,1122 * 1,96422 = 2,2953855
|2,4767805 / 69,725013*100

≈ '''3,55'''
|2,2953855 / 69,725013*100

≈ '''3,29'''
|-
|D
|3,85525+33,1 * 2,00429 = 70,19725 ≈ '''70,2'''
|0,27991+1,3339 * 1,62403 = 2,4462036
| colspan="2" |0,12863+1,1122* 1,98973 = 2,3416077
|2,4462036 / 70,7197249*100 ≈ '''3,48'''
|2,3416077 / 70,7197249*100 ≈ '''''3,34'''''
|-
|
|
|
|
|
|
|
|}
</center>
'''Note''' that intercepts and slopes of the applied regression formulae are underscored.

===== Fat correction for equal measure sampling =====
With Equal measure sampling, it is advisable to use Equation 8 (or the like) to correct fat contents:

Equation 8. Fat correction for equal measure sampling.

Fat, % = Analysed fat, % + 0.69 – 1.3 x (morning milk/ 24-hour milk)

The relation of morning milk to 24-hour milk is to be calculated to at least four decimals.

==== 1.1 Method of Kyntäjä & Nokka (2021)<ref name=":3" />: 24-hour correction factors for fat percentage ====
This method can be applied to calculate 24-hour correction factors for fat percentage, in case the milk recording is based on two milkings, with at least one known milk yield and one sample. A 24-hour recording day is assumed.

The conventional way to calculate correction factors is based on a data set where all milkings have been recorded and analysed separately. This approach requires a lot of effort and extra analysis, and is not cheap to organise. Organisations that have access to a large number of records may be able to use those data to calculate correction factors even if they have no extra analysis.

Requirements for the data set:

# The data set has to be large enough. Every single factor needs to be based on at least 10,000 or, even better, 100,000 observations.
# Each individual data set must contain at least one preceding milking interval, milk weight, and analysed sample. If it contains more milk weights, intervals etc. that is even better. It is also good to include breed, lactation number, days in milk and other data that may have an effect on the factors.

===== Calculation example of the method of Kyntäjä & Nokka (2021)<ref>Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. ICAR Technical Series no. 25: 171-175.</ref> =====

====== The accumulated data set ======
Since 2003, Finland had accumulated a data set of 7.5 million recordings with data on the time of the sampled and preceding milking as reported by the farmer, the lab analysis results, and the 24-hour milk yield. Grouped according to the preceding interval, the analysed fat content gives a nice sigmoid curve with the highest fat content found after a 540 to 630 minutes’ interval (9 to 10.5 hours) and the lowest at 810 to 930 minutes (13.5 to 15.5 hours).
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 16. Average analysed milk fat percentage by preceding interval class, 2003 – 2020.'''''
|- style="background-color:#efefef;"
|'''Interval before'''

'''Sampling (minutes)'''
|'''Number of samples'''
|'''Median interval in the class'''
|'''Average fat content analysed (%)'''
|-
|<510
|93,577
|495
|4.20
|-
|510-539
|19,523
|525
|4.70
|-
|540-569
|111,268
|555
|4.79
|-
|570-599
|253,807
|585
|4.83
|-
|600-629
|1,461,587
|615
|4.75
|-
|630-659
|919,968
|645
|4.66
|-
|660-689
|1,168,683
|675
|4.56
|-
|690-719
|223,877
|705
|4.42
|-
|720-749
|517,447
|735
|4.28
|-
|750-779
|212,428
|765
|4.16
|-
|780-809
|924,014
|795
|4.12
|-
|810-839
|698,463
|825
|4.09
|-
|840-869
|1,104,778
|855
|4.07
|-
|870-899
|154,561
|885
|4.05
|-
|900-929
|77,024
|915
|4.07
|-
|>929
|26,977
|945
|4.13
|}
</center>

The results were also divided into subgroups according to lactation number, phase of lactation, and breed. The effect of the preceding milk interval on milk fat seems to be bigger with older cows and in the beginning of lactation. It was also bigger with Ayrshire cows as compared with Holsteins. At this point, however, the decision was made not to take these factors into account when calculating new correction factors.

====== Calculation of new factors ======
The results above were turned into a simple set of correction factors, dependent solely on the preceding interval. In order to do this, two assumptions were made:

# A 24-hour recording day was assumed. This way, we can deduce the second milking interval from the one we know and mirror the fat percent for that milking.
# Milk secretion rate was assumed to be constant around the 24-hour period. This allows us to deduce the share of the 24-hour yield produced at each milking.

These assumptions allow us to create the new correction factors by mirroring the milk yield and milk fat content in the milking whose actual data we have not got. This way, we get the following formula:

Equation 9. Correction factor.
[[File:Equation9.png|none|thumb|545x545px]]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left" |'''''Table 17. Calculation of the mirrored milking and the correction factors'''''
|- style="background-color:#efefef;"
|'''Interval before sampling (minutes)'''
|'''Average fat in the sampled milking (%)'''
|'''Share of 24-hour milk in the sampled milking'''
|'''Mirrored interval (minutes)'''
|'''Average fat in the mirrored milking (%)'''
|'''Calculated 24-hour average fat(%)'''
|'''Correction factor'''
|-
|<510
|4.21
|0.34
|>929
|4.14
|4.16
|0.989
|-
|510-539
|4.77
|0.36
|900-929
|4.08
|4.33
|0.907
|-
|540-569
|4.82
|0.39
|870-899
|4.05
|4.35
|0.903
|-
|570-599
|4.84
|0.41
|840-869
|4.07
|4.38
|0.906
|-
|600-629
|4.76
|0.43
|810-839
|4.09
|4.37
|0.919
|-
|630-659
|4.66
|0.45
|780-809
|4.12
|4.36
|0.936
|-
|660-689
|4.56
|0.47
|750-779
|4.16
|4.35
|0.953
|-
|690-719
|4.43
|0.49
|720-749
|4.29
|4.36
|0.984
|-
|720-749
|4.29
|0.51
|690-719
|4.43
|4.36
|1.016
|-
|750-779
|4.16
|0.53
|660-689
|4.56
|4.35
|1.046
|-
|780-809
|4.12
|0.55
|630-659
|4.66
|4.36
|1.059
|-
|810-839
|4.09
|0.57
|600-629
|4.76
|4.37
|1.070
|-
|840-869
|4.07
|0.59
|570-599
|4.84
|4.38
|1.076
|-
|870-899
|4.05
|0.61
|540-569
|4.82
|4.35
|1.073
|-
|900-929
|4.08
|0.64
|510-539
|4.77
|4.33
|1.062
|-
|>929
|4.14
|0.66
|<510
|4.21
|4.16
|1.006
|}
</center>

=== Methods to calculate 24-hour yields in Automatic Milking Systems ===

==== General remarks about calculation of 24-hour milk yield ====
It is characteristic for AMS systems that individual cows set their own milking rhythm, thus making it largely irrelevant to use the traditional model of measuring milk yields and sampling at all milkings in the herd during the recording day. In order to determine how much an individual cow’s real 24-hour milk, fat and protein yield is, more complex calculations are required, especially with milk fat that varies considerably from milking to milking. For protein content and cell counts, no correction is needed for a one-milking sample.

The basic idea with calculating a 24-hour milk yield from AMS data is that milk yields per milking are converted into milk yield per time unit (minute or hour) during the preceding interval. This milk yield per time unit is then converted into milk yield in 24 hours. In order to do this, the data set must also contain time stamps for each milking.

How many milkings or how long a measurement period is used for creating 24-hour yields depends on the milk recording organisation. The fewer milkings are used the more random variance there will be in the individual cow milk yields. The absolute minimum is two milkings with preceding intervals, while a measuring period of 96 hours is recommended.

The sampled milking must always be inside the milk yield measurement period. For the calculation of fat and protein yields, it is recommended to use only those milk yields that are from the same period or day. With Z sampling, the 24-hour fat and protein yields may be calculated based on a shorter measurement period than what is used for calculating the 24-hour milk yields.

==== Calculation of milk yield using data of several days (Lazenby ''et al''., 2002<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Automatic Milking Systems (AMS). The average of most recent milk weights can be calculated using a number of preceding milkings or a number of preceding days. If number of milkings is used, the optimal estimate of the milking rate is obtained using an average of current milking together with the 12 most recent milkings back in time. The optimal estimate is the maximum value of the difference curve at which the correlation with the ‘true’ 24-hour milk yield is greatest and the variance across milkings is minimized. If number of days is used, the optimal estimate of the milking rate is obtained using an average of all milkings occurred in the last 96 hours (4 most recent days). In Table 18 the percent of maximum difference for various number of milkings and days is reported. The optimal estimate is independent from stage of lactation and parity.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 18. Percent maximum for different number of days and milkings.'''''
|- style="background-color:#efefef;"
|'''Days'''
|'''Percent Max.'''
|'''Current milking'''

'''+ most recent milkings'''
|'''Percent max.'''
|-
|1
|49.38
|10
|97.85
|-
|2
|77.26
|11
|99.08
|-
|3
|92.34
|12
|99.70
|-
|4
|98.91
|13
|99.81
|-
|5
|98.50
|14
|99.40
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table19.png|center|thumb|911x911px]]
Therefore, 24-hour yield estimation using most recent milkings (1+12) is computed using Equation 10.

''Equation 10. 24-hour yield estimation using 12 previous milkings from AMS.''
[[File:Equation10.png|none|thumb|527x527px]]
and, 24-hour yield estimation using all milkings occurred in the last 96 hours (most recent 4 days), all milking in the last 4 days are included is computed using Equation 11.

''Equation 11. 24 hours yield estimation using milkings from the last 96 hours from AMS''
[[File:Equation11.png|none|thumb|534x534px]]

===== Advantages and disadvantages of this method =====
In terms of Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between milk weights and contents may arise if contents are recorded on one day only. Moreover, some cows may begin or finish their lactation during the period of recording. In this case the computation of milk yield must be adapted. The number of data that need to be validated is higher (for instance, contents have short interval between two milkings).

==== Calculation of milk yield using data on 1 day (Bouloc ''et al''., 2002<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
When the number of milkings is reduced to milkings obtained during one day only, the accuracy of the estimation of the true performance is the same as classical milk recording methods with the same interval between two test days. For instance, Milk Yield estimated from all the milkings recorded during 24 hours, and with an interval between two test days of four weeks has the same accuracy as A4.

==== Calculation of fat and protein yield (Galesloot & Peeters, 2000<ref name=":1" />) ====
Calculation of fat and protein percent must be based on milk weights at time of sampling. The 24-hour protein percentage can be predicted by the protein percentage of the sample without adjustment. However, the 24-hour fat percentage is more difficult to predict, as levels of fat percent are inversely proportional to the amount of milk yield. It is important then to have a close connection between time of samples and actual milk yields.

The Peeters and Galesloot method is a multiple linear regression model for estimating 24-hour fat percent and yields from one-sampled milking during the AMS sampling period. Six different statistical models were tested. This method takes into account fat percent, protein percent, milk weight and milking interval of the sampled milking, milking interval and milk weight of the previous milking (simple model). Another model, based on six different classification of variables (Ca - Cf) such as, time of sampled milking, interval preceding the sampled milking, ratio of fat to protein percent, parity, lactation stage, can be applied (complex model).

===== Simple model =====
24-hour Fat% = b0 + b1* Fat%(n) + b2* Prot%(n) + b3* Int(n) + b4* Int(n-1) + b5* Milk(n) + b6* Milk (n-1) + e

b0= Intercept, b1 to b6 = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, e = Residual effect.

===== Complex model =====
24-hour Fat%i = b0i + b1i* Fat%(n) + b2i* Prot%(n) + b3i* Int(n) + b4i* Int(n-1) + b5i* Milk(n) + b6i* Milk(n-1) + ei

b0i = Intercept, b1i to b6i = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, ei = Residual effect

i = subclass of classification for class variables Cx for x = a, b, c, d, e, f

Ca = Day Time of sampled milking (h) 0-5.59, 6.00-11.59, 12.00-17.59, 18.00-23.59

Cb = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440

Cc = Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

Cd = Parity 1, 2, ≥ 3

Ce = Lactation stage 1-99, 100-199, ≥200

Cf = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440 and Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

The best prediction of 24-hour fat percent and 24-hour fat yields from this method, includes fat percent, protein percent, milk weight and milking interval of the sampled milking, milk weight and milking interval of the preceding milking and the interaction between milking interval, the ratio of fat to protein percent of the sampled milking (complex model corresponding to Cf classification).

The Peeters and Galesloot method has been updated by Roelofs et al. (2006)<ref>Peeters, R. and P. J. B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. J Dairy Sci. 85:682-688.</ref>. The Roelofs method is described in [[Section 02 – Cattle Milk Recording#Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme|Appendix 2]] of this Section.

N.B. This method has been developed by CRV. CRV has available a set of parameters, estimated with this method. For more information about costs and advice on application of this method, please contact CRV. ICAR has no benefit from the application of this method or any other method described in these guidelines.

==== Calculation example of 24-hour fat and protein yields with sampling scheme M ====
With this method, all milkings in a 24-hour recording period must be sampled. The obtained separate analysis results are then used to compute a 24-hour yield of milk solids, and a weighted average of their content.

Individual milkings (last 96 hours) and recording day contents:
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left" |'''''Table 20. Calculation of 24-hour fat and protein contents with sampling scheme M.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY/MM/DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat%'''
|'''Protein%'''
|-
|1
|2021/09/09
|20:45
|525
|13.7
|26.1
|
|
|-
|2
|2021/09/10
|5:30
|617
|16.0
|25.9
|
|
|-
|3
|2021/09/10
|15:47
|720
|18.7
|26.0
|
|
|-
|4
|2021/09/11
|3:25
|645
|16.8
|26.0
|
|
|-
|5
|2021/09/11
|14:10
|899
|18.3
|20.3
|
|
|-
|6
|2021/09/11
|23:27
|557
|14.6
|26.2
|
|
|-
|7
|2021/09/12
|10:51
|684
|17.4
|25.4
|4.53
|3.17
|-
|8
|2021/09/12
|19:44
|533
|14.1
|26.5
|4.92
|3.18
|-
|9
|2021/09/13
|1:35
|351
|9.9
|28.2
|5.92
|3.07
|}
</center>

For example, calculation of fat% on recording day:

24-hour Fat% = (9.9 kg milk x 5.92% fat + 14.1 kg milk x 4.92 % fat + 17.4 kg milk x 4.53 % fat) / (9.9 + 14.1 + 17.4) kg milk = 5.00 %

To calculate the 24-hour fat yield, the calculated 24-hour milk yield is multiplied by the fat content thus obtained (5.00 %).

The same method is used for protein, somatic cell count, urea, lactose and other milk constituents.

Estimation of milk contents: It is recommended to set the robot not to take samples if the preceding milking of the individual cow is not more than 4 hours earlier. If such milkings occur the milk sampled from them is not suitable for 24-hour fat calculation.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left"|'''''Table 21. Calculation of 24-hour fat and protein contents with sampling scheme M where one milking interval was shorter than 4 hours.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY-MM-DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat %'''
|'''Protein%'''
|-
|1
|2021/11/12
|20:05
|590
|15.4
|26.4
|
|
|-
|2
|2021/11/13
|6:31
|626
|16.3
|26.0
|
|
|-
|3
|2021/11/13
|17:12
|641
|17.1
|26.7
|
|
|-
|4
|2021/11/14
|4:40
|688
|17.5
|25.4
|
|
|-
|5
|2021/11/14
|15:11
|631
|16.4
|26.0
|
|
|-
|6
|2021/11/15
|2:25
|674
|16.5
|24.5
|
|
|-
|7
|2021/11/15
|9:47
|452
|10.8
|23.9
|
|
|-
|8
|2021/11/15
|18:30
|523
|13.6
|26.0
|4.71
|3.36
|-
|9
|2021/11/15
|21:15
|165
|3.1
|18.8
|5.161
|3.481
|-
|10
|2021/11/16
|7:49
|634
|16.5
|26.0
|4.47
|3.21
|}
1 Time between two consecutive milkings shorter than 4 hours, data not taken into account for calculation of milk contents.
</center>

Calculation of the fat content of milk during the recording day:

24-hour Fat% = (16.5 kg milk x 4.47 % fat + 13.6 kg milk x 4.71 % fat) / (16.5 kg + 13.6 kg) = 4.57 %

The same method is used for protein, somatic cells, urea, lactose and other milk constituents.

=== Methods to calculate 24-hour yields from electronic milk meters ===

==== Using data on more than one day (Hand ''et al''., 2006<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. J. Dairy Sci. 89:1723–1726.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Electronic Milk Meters. The average of most recent milk weights can be calculated using a number of preceding days. Table 22 reports the concordance correlations for a range of multiple-day averages. As soon as at least the 3 preceding days are used in the calculation, the concordance correlation reaches a high value of at least 0.981. There are no significant differences between 3, 4, 5, 6 and 7-day averages. The correlations are independent from stage of lactation and parity. Thus, 24-hour yields can be the average of from 3 to 7 daily milkings previous to the test day when fat and protein samples were taken.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 22. Concordance correlations for different multiple-day averages.'''''
|- style="background-color:#efefef;"
|'''Multiple-day average'''
|'''Concordance correlation'''
|-
|1
|0.957
|-
|2
|0.975
|-
|3
|0.981
|-
|4
|0.981
|-
|5
|0.982
|-
|6
|0.981
|-
|7
|0.981
|-
|10
|0.979
|-
|14
|0.977
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table20.png|center|thumb|923x923px]]

Therefore, 24-hour yield estimation averaging over 5 days is given by Equation 12.

''Equation 12. 24-hour yield estimation averaging over 5 days.''
[[File:Equation12.png|center|thumb|601x601px]]

===== Advantages and disadvantages of this method =====
Concerning Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between Milk weights and contents have been shown. The estimation bias increases proportionally to the number of days use to compute the 24-hour average. Thus, this method is recommended only if milk weight is the only variable of interest. If milk contents are of interest then the milk weight should be calculated using the milkings from the same day of sampling.

==== Estimation of 24-hour fat and protein yield ====
Fat and protein yields should be determined from the 24-hour yield on the day of sampling, and not the averaged value.

=== Calculation of daily fat percentage from single samples by Gerke et al., 2025 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Gerke.xlsx here]

Constant access to the automatic milking system (AMS) leads to varying milking frequency of cows and subsequently varying milking interval lengths (MI) and milk yield (MY) of single milkings. This influences milk production and can result in variable milk composition in individual milkings during the day. Therefore, the fat percentage from one sampled milking must be adjusted before it can be used as a daily value. The method described specifies the data required and the calculation procedure for deriving a corrected 24 h milk fat percentage from a single sample on test day (TD) in AMS herds.

==== Model specification ====
The multiple linear regression includes transformation, interaction, and polynomial parameters to model non-linearity and thereby improve prediction accuracy. Beside F% of a single milking (''m'') on TD, the model focused on lactation characteristics and milk recording data of up to 4 preceding milkings. With milking intervals ranging between 4 and 20 hours, the method can be applied to milk recording samples from cows with 2 or 3 milkings whose milking intervals lengths (MI) before sampling accumulate to less than 24 h.

The functional form of the model described below specifies the data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample:[[File:Image A.png|center|thumb|636x636px|'''Data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample''']]
</div>where:

DF% = estimated 24 h fat percentage on TD

''m'' = sampled milking on TD

''m-x'' = x milkings before the milking where the sample was taken (x: 1-3)

F% = fat percentage of the sampled milking ''m''

MY(''m'') = milk yield (kg) of ''m''

MI(''m'') = length of time interval (min) preceding the sampled milking ''m''

MY(''m''-x) = milk yields of the 1-3 preceding milkings of ''m''

MI(''m''-x) = milking interval length corresponding to MY(''m''-x)

DIM = days in milk on TD ranging between 5 and 330 d

Parity = parity class (e.g primiparous = 1 and multiparous = 0)

Daytime = time-of-day group of ''m'' (e.g. morning/noon/evening)

e = residual error

The method and its implementation are described in detail by Gerke et al. (2025).

==== Calculation and examples ====
The mathematical notation, with the corresponding regression coefficients in Table 1 for calculating the daily fat percentage (DF%):[[File:Calculating the daily fat percentage (DF%).jpg|center|Calculating the daily fat percentage (DF%)|thumb|511x511px]][[File:Calculating the daily fat percentage (DF%) 2.jpg|center|frame|'''Table 1. Coefficients for regression formula.''']]
</div>
[[File:Example data required for estimating 24 h fat percentage (DF%).jpg|alt=Example data required for estimating 24 h fat percentage (DF%)|center|frame|'''Table 2.''' '''Example data required for estimating 24 h fat percentage (DF%)''']]
Based on the data assembled on TD (Table 2), the corrected 24 h fat percentage (DF%) can be calculated using the mathematical formula und its corresponding coefficients listed in Table 1 as shown in the following examples:
[[File:Corrected 24 h fat percentage.jpg|alt=Corrected 24 h fat percentage|center|thumb|661x661px|'''Corrected 24 h fat percentage''']]

=== Reference ===
Gerke, J. S., Kammer, M., Werner, A., Köstler, R., Piepenburg, J., Mayerhofer, M., … Duda, J. (2025). Estimating daily fat percentage from single samples in herds with automatic milking system using a regression model. ''Livestock Science'', ''293'', 105649. doi: 10.1016/j.livsci.2025.105649

=== Calculation of daily fat percentage from single samples by Jenko et al., 2008, 2010 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Jenko.xlsx here]

This method estimates daily milk yield (DMY), daily fat yield (DFY), and daily protein yield (DPY) in the alternate one-milking recording (T) scheme. Daily fat percentage (DFP) and daily protein percentage (DPP) are then derived from the daily yield (DY) estimates. Utilizing this method allows us to remove the risk of underestimating high and overestimating low DY and contents.

The following formula is used to estimate the DY from the partial yield (PY) and the estimated PY/DY ratio (y):

DY=PYi/yi

where the subscript i is either morning (a.m.) or evening (p.m.).

The value of y is calculated based on the milking interval in minutes (MI), estimated intercept (µ) and regression coefficients (b1 and b2) for yield traits in a.m. or p.m. milking using the following equations for DMY and DPY:

'''Equation 1. Model for milk yield and protein yield.'''

yi = µ + b1 × MI

and for DFY

'''Equation 2. Model for fat yield.'''

yi = µ + b1 × MI + b2 × MI2

The intercept and regression coefficients can be either estimated from the data with records from both a.m. and p.m. milking or the estimates from Table 1 can be applied.

'''Table 1. Intercept and regression coefficients for calculation of daily yield.'''
{| class="wikitable"
|'''Daily yield'''
|'''Milking'''
|'''µ'''
|'''b1'''
|'''b2'''
|-
|DMY
|a.m.
|0,1081000000
|0,0005503000
|
|-
|
|p.m.
|0,0884200000
|0,0005683000
|
|-
|DPY
|a.m.
|0,1124000000
|0,0005419000
|
|-
|
|p.m.
|0,0966400000
|0,0005593000
|
|-
|DFY .
|a.m.
|0,5903000000
|<nowiki>-0,0005093000</nowiki>
|0,0000005377
|-
|
|p.m.
|0,1574000000
|0,0006705000
|<nowiki>-0,0000002744</nowiki>
|}
Finally, daily fat percentage (DFP) and daily protein percentage (DPP) are calculated from the estimated DY:

DFP=DFY/DMY × 100

DPP=DPY/DMY × 100

==== Calulation example with method of Jenko et al. (2008, 2010) ====
Example of the calculations of daily yields from morning milking and evening milking is presented in tables 3 and 4. Data from the Delorenzo and Wiggans method is used in the calculations (Table 2).

'''Table 2. Data for morning and evening milking.'''
{| class="wikitable"
|'''Milking'''
|'''a.m.'''
|'''p.m.'''
|-
|Beginning of recording
|06:15
|20:22
|-
|Start of preceding milking
|17:25
|06:35
|-
|Milking interval (min)
|770
|827
|-
|'''Milking results'''
|
|
|-
|Milk (kg)
|12,00
|14,00
|-
|Protein (%)
|3,45
|3,40
|-
|Fat (%)
|4,12
|4,00
|}

'''Table 3. Calculation of partial yield (PY) and calculation of y value.'''
{| class="wikitable"
|Trait
|Milking
|PY (%)
|PY (kg)
|y
|-
|Milk
|a.m.
|
|12,00
|0,1081000000 + 0,0005503000 x 770 = 0,531831
|-
|
|p.m.
|
|14,00
|0,0884200000 + 0,0005683000 x 827 = 0,558404
|-
|Protein
|a.m.
|3,45
|12,00 / 3,45 = 0,41
|0,1124000000 + 0,0005419000 x 770 = 0,529663
|-
|
|p.m.
|3,40
|14,00 / 3,40 = 0,48
|0,0966400000 + 0,0005593000 x 827 = 0,559181
|-
|Fat
|a.m.
|

4,12
|12,00 / 4,12 = 0,49
|0,5903000000 -0,0005093000 x 770 + 0,0000005377 x 7702 = 0,516941
|-
|
|p.m.
|

4,00
|12,00 / 4,00 = 0,56
|0,1574000000 +0,0006705000 x 827 - 0,0000002744 x 8272 = 0,524233
|}

'''Table 4. Calculation of daily yield (DY, kg) and daily components (DY, %).'''
{| class="wikitable"
|Trait
|DY
|Milking
|DY (kg)
|DY (%)
|-
|Milk
|DMY
|a.m.
|12,00 / 0,531831 = 22,56356
|
|-
|
|
|p.m.
|14,00 / 0,531831 = 25,07145
|
|-
|Protein
|DPY
|a.m.
|0,41 / 0,529663 = 0,781629
|(0,781629 / 22,56356) x 100 = 3,46
|-
|
|
|p.m.
|0,48 / 0,559181 = 0,851245
|(0,851245 / 25,07145) x 100 = 3,40
|-
|Fat
|DFY
|a.m.
|0,49 / 0,516941 = 0,956395
|(0,956395 / 22,56356) x 100 = 4,24
|-
|
|
|p.m.
|0,56 / 0,524233 = 1,068227
|(1,068227 / 25,07145) x 100 = 4,26
|}

</div>
</div>

==== References ====

* Jenko, J., Perpar, T., Logar, B., Sadar, M., Ivanovič, B., Jeretina, J., Verbič, J., Podgoršek, P. 2008. Comparison of different models for estimating daily yields from a.m./p.m. milkings in Slovenian dairy scheme. Presented at the 36th ICAR Session, Niagara Falls, New York, United States, June 16-20, 2008.
* Jenko, J., Perpar, T., Gorjanc G., Babnik, D. 2010. Evaluation of different approaches for the estimation of daily yield from single milk testing scheme in cattle, J. Dairy Res., 77 (2010), pp. 137-143; DOI: 10.1017/S0022029909990586

== Procedure 2 – Computing of Accumulated Lactation Yield ==
<div class="mw-collapsible mw-collapsed">
<div>
=== The Test Interval Method (TIM) (Sargent, 1968<ref>Sargent, F. D., V. H. Lyton, and 0. G. Wall, J r . 1968. Test interval method of calculating Dairy Herd Improvement Association records. J. Dairy Sci. 51:170.</ref>) ===
Test Interval Method is the reference method for calculating accumulated yields. Another adaptation of the method is the Centering Date Method where the yields from the preceding recording are used until the mid point of the recording interval and then substituted by the yields from the following recording.

The following equations are used to compute the lactation record for milk yield (MY), for fat (and protein) yield (FY), and for fat (and protein) percent (FP).
[[File:Equation1111.png|none|thumb|653x653px]]
Where:
M1, M2, Mn are the weights in kilograms, given to one decimal place, of the milk yielded in the 24 hours of the recording day.

F1, F2, Fn are the fat yields estimated by multiplying the milk yield and the fat percent (given to at least two decimal places) collected on the recording day.

I1, I2, In-1 are the intervals, in days, between recording dates.

I0 is the interval, in days, between the lactation period start date and the first recording date.

In is the interval, in days, between the last recording date and the end of the lactation period.

The equation applied for fat yield and percentage must be applied for any other milk components such as protein and lactose.

Details of how to apply the formulae are shown in Table 3 using the example data in Table 1, below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" align = "left" |'''''Table 1. Raw data used in example (TIM).'''''
|- style="background-color:#efefef;"
| colspan="6" align = "left"|'''Data:'''

'''Calving March 25'''
|- style="background-color:#efefef;"
|
|'''Date of'''

'''recording'''
|'''Number'''

'''of days'''
|'''Quantity of milk'''

'''weighed in kg'''
|'''Fat'''

'''percentage'''
|'''Fat'''

'''in grams'''
|-
|April
|8
|14
|28.2
|3.65
|1 029
|-
|May
|6
|28
|24.8
|3.45
|856
|-
|June
|5
|30
|26.6
|3.40
|904
|-
|July
|7
|32
|23.2
|3.55
|824
|-
|August
|2
|26
|20.2
|3.85
|778
|-
|August
|30
|28
|17.8
|4.05
|721
|-
|September
|25
|26
|13.2
|4.45
|587
|-
|October
|27
|32
|9.6
|4.65
|446
|-
|November
|22
|26
|5.8
|4.95
|287
|-
|December
|20
|28
|4.4
|5.25
|231
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left"|'''''Table 2. Lactation period summary (TIM).'''''
|-
|Beginning of lactation:
|March 26
|-
|End of lactation:
|January 3
|-
|Duration of lactation period:
|284 days
|-
|Number of testings (weighings):
|10
|}
</center>
<center>
{| class="wikitable"
| colspan="8" |'''''Table 3. Computations using Test Interval Method.'''''
|- style="background-color:#efefef;"
| colspan="3" rowspan="2" |'''Interval'''

'''both days included'''
|
| colspan="2" |'''Daily production'''
| colspan="2" |'''Sum'''
|- style="background-color:#efefef;"
|'''Days'''
|'''Kg milk'''
|'''Grams of fat'''
|'''Kg milk'''
|'''Kg fat'''
|-
|Mar 26
|<nowiki>-</nowiki>
|Apr 8
|14
|28.2
|1 029
|395
|14.410
|-
|Apr 9
|<nowiki>-</nowiki>
|May 6
|28
|(28.2+24.8)/2
|(1 029+856) /2
|742
|26.389
|-
|May 7
|<nowiki>-</nowiki>
|June 5
|30
|(24.8+26.6) /2
|(856+904) /2
|771
|26.400
|-
|June 6
|<nowiki>-</nowiki>
|July 7
|32
|(26.6+23.2) /2
|(904+824) /2
|797
|27.648
|-
|July 8
|<nowiki>-</nowiki>
|Aug. 2
|26
|(23.2+20.2) /2
|(824+778) /2
|564
|20.817
|-
|Aug. 3
|<nowiki>-</nowiki>
|Aug 30
|28
|(20.2+17.8) /2
|(778+721) /2
|532
|20.980
|-
|Aug 31
|<nowiki>-</nowiki>
|Sept. 25
|26
|(17.8+13.2) /2
|(721+587) /2
|403
|17.008
|-
|Sept. 26
|<nowiki>-</nowiki>
|Oct. 27
|32
|(13.2+9.6) /2
|(587+446) /2
|365
|16.541
|-
|Oct. 28
|<nowiki>-</nowiki>
|Nov. 22
|26
|(9.6+5.8) /2
|(446+287) /2
|200
|9.536
|-
|Nov. 23
|<nowiki>-</nowiki>
|Dec. 20
|28
|(5.8+4.4) /2
|(287+231) /2
|143
|7.253
|-
|Dec. 21
|<nowiki>-</nowiki>
|Jan. 3
|14
|4.4
|231
|62
|3.234
|-
|
|
|
|284
|
|
|4973
|190.216
|-
| colspan="8" |
|-
| colspan="8" |Total quantity of milk: 4 973. kg
|-
| colspan="8" |Total quantity of fat: 190 kg
|-
| colspan="8" |Average fat percentage (190.216 / 4973) x 100 = 3.82%
|}
</center>

=== Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. Livest. Prod. Sci. 17:l.</ref>) ===
With the method 'Interpolation using Standard Lactation Curves' missing test day yields and 305 day projections are predicted. The method makes use of separate standard lactation curves representing the expected course of the lactation, for a certain herd production level, age at calving and season of calving and yield trait. By interpolation using standard lactation curves, the fact that after calving milk yield generally increases and subsequently decreases is taken into account. The daily yields are predicted for fixed days of the lactation: day 0, 10, 30, 50 etc.

The cumulative yield is calculated as follows in :
[[File:Equation2222222.png|none|thumb|474x474px]]
where:

yi = the i-th daily yield;

INTi = the interval in days between the daily yields yi and yi+1;

''n'' = total number of daily yields (measured daily yields and predicted daily yields).

The next example illustrates the calculation of a record in progress. The cow was tested at day 35 and day 65 of the lactation. To determine the lactation yield, daily milk yields are determined for day 0, 10, 30 and 50 of the lactation, by means of the standard lactation curves. The daily yields are in Table 4.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Measured and derived daily yields, used to calculate the record in progress in the example (ISLC).'''''
|- style="background-color:#efefef;"
|'''Day of lactation'''
|'''Milk (kg)'''
|'''Note'''
|-
|0
|25.9
|Predicted
|-
|10
|27.8
|Predicted
|-
|30
|31.7
|Predicted
|-
|35
|31.8
|Measured
|-
|50
|32.9
|Interpolated using standard lactation curve
|-
|65
|33.0
|Measured
|}
</center>

Next, the record in progress can be calculated by means of the formula for a cumulative yield as follows:

[(10 - 1) * 25.9 + (10+1) * 27.8] / 2 +

[(20 - 1) * 27.8 + (20+1) * 31.7] / 2 +

[(5 - 1) * 31.7 + (5+1) * 31.8] / 2 +

[(15 - 1) * 31.8 + (15+1) * 32.9] / 2 +

[(15 - 1) * 32.9 + (15+1) * 33.0] / 2 = 2005.3 kg.

This corresponds to the surface below the line through the predicted and measured daily yields (see Figure 1).
[[File:Figure1.png|center|thumb|621x621px|''Figure 1. Example of calculation of record in progress.'']]

=== Best prediction (BP) (VanRaden, 1997<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. J. Dairy Sci. 80:3015-3022.</ref>) ===
Recorded milk weights are combined into a lactation record using standard selection index methods. Let vector y contain M1, M2, to Mn and let E('''y''') contain corresponding the expected values for each recorded day. The E(y) are obtained from standard lactation curves for the population or for the herd and should account for the cow's age and other environmental factors such as season, milking frequency, etc. The yields in '''y''' covary as a function of the recording interval between them (I). Diagonal elements in Var(y) are the population or herd variance for that recording day and off diagonals are obtained from autoregressive or similar functions such as Corr(M1, M2)=0.995I for first lactations or 0.992I for later lactations. Covariances of one observation with the lactation yield, for example Cov(M1, MY), are the sum of 305 individual covariances. E(MY) is the sum of 305 daily expected values. Lactation milk yield is then predicted as Equation 3:
[[File:Equation333333.png|none|thumb|640x640px]]
With best prediction, predicted milk yields have less variance than true milk yields. With TIM, estimated yields have more variance than true yields. The reason is that predicted yields are regressed toward the mean unless all 305 daily yields are observed. With best prediction, the predicted MY for a lactation without any observed yields is E(MY) which is the population or herd mean for a cow of that age and season. With TIM, the estimated MY is undefined if no daily yields are recorded.

Milk, fat, and protein yields can be processed separately using single-trait best prediction or jointly using multi-trait best prediction. Replacement of M1, M2, to Mn with F1, F2, to Fn or P1, P2, to Pn gives the single-trait predictions for fat or for protein. Multi-trait predictions require larger vectors and matrices but similar algebra. Products of trait correlations and autoregressive correlations, for example, may provide the needed covariances.

=== Multiple-Trait Procedure (MTP) (Schaeffer & Jamrozik, 1996<ref>Schaeffer, L.R., and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. J. Dairy Sci. 79:2044-2055.</ref>) ===
The Multiple-Trait Procedure predicts 305-d lactation yields for milk, fat, protein and SCS, incorporating information about standard lactation curves and covariances between milk, fat, and protein yields and SCS. Test day yields are weighted by their relative variances, and standard lactation curves of cows of similar breed, region, lactation number, age, and season of calving are used in the estimation of lactation curve parameters for each cow. The multiple-trait procedure can handle long intervals between test days, test days with milk only recorded, and can make 305-d predictions on the basis of just one test day record per cow. The procedure also lends itself to the calculation of peak yield, day of peak yield, yield persistency, and expected test-day yields, which could be useful management tools for a producer on a milk recording program.

The MTP method is based upon Wilmink's model in conjunction with an approach incorporating standard curve parameters for cows with the same production characteristics. Wilmink's function for one trait is given by Equation 4.

Equation 4. Wilmink function for one trait (MTP).

y = A + B''t'' ± C''exp'' (-0.05''t'') + ''e''

where y is yield on day t of lactation, A, B, and C are related to the shape of the lactation curve.

The parameters A, B, and C need to be estimated for each yield trait. The yield traits have high phenotypic correlations, and MTP would incorporate these correlations. Use of MTP would allow for the prediction of yields even if data were not available on each test day for a cow.

The vector of parameters to be estimated for one cow are designated:
[[File:Vectro.png|center|thumb]]
where M, F, and P represent milk, fat, and protein, respectively, and S represents somatic cell score. The vector c is to be estimated from the available test-day records. Let c0 represent the corresponding parameters estimated across all cows with the same production characteristics as the cow in question.

Let
[[File:Vector2.png|center|thumb]]

be the vector of yield traits and somatic cell scores on test ''k'' at day ''t'' of the lactation.

The incidence matrix, ''Xk'', is constructed as follows:
[[File:Vector3.png|center|thumb|558x558px]]

The MTP equations are:
[[File:Equation55555.png|none|thumb|560x560px]]
and ''n'' is the number of tests for that cow. ''Rk'' is a matrix of order 4 that contains the variances and covariances among the yields on ''kth'' test at day ''t'' of lactation. The elements of this matrix were derived from regression formulas based on fitting phenotypic variances and covariances of yields to models with ''t'' and ''t2'' as covariables. Thus, element ''ij'' of ''Rk'' would be determined by

rij(t) = ß0ij + ß1ij (t) + ß2ij (t2)

G is a 12 x 12 matrix containing variances and covariances among the parameters in '''ĉ''' and represents the cow to cow variation in these parameters, which includes genetic and permanent environmental effects, but ignores genetic covariances between cows. The parameters for '''''G''''' and '''''Rk''''' vary depending on the breed, but must be known. Initially, these matrices were allowed to vary by region of Canada in addition to breed, but this meant that there could exist two cows with identical production records on the same days in milk, but because one cow was in one region and the other cow was in another region, then the accuracy of their predictions would be different. This was considered to be too confusing for dairy producers, so that regional differences in variance-covariance matrices were ignored and one set of parameters would be used for all regions for a particular breed. Estimation of G is described later.

If a cow has a test, but only milk yield is reported, then

y’k(Mk 0 0 0)

and
[[File:And.png|center|thumb|540x540px]]

The inverse of '''''Rk''''' is the regular inverse of the nonzero submatrix within '''''Rk''''', ignoring the zero rows and columns. Thus, missing yields can be accommodated in MTP.

Accuracy of predicted 305-d lactation totals depends on the number of test-day records during the lactation and DIM associated with each test. Thus, any prediction procedure will require reliability figures to be reported with all predictions, especially if fewer tests at very irregular intervals are going to be frequent in milk recording. At the moment, an approximate procedure is applied that uses the inverse elements of '''(X’R-1X + G-1) -1.'''

==== 1.1 Example calculations ====
Four test day records on a 25 month old, Holstein cow calving in June from Ontario are given in the Table 5 below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 5. Example test day data for a cow (MTP).'''''
|- style="background-color:#efefef;"
|'''Test no.'''
|'''DIM=''t'''''
|'''Exp(-0.05''t'')'''
|'''Milk (kg)'''
|'''Fat (kg)'''
|'''Protein (kg)'''
|'''SCS'''
|-
|1
|15
|0.47237
|28.8
|
|
|3.130
|-
|2
|54
|0.06721
|29.2
|1.12
|0.87
|2.463
|-
|3
|188
|0.000083
|23.7
|0.97
|0.78
|2.157
|-
|4
|250
|0.0000037
|20.8
|
|
|2.619
|}
</center>

Notice that two tests do not have fat and protein yields, and that intervals between tests are irregular and large. The vector of standard curve parameters based on all available comparable cow, is
[[File:Vector4.png|center|thumb]]
The R^(-1)_k matrices for each test day need to be constructed. These matrices are derived from regression equations. The equations for Holsteins were:
<center>
{| class="wikitable" style="text-align: center;"
|''rMM(t) =''
|71.0752 - 0.281201''t'' + 0.0004977''t2''
|-
|''rMF(t) =''
|2.4365 - 0.013274''t'' + 0.0000302''t2''
|-
|''rMP(t) =''
|2.0504 - 0.008286''t'' + 0.0000163''t2''
|-
|''rMS(t) =''
|<nowiki>-1.7993 + 0.013209</nowiki>''t'' - 0.000056''t2''
|-
|''rFF(t) =''
|0.1312 - 0.000725''t'' + 0.000001586''t2''
|-
|''rFP(t) =''
|0.0739 - 0.000386''t'' + 0.000000926''t2''
|-
|''rFS(t) =''
|<nowiki>- 0.0386 + 0.000292</nowiki>''t'' - 0.000001796''t2''
|-
|''rPP(t) =''
|0.066 - 0.000267''t'' + 0.0000005636''t2''
|-
|''rPS(t) =''
|<nowiki>- 0.0404 + 0.000369</nowiki>''t'' - 0.000001743''t2''
|-
|''rSS(t) =''
|3.0404 - 0.000083''t'' - 0.000006105''t2''
|}
</center>

The inverses of the residual variance-covariance matrices for yields for the four test days are as follows:
<center>
{| class="wikitable" style="text-align: center;"
|
|0.0151259
|0
|0
|0.0080354
|-
|'''R^(-1)_1''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0080354
|0
|0
|0.3334553
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.1685584
|0.345947
|<nowiki>-4.851935</nowiki>
|0.0254775
|-
|'''R^(-1)_2''' = =
|<nowiki>-0.345947</nowiki>
|26.830915
|<nowiki>-17.40281</nowiki>
|<nowiki>-0.041445</nowiki>
|-
|
|<nowiki>-4.851935</nowiki>
|<nowiki>-17.40281</nowiki>
|187.18579
|<nowiki>-0.584885</nowiki>
|-
|
|0.0254775
|<nowiki>-0.041445</nowiki>
|<nowiki>-0.584885</nowiki>
|0.3365425
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.2620161
|0.1479068
|<nowiki>-7.943903</nowiki>
|0.0316069
|-
|'''R^(-1)_3''' = =
|0.1479068
|54.446977
|<nowiki>-56.01333</nowiki>
|0.3306741
|-
|
|<nowiki>-7.943903</nowiki>
|<nowiki>-56.01333</nowiki>
|317.9609
|<nowiki>-0.92601</nowiki>
|-
|
|0.0316069
|0.3306741
|<nowiki>-0.92601</nowiki>
|0.3654369
|}
{| class="wikitable" style="text-align: center;"
|

|0.0329465
|0
|0
|0.0251039
|-
|'''R^(-1)_4''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0251039
|0
|0
|0.3981981
|}

Inverse matrix G^(-1) of order 12 is the same for all cows of the same breed:

[[File:Left 6x6.jpg|center|thumb|600x600px|Inverse matrix G^(-1) of order 12]]

</center>
Note that many covariances between different parameters of the lactation curves have been set to zero. When all covariances were included, the prediction errors for individual cows were very large, possibly because the covariances were highly correlated to each other within and between traits. Including only covariances between the same parameter among traits gave much smaller prediction errors.

The elements of the MTP equations of order 12 for this cow are shown in partitioned format also:

'''X’R-1X ='''
<center>[[File:Elements of the MTP equations of order 12.jpg|center|thumb|600x600px|Elements of the MTP equations of order 12]]
</center>
[[File:Equation7.png|center|thumb|632x632px]]

The solution vector for this cow is
[[File:Equation6666.png|center|thumb]]

To predict 305-day yields, Y305
[[File:Equation7777.png|none|thumb|551x551px]]
Equation 6 is used separately for each trait (milk, fat, protein, and SCS). The results for this cow were 7456 kg milk, 301 kg fat, and 239 kg protein. The result for SCS is divided by 305 to give an average daily SCS of 2.477.
</div>
</div>

= Appendices =
== Appendix 1 - Adjustment factors to calculate 24-hour yields using the Liu method ==
<div class="mw-collapsible mw-collapsed">
<div>
In Table 6 the adjustment factors to calculate 24-hour yields, using the Liu method, can be found. The description of the Liu method can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2.]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" |'''''Table 1. Adjustment factors to calculate 24-hour yields using the Liu method. Milking time (MT) is either 1 (PM) or 2 (AM), i = parity class, j= milking interval class and k = stage of lactation class.'''''
|- style="background-color:#efefef;"
|'''MT'''
|'''i'''
|'''j'''
|'''k'''
| colspan="2" |'''Milk yield (DMY)'''
| colspan="2" |'''Fat yield (DFY)'''
| colspan="2" |'''Protein yield (DPY)'''
|-
| colspan="4" |
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|-
|1
|1
|1
|1
|5.29333
|1.83283
|0.30911
|1.43518
|0.18984
|1.77461
|-
|1
|1
|1
|2
|4.17676
|1.97447
|0.2803
|1.56914
|0.12246
|2.00568
|-
|1
|1
|1
|3
|4.26476
|1.95945
|0.18826
|1.82468
|0.12624
|2.0137
|-
|1
|1
|1
|4
|3.41282
|2.01814
|0.25025
|1.64707
|0.12519
|1.99629
|-
|1
|1
|1
|5
|1.79548
|2.22665
|0.06578
|2.09515
|0.05249
|2.24065
|-
|1
|1
|1
|6
|3.7751
|1.95508
|0.12854
|1.93892
|0.11936
|2.00979
|-
|1
|1
|1
|7
|1.544
|2.1478
|0.06425
|2.06779
|0.0569
|2.13851
|-
|1
|1
|2
|1
|5.8584
|1.79409
|0.33193
|1.42953
|0.20756
|1.7288
|-
|1
|1
|2
|2
|5.45524
|1.84258
|0.32877
|1.43235
|0.21332
|1.74001
|-
|1
|1
|2
|3
|4.64052
|1.86706
|0.27155
|1.57017
|0.16439
|1.84539
|-
|1
|1
|2
|4
|2.86835
|2.06209
|0.18647
|1.79403
|0.10803
|2.0193
|-
|1
|1
|2
|5
|2.11336
|2.12055
|0.10435
|1.97206
|0.07193
|2.10651
|-
|1
|1
|2
|6
|2.00673
|2.0636
|0.1386
|1.83336
|0.06892
|2.06532
|-
|1
|1
|2
|7
|1.71752
|2.11269
|0.06501
|2.0379
|0.05569
|2.12881
|-
|1
|1
|3
|1
|2.80244
|2.02183
|0.17663
|1.72438
|0.11078
|1.96422
|-
|1
|1
|3
|2
|3.47396
|1.98268
|0.2135
|1.6805
|0.10471
|1.99092
|-
|1
|1
|3
|3
|2.81702
|2.04348
|0.20754
|1.71868
|0.1127
|1.98403
|-
|1
|1
|3
|4
|3.1989
|1.998
|0.21578
|1.6991
|0.10802
|1.99517
|-
|1
|1
|3
|5
|2.47055
|2.04826
|0.15418
|1.83151
|0.07492
|2.07547
|-
|1
|1
|3
|6
|1.923
|2.07728
|0.11783
|1.89678
|0.06457
|2.08391
|-
|1
|1
|3
|7
|1.85264
|2.0873
|0.13047
|1.86711
|0.071
|2.06917
|-
|1
|1
|4
|1
|2.75042
|1.96631
|0.24794
|1.61741
|0.09248
|1.95376
|-
|1
|1
|4
|2
|2.97505
|1.96711
|0.20029
|1.71842
|0.09381
|1.97081
|-
|1
|1
|4
|3
|2.33365
|2.02986
|0.17021
|1.79996
|0.07631
|2.03167
|-
|1
|1
|4
|4
|3.41505
|1.94107
|0.1845
|1.76799
|0.10989
|1.95456
|-
|1
|1
|4
|5
|2.67488
|1.97797
|0.13433
|1.85893
|0.09432
|1.97755
|-
|1
|1
|4
|6
|1.89907
|2.04841
|0.08715
|1.96251
|0.07132
|2.04225
|-
|1
|1
|4
|7
|1.80326
|2.03554
|0.1251
|1.86477
|0.06072
|2.04747
|-
|1
|1
|5
|1
|2.76763
|1.92863
|0.15754
|1.72474
|0.10187
|1.88749
|-
|1
|1
|5
|2
|3.36896
|1.92048
|0.2236
|1.64149
|0.12369
|1.8823
|-
|1
|1
|5
|3
|2.22763
|2.00452
|0.17614
|1.7474
|0.08019
|1.9782
|-
|1
|1
|5
|4
|2.44625
|1.97049
|0.17217
|1.74753
|0.0889
|1.94647
|-
|1
|1
|5
|5
|2.379
|1.97307
|0.15965
|1.76134
|0.0896
|1.94575
|-
|1
|1
|5
|6
|1.62948
|2.02491
|0.11021
|1.85546
|0.0852
|1.94593
|-
|1
|1
|5
|7
|1.45651
|2.0254
|0.07479
|1.92789
|0.05846
|2.00196
|-
|1
|1
|6
|1
|2.01088
|1.9497
|0.16548
|1.68143
|0.101
|1.85846
|-
|1
|1
|6
|2
|2.96605
|1.93064
|0.25841
|1.52566
|0.12097
|1.86061
|-
|1
|1
|6
|3
|2.2281
|1.96085
|0.19036
|1.69013
|0.08032
|1.9375
|-
|1
|1
|6
|4
|2.39473
|1.952
|0.17854
|1.72423
|0.06863
|1.97582
|-
|1
|1
|6
|5
|2.37955
|1.94127
|0.19579
|1.66419
|0.08447
|1.93156
|-
|1
|1
|6
|6
|0.36203
|2.12393
|0.14291
|1.75822
|0.03845
|2.04562
|-
|1
|1
|6
|7
|1.5702
|1.96794
|0.1336
|1.76796
|0.06449
|1.94829
|-
|1
|1
|7
|1
|3.93654
|1.82772
|0.2359
|1.61894
|0.15032
|1.76054
|-
|1
|1
|7
|2
|4.39662
|1.81581
|0.24969
|1.5881
|0.16909
|1.74794
|-
|1
|1
|7
|3
|3.78325
|1.82778
|0.19228
|1.71802
|0.12368
|1.8268
|-
|1
|1
|7
|4
|3.39116
|1.86302
|0.1969
|1.71838
|0.12282
|1.848
|-
|1
|1
|7
|5
|3.20111
|1.83255
|0.09893
|1.86309
|0.1044
|1.84257
|-
|1
|1
|7
|6
|3.75639
|1.78665
|0.25205
|1.56174
|0.14105
|1.76802
|-
|1
|1
|7
|7
|1.42153
|1.95649
|0.09226
|1.85882
|0.04636
|1.96245
|-
|1
|1
|8
|1
|2.3454
|1.90436
|0.14321
|1.77423
|0.10703
|1.82306
|-
|1
|1
|8
|2
|3.97557
|1.82746
|0.26651
|1.58374
|0.15298
|1.76385
|-
|1
|1
|8
|3
|4.26939
|1.80503
|0.22918
|1.64925
|0.12924
|1.81061
|-
|1
|1
|8
|4
|2.90779
|1.89861
|0.18578
|1.73968
|0.13948
|1.79679
|-
|1
|1
|8
|5
|2.8265
|1.87632
|0.19374
|1.67929
|0.12377
|1.80944
|-
|1
|1
|8
|6
|2.26312
|1.87397
|0.09917
|1.82528
|0.08819
|1.84453
|-
|1
|1
|8
|7
|0.31382
|2.04402
|0.05049
|1.95773
|0.02612
|1.99012
|-
|1
|2
|1
|1
|4.63752
|1.99615
|0.31102
|1.58962
|0.16637
|1.96686
|-
|1
|2
|1
|2
|5.56226
|1.91521
|0.26761
|1.64342
|0.16973
|1.94145
|-
|1
|2
|1
|3
|4.51983
|1.96962
|0.26221
|1.65088
|0.12245
|2.03857
|-
|1
|2
|1
|4
|4.51563
|1.93033
|0.18468
|1.80715
|0.15252
|1.94807
|-
|1
|2
|1
|5
|2.60334
|2.07338
|0.16011
|1.81257
|0.09892
|2.05493
|-
|1
|2
|1
|6
|2.86068
|1.98457
|0.15381
|1.79197
|0.08619
|2.04046
|-
|1
|2
|1
|7
|1.6596
|2.11753
|0.13089
|1.83687
|0.09908
|1.96479
|-
|1
|2
|2
|1
|3.94656
|2.03607
|0.23716
|1.6988
|0.19559
|1.88765
|-
|1
|2
|2
|2
|4.20525
|1.98621
|0.3553
|1.46663
|0.1657
|1.92175
|-
|1
|2
|2
|3
|3.31729
|2.04589
|0.29682
|1.57761
|0.12491
|2.00945
|-
|1
|2
|2
|4
|1.95977
|2.13926
|0.16059
|1.79846
|0.06713
|2.12835
|-
|1
|2
|2
|5
|1.49014
|2.14889
|0.10057
|1.90772
|0.05279
|2.14047
|-
|1
|2
|2
|6
|0.82235
|2.22517
|0.07573
|1.94963
|0.04014
|2.17549
|-
|1
|2
|2
|7
|1.53608
|2.08972
|0.11472
|1.81148
|0.0676
|2.03957
|-
|1
|2
|3
|1
|3.85525
|2.00429
|0.27991
|1.62403
|0.12863
|1.98973
|-
|1
|2
|3
|2
|4.1508
|1.9852
|0.3635
|1.47515
|0.13952
|1.97074
|-
|1
|2
|3
|3
|3.31493
|2.02332
|0.31131
|1.55183
|0.11703
|2.00696
|-
|1
|2
|3
|4
|2.47354
|2.0652
|0.20828
|1.71637
|0.09402
|2.04147
|-
|1
|2
|3
|5
|1.68517
|2.08809
|0.14418
|1.80246
|0.06917
|2.05808
|-
|1
|2
|3
|6
|1.316
|2.12714
|0.11206
|1.87179
|0.04723
|2.12486
|-
|1
|2
|3
|7
|0.4841
|2.20538
|0.04633
|2.02915
|0.02369
|2.18113
|-
|1
|2
|4
|1
|2.82623
|2.01819
|0.25826
|1.69268
|0.11251
|1.97665
|-
|1
|2
|4
|2
|3.24039
|1.9811
|0.36283
|1.50648
|0.11719
|1.96246
|-
|1
|2
|4
|3
|2.4545
|2.03386
|0.19627
|1.75339
|0.09698
|2.00807
|-
|1
|2
|4
|4
|2.46446
|2.01626
|0.17827
|1.76414
|0.08026
|2.02912
|-
|1
|2
|4
|5
|2.11339
|2.00724
|0.14884
|1.77964
|0.07749
|2.00585
|-
|1
|2
|4
|6
|1.51141
|2.04563
|0.11559
|1.82474
|0.06194
|2.02586
|-
|1
|2
|4
|7
|0.95936
|2.09963
|0.07044
|1.95281
|0.03645
|2.0993
|-
|1
|2
|5
|1
|3.36561
|1.97323
|0.2649
|1.65361
|0.13019
|1.92402
|-
|1
|2
|5
|2
|3.66222
|1.95479
|0.35065
|1.51028
|0.14652
|1.89882
|-
|1
|2
|5
|3
|3.20442
|1.96165
|0.28676
|1.58823
|0.12031
|1.93028
|-
|1
|2
|5
|4
|1.78673
|2.0426
|0.17183
|1.75198
|0.0678
|2.02025
|-
|1
|2
|5
|5
|1.61868
|2.01988
|0.11914
|1.80878
|0.06624
|1.99283
|-
|1
|2
|5
|6
|1.30123
|2.02218
|0.10515
|1.80653
|0.05345
|2.00292
|-
|1
|2
|5
|7
|0.65695
|2.08269
|0.06835
|1.89102
|0.0332
|2.0525
|-
|1
|2
|6
|1
|2.3773
|1.9669
|0.24867
|1.6336
|0.08319
|1.94741
|-
|1
|2
|6
|2
|2.82556
|1.95506
|0.31731
|1.51798
|0.12008
|1.89324
|-
|1
|2
|6
|3
|2.7235
|1.94883
|0.30621
|1.5177
|0.09365
|1.93764
|-
|1
|2
|6
|4
|1.77727
|1.98273
|0.17989
|1.69341
|0.07314
|1.95161
|-
|1
|2
|6
|5
|0.81041
|2.05295
|0.13961
|1.74391
|0.04468
|2.01091
|-
|1
|2
|6
|6
|0.72188
|2.0465
|0.09874
|1.79927
|0.03137
|2.03309
|-
|1
|2
|6
|7
|1.21598
|1.97942
|0.07065
|1.87211
|0.04484
|1.98491
|-
|1
|2
|7
|1
|3.55054
|1.89128
|0.27402
|1.61031
|0.10827
|1.89085
|-
|1
|2
|7
|2
|5.0062
|1.81574
|0.3119
|1.54857
|0.18009
|1.76865
|-
|1
|2
|7
|3
|3.95204
|1.84947
|0.30465
|1.53907
|0.16048
|1.789
|-
|1
|2
|7
|4
|2.36233
|1.9168
|0.18751
|1.70412
|0.09531
|1.88355
|-
|1
|2
|7
|5
|1.48851
|1.94443
|0.09973
|1.81041
|0.05904
|1.92497
|-
|1
|2
|7
|6
|1.22525
|1.94454
|0.06617
|1.87082
|0.05516
|1.91259
|-
|1
|2
|7
|7
|1.13847
|1.93756
|0.08109
|1.83388
|0.04706
|1.93165
|-
|1
|2
|8
|1
|4.09874
|1.87708
|0.20312
|1.73434
|0.15506
|1.83083
|-
|1
|2
|8
|2
|4.66403
|1.84302
|0.31808
|1.56093
|0.18049
|1.78288
|-
|1
|2
|8
|3
|3.24375
|1.89351
|0.2827
|1.59546
|0.13583
|1.83427
|-
|1
|2
|8
|4
|2.24175
|1.92084
|0.17795
|1.72611
|0.09636
|1.87438
|-
|1
|2
|8
|5
|1.63783
|1.93625
|0.1225
|1.78642
|0.0659
|1.90934
|-
|1
|2
|8
|6
|2.01753
|1.89095
|0.13742
|1.74752
|0.08289
|1.86553
|-
|1
|2
|8
|7
|0.97568
|1.97215
|0.05926
|1.88807
|0.04057
|1.95672
|-
|2
|1
|1
|1
|3.44076
|1.73133
|0.27759
|1.55037
|0.13323
|1.68913
|-
|2
|1
|1
|2
|4.99596
|1.64527
|0.2322
|1.58033
|0.17533
|1.62422
|-
|2
|1
|1
|3
|3.83372
|1.68144
|0.25087
|1.52033
|0.14525
|1.66706
|-
|2
|1
|1
|4
|3.87034
|1.68102
|0.20979
|1.60153
|0.13627
|1.68885
|-
|2
|1
|1
|5
|1.76134
|1.80424
|0.15241
|1.70485
|0.06231
|1.81524
|-
|2
|1
|1
|6
|0.79304
|1.89072
|0.09906
|1.80312
|0.03277
|1.89435
|-
|2
|1
|1
|7
|1.43535
|1.80614
|0.0593
|1.81589
|0.0407
|1.85002
|-
|2
|1
|2
|1
|3.72284
|1.68499
|0.19226
|1.66567
|0.1237
|1.66453
|-
|2
|1
|2
|2
|4.42667
|1.66508
|0.24314
|1.55652
|0.14361
|1.66251
|-
|2
|1
|2
|3
|2.7019
|1.75871
|0.32717
|1.38452
|0.11056
|1.72312
|-
|2
|1
|2
|4
|2.41538
|1.75937
|0.14575
|1.68355
|0.09038
|1.74138
|-
|2
|1
|2
|5
|1.65412
|1.81649
|0.13926
|1.70623
|0.0597
|1.81378
|-
|2
|1
|2
|6
|2.0843
|1.7735
|0.21052
|1.57508
|0.07244
|1.78566
|-
|2
|1
|2
|7
|1.43238
|1.80651
|0.08031
|1.78712
|0.05269
|1.81727
|-
|2
|1
|3
|1
|2.45314
|1.77068
|0.18152
|1.73443
|0.07657
|1.78025
|-
|2
|1
|3
|2
|3.01217
|1.70966
|0.19388
|1.66175
|0.05624
|1.80606
|-
|2
|1
|3
|3
|2.09997
|1.74945
|0.14493
|1.68277
|0.05446
|1.7922
|-
|2
|1
|3
|4
|2.36683
|1.71741
|0.12244
|1.71407
|0.06775
|1.75721
|-
|2
|1
|3
|5
|1.56776
|1.75755
|0.08776
|1.76946
|0.04244
|1.79675
|-
|2
|1
|3
|6
|1.63824
|1.75452
|0.09422
|1.76794
|0.04181
|1.80604
|-
|2
|1
|3
|7
|0.74114
|1.83421
|0.08039
|1.78306
|0.02347
|1.85596
|-
|2
|1
|4
|1
|1.47047
|1.78588
|0.17271
|1.69379
|0.06511
|1.74985
|-
|2
|1
|4
|2
|2.22168
|1.72985
|0.20701
|1.59429
|0.08178
|1.71455
|-
|2
|1
|4
|3
|2.50108
|1.69618
|0.16828
|1.61962
|0.08598
|1.70516
|-
|2
|1
|4
|4
|1.97141
|1.7202
|0.1446
|1.66357
|0.06856
|1.73201
|-
|2
|1
|4
|5
|1.17054
|1.75879
|0.1172
|1.69234
|0.04624
|1.75806
|-
|2
|1
|4
|6
|1.74755
|1.70968
|0.12562
|1.67603
|0.0629
|1.72333
|-
|2
|1
|4
|7
|0.52482
|1.80155
|0.07345
|1.75615
|0.02671
|1.79288
|-
|2
|1
|5
|1
|1.76464
|1.76219
|0.24301
|1.59094
|0.07156
|1.73136
|-
|2
|1
|5
|2
|1.99594
|1.73438
|0.1984
|1.5954
|0.06489
|1.73449
|-
|2
|1
|5
|3
|1.8804
|1.72362
|0.13019
|1.67977
|0.06783
|1.71916
|-
|2
|1
|5
|4
|1.83337
|1.71477
|0.11197
|1.70244
|0.05764
|1.73194
|-
|2
|1
|5
|5
|1.49752
|1.72615
|0.13128
|1.65461
|0.04656
|1.7433
|-
|2
|1
|5
|6
|1.3042
|1.7305
|0.07173
|1.75315
|0.04482
|1.7399
|-
|2
|1
|5
|7
|2.00868
|1.67669
|0.12298
|1.64761
|0.09175
|1.64669
|-
|2
|1
|6
|1
|0.84993
|1.75972
|0.12918
|1.74026
|0.0328
|1.74802
|-
|2
|1
|6
|2
|1.93666
|1.67406
|0.16606
|1.59943
|0.04535
|1.7106
|-
|2
|1
|6
|3
|2.12115
|1.64964
|0.19988
|1.50821
|0.05229
|1.68986
|-
|2
|1
|6
|4
|0.68831
|1.73901
|0.09674
|1.6838
|0.01696
|1.75787
|-
|2
|1
|6
|5
|1.13081
|1.69479
|0.06413
|1.72559
|0.04936
|1.67757
|-
|2
|1
|6
|6
|0.5893
|1.72537
|0.02598
|1.80138
|0.01591
|1.74082
|-
|2
|1
|6
|7
|0.72519
|1.71955
|0.03157
|1.78405
|0.02889
|1.71972
|-
|2
|1
|7
|1
|1.85937
|1.66064
|0.2416
|1.49676
|0.06807
|1.63599
|-
|2
|1
|7
|2
|1.8527
|1.64892
|0.2374
|1.43845
|0.06336
|1.6431
|-
|2
|1
|7
|3
|1.56905
|1.66084
|0.15434
|1.55598
|0.04336
|1.68109
|-
|2
|1
|7
|4
|0.74968
|1.69857
|0.13496
|1.56636
|0.02871
|1.6933
|-
|2
|1
|7
|5
|1.08222
|1.65925
|0.10847
|1.613
|0.03305
|1.67829
|-
|2
|1
|7
|6
|1.1124
|1.68059
|0.14267
|1.57525
|0.04416
|1.6776
|-
|2
|1
|7
|7
|0.88031
|1.6751
|0.10534
|1.60483
|0.04216
|1.66444
|-
|2
|1
|8
|1
|0.62802
|1.72402
|0.19225
|1.54631
|0.03247
|1.69368
|-
|2
|1
|8
|2
|0.83902
|1.68303
|0.15492
|1.53421
|0.05922
|1.61411
|-
|2
|1
|8
|3
|1.33727
|1.63407
|0.19835
|1.43309
|0.05874
|1.61141
|-
|2
|1
|8
|4
|1.06381
|1.64762
|0.11026
|1.58762
|0.04019
|1.64574
|-
|2
|1
|8
|5
|1.13714
|1.61716
|0.13322
|1.53166
|0.05648
|1.59149
|-
|2
|1
|8
|6
|1.19134
|1.60463
|0.11089
|1.54864
|0.06258
|1.56912
|-
|2
|1
|8
|7
|1.58872
|1.60204
|0.066
|1.64659
|0.04748
|1.63282
|-
|2
|2
|1
|1
|3.46775
|1.78609
|0.28956
|1.68515
|0.15003
|1.72171
|-
|2
|2
|1
|2
|5.69879
|1.67614
|0.3725
|1.5045
|0.19774
|1.64659
|-
|2
|2
|1
|3
|5.18985
|1.66571
|0.40124
|1.40574
|0.17828
|1.65793
|-
|2
|2
|1
|4
|3.43435
|1.74182
|0.20332
|1.66994
|0.11075
|1.76221
|-
|2
|2
|1
|5
|2.48643
|1.76219
|0.13714
|1.7396
|0.09636
|1.75624
|-
|2
|2
|1
|6
|1.41151
|1.82292
|0.15415
|1.6725
|0.06549
|1.80013
|-
|2
|2
|1
|7
|0.9096
|1.8409
|0.08811
|1.7823
|0.03467
|1.85275
|-
|2
|2
|2
|1
|1.85358
|1.83615
|0.28355
|1.64765
|0.06055
|1.83138
|-
|2
|2
|2
|2
|3.81188
|1.74978
|0.25972
|1.62799
|0.11238
|1.7646
|-
|2
|2
|2
|3
|3.16717
|1.76679
|0.29832
|1.53409
|0.09407
|1.78959
|-
|2
|2
|2
|4
|2.33664
|1.78934
|0.22694
|1.60101
|0.07273
|1.80371
|-
|2
|2
|2
|5
|2.01675
|1.79303
|0.10664
|1.79792
|0.06062
|1.8184
|-
|2
|2
|2
|6
|1.80809
|1.80081
|0.13659
|1.70935
|0.07335
|1.79213
|-
|2
|2
|2
|7
|1.01661
|1.8295
|0.0548
|1.84688
|0.03414
|1.84213
|-
|2
|2
|3
|1
|2.01474
|1.8142
|0.21867
|1.74325
|0.05359
|1.83088
|-
|2
|2
|3
|2
|3.53989
|1.71985
|0.28196
|1.60868
|0.10823
|1.73763
|-
|2
|2
|3
|3
|3.38412
|1.69907
|0.27409
|1.56164
|0.11042
|1.71397
|-
|2
|2
|3
|4
|2.2171
|1.74622
|0.16076
|1.70107
|0.07372
|1.75906
|-
|2
|2
|3
|5
|1.11799
|1.80944
|0.11087
|1.75678
|0.03792
|1.81891
|-
|2
|2
|3
|6
|1.40464
|1.76033
|0.10048
|1.72933
|0.05342
|1.75745
|-
|2
|2
|3
|7
|0.11328
|1.8972
|0.04052
|1.87101
|0.00787
|1.88753
|-
|2
|2
|4
|1
|2.59777
|1.74476
|0.28154
|1.66509
|0.10763
|1.71072
|-
|2
|2
|4
|2
|3.53853
|1.69511
|0.38311
|1.46839
|0.13243
|1.66523
|-
|2
|2
|4
|3
|2.80538
|1.70587
|0.26686
|1.55787
|0.1126
|1.68024
|-
|2
|2
|4
|4
|2.18191
|1.72068
|0.18333
|1.65612
|0.085
|1.71029
|-
|2
|2
|4
|5
|1.23383
|1.7716
|0.12824
|1.71179
|0.04845
|1.76628
|-
|2
|2
|4
|6
|0.85652
|1.79279
|0.0763
|1.79314
|0.03563
|1.78528
|-
|2
|2
|4
|7
|0.97995
|1.77178
|0.0797
|1.7577
|0.03846
|1.77043
|-
|2
|2
|5
|1
|2.47016
|1.74985
|0.32061
|1.60073
|0.10455
|1.71058
|-
|2
|2
|5
|2
|3.76194
|1.68979
|0.32787
|1.54675
|0.11781
|1.69109
|-
|2
|2
|5
|3
|2.61421
|1.70766
|0.20307
|1.64866
|0.08315
|1.71378
|-
|2
|2
|5
|4
|1.6809
|1.74028
|0.16795
|1.66491
|0.06202
|1.73305
|-
|2
|2
|5
|5
|1.31241
|1.75722
|0.14383
|1.68302
|0.05338
|1.74562
|-
|2
|2
|5
|6
|1.66563
|1.71781
|0.12721
|1.69231
|0.06147
|1.72101
|-
|2
|2
|5
|7
|0.87471
|1.74991
|0.07882
|1.71706
|0.04173
|1.73246
|-
|2
|2
|6
|1
|1.70055
|1.72832
|0.20839
|1.67759
|0.06001
|1.71779
|-
|2
|2
|6
|2
|3.20558
|1.65143
|0.33676
|1.47797
|0.09642
|1.6546
|-
|2
|2
|6
|3
|1.5827
|1.71538
|0.19719
|1.62038
|0.05324
|1.71254
|-
|2
|2
|6
|4
|1.7692
|1.69473
|0.14854
|1.66225
|0.05758
|1.69946
|-
|2
|2
|6
|5
|1.33003
|1.70542
|0.10726
|1.69398
|0.04565
|1.7096
|-
|2
|2
|6
|6
|1.01266
|1.71155
|0.09376
|1.70285
|0.04005
|1.70822
|-
|2
|2
|6
|7
|0.9856
|1.70091
|0.06454
|1.73063
|0.0394
|1.69796
|-
|2
|2
|7
|1
|2.02441
|1.67788
|0.30435
|1.5407
|0.08673
|1.63673
|-
|2
|2
|7
|2
|1.43949
|1.71143
|0.30098
|1.47963
|0.06527
|1.67295
|-
|2
|2
|7
|3
|1.68946
|1.66442
|0.24777
|1.47116
|0.06594
|1.64834
|-
|2
|2
|7
|4
|1.10967
|1.68591
|0.15663
|1.60109
|0.04949
|1.67069
|-
|2
|2
|7
|5
|0.77866
|1.70882
|0.11248
|1.64389
|0.03402
|1.70215
|-
|2
|2
|7
|6
|0.67502
|1.69719
|0.10289
|1.62419
|0.03507
|1.67744
|-
|2
|2
|7
|7
|0.65216
|1.70336
|0.05545
|1.73388
|0.02233
|1.72102
|-
|2
|2
|8
|1
|1.33877
|1.67358
|0.18369
|1.64385
|0.06055
|1.63818
|-
|2
|2
|8
|2
|0.71697
|1.71038
|0.25461
|1.49037
|0.04798
|1.66397
|-
|2
|2
|8
|3
|2.13197
|1.62429
|0.2393
|1.47673
|0.08136
|1.6065
|-
|2
|2
|8
|4
|1.16932
|1.66188
|0.13759
|1.60108
|0.0463
|1.64856
|-
|2
|2
|8
|5
|1.48369
|1.62387
|0.12547
|1.58988
|0.06919
|1.5925
|-
|2
|2
|8
|6
|1.18879
|1.65442
|0.10031
|1.62813
|0.07392
|1.58846
|-
|2
|2
|8
|7
|0.58052
|1.68546
|0.02696
|1.7382
|0.01982
|1.70519
|}
</center>
</div>
</div>

== Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme ==
<div class="mw-collapsible mw-collapsed">
<div>
=== Abstract ===
Based on comments on imprecision of the estimation method for 24-hour fat % in AM/PM milk recording schemes the regression formula was extended and re-estimated. Non-linearity for the existing effects of protein % of the milk sample, interval before sampling, milk amount of sample, milk amount of previous milking and interval before the previous milking was incorporated by using polynomials. Extensions were made by adding the effects of time of sampling, parity and month of sampling as class variables and lactation stage as polynomial. In total a reduction of the standard deviation of the difference between true and estimated 24-hour fat % of 2.4% was reached (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

'''''Keywords''''': estimation, fat %, AM/PM.

=== Introduction ===
The AM/PM milk recording routine is based on only one morning (a.m.) or evening (p.m.) milk sample which are collected in an alternating way. A condition to take part in this AM/PM milk recording in The Netherlands is that on farm electronic milk measurements (EMM) are available. EMM-data consists of time of milking and milk quantity of every milking. Based on one milk sample and the EMM-data the 24-hour fat % is estimated (Peeters & Galesloot, 2002<ref name=":2">Peeters, R. and P. Galesloot, 2002.Estimating daily fat yield from a single milking on test day for herds with a robotic milking system. J. Dairy Sci. 85, 682-688.</ref>). Also for farms with an automatic milking system (AMS) this estimation is used when only one milk sample is available for analysis on milk composition.

Based on comments from farmers on fluctuations in 24-hour fat % preliminary research was conducted. This showed that the current estimation caused an underestimation of 24-hour fat % based on an a.m.-sample of 0.09% while the estimate based on a p.m.-sample was overestimated by 0.05%. Possible causes for this fluctuation are differences in milk-fat synthesis between day- and night-time as was shown by Gilbert et al. (1972) <ref>Gilbert, G.R., G.L. Hargrove and M. Kroger, 1972. Diurnal variations in milk yield, fat yield, milk fat % and milk protein % by the test interval method. J. Dairy Sci. 56, 409-410.</ref>and Lee & Wardorp (1984)<ref>Lee, A.J. and Wardorp, 1984. Predicting daily milk yield, fat percent, and protein percent from morning or afternoon tests. J. Dairy Sci. 67, 351-360.</ref>. Other factors of imprecision in the current estimation can be caused by lactation stage and parity, two factors that are accounted for in the method of Liu et al. (2000)<ref>Liu, Z., R. Reents, F. Reinhardt and K Kuwan, 2000. Approaches to estimating daily yield from single milk testing schemes and use of a.m.-p.m. records in test-day model genetic evaluation in dairy cattle. J. Dairy Sci. 83, 2672-2682.</ref>.

The objective of this research is to re-estimate the regression formula which is used to estimate the 24-hour fat %s in AM/PM milk recording and AMS recordings with only one sample. By testing for non-linearity of current effects and introducing new explanatory variables the aim is to increase the accuracy of the estimated 24-hour fat %.

=== Material and Methods ===
The data needed for the objective had to meet a number of criteria. The most important criteria were that the data comprised:

* differences in interval between milking times;
* different milking times;
* multiple samples per cow per herd test date;
* milking time and quantity of all milkings;

Only data of farms that use an AMS met all of these criteria. Therefore the research was conducted on data of all farms that used an AMS from January 20th 2001 until July 1st 2004. Records with only one sample per herd test date were excluded from the analysis.

In order to estimate as well as validate the new regression formula the each herd test date was assigned at random into two separate datasets. Dataset 1 was used for estimation and contained 371.528 samplings on 50.591 cows on 537 farms. Dataset 2 was used for validation and contained 371.885 milkings on 50.643 cows on 538 farms. Some characteristics of variables of both datasets are presented in Table 1.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" |'''''Table 1. Characteristics of variables in dataset 1 (estimation) and dataset 2 (validation).'''''
|-
| rowspan="2" |'''Variable'''
| colspan="2" |'''Dataset 1 (estimation)'''
| colspan="2" |'''Dataset 2 (validation)'''
|-
|'''Mean'''
|'''Std'''
|'''Mean'''
|'''Std'''
|-
|Sample milk amount (kg)
|10.1
|3.1
|10.1
|3.1
|-
|Sample fat (%)
|4.40
|0.76
|4.41
|0.76
|-
|Sample protein (%)
|3.49
|0.35
|3.49
|0.35
|-
|Time at sampling
|12.29
|7.24
|12.31
|7.24
|-
|Interval before sample (min)
|520
|154
|521
|155
|-
|Interval before prev. milking (min)
|526
|158
|527
|159
|}
</center>

=== Methods ===
The analysis started with the currently used regression formula which uses the effects: fat %, protein %, milk amount of sampling, interval before sampling, milk amount of the previous milking and interval before the previous milking (Peeters & Galesloot, 2002<ref name=":2" />). All these effects are considered to be linear. As an extra check of the data this regression formula was re-estimated and compared to the currently used regression formula. In order to estimate the regression formula first of all the 24-hour fat % was determined by using a weighted average of all milk samples for that cow on that herd test date.

Subsequently, a number of changes to the regression formula were tested for their effect on the accuracy of the 24-hour fat %. The changes that are tested are:

# non-linearity of the current effects;
# effect of time at sampling;
# effect of lactation stage;
# effect of parity;
# month of milk recording;

The effects were all tested in a similar way by plotting the residuals of the regression formula without the effect that is tested to the tested effect. Based on this plot a possible relation between residual and effect becomes clear and the best way of incorporating the effect is shown. The conclusion if an effect had a positive effect on the accuracy of the regression formula was based on the standard deviation of the difference between estimated and true 24-hour fat %. Also the correlation between the two fat %s and the b-factor (regression coefficient) of the linear regression between the two fat %s were considered.

=== Results ===
The regression coefficients of the re-estimated regression formula differed slightly from the estimates by Peeters & Galesloot (2002)<ref name=":1" />, probably due to the different dataset.

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %.
[[File:Imagefig1.png|center|thumb|''Figure 1a: Average residual per class for the variables sample fat %'']]
[[File:Imagefig1b.png|center|thumb|''Figure 1b: Sample protein %'' ]]
[[File:Imagefig1c.png|center|thumb|''Figure 1c : Interval before sampling'']]
[[File:Imagefig1d.png|center|thumb|''Figure 1d : Interval before previous milking'']]
[[File:Imagefig1e.png|center|thumb|''Figure 1e : Sample milk amount'']]
[[File:Imagefig1f.png|center|thumb|''Figure 1f: Milk amount before sampling'']]

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %. Of all variables, only fat % of the milk sample (Figure 1a) seemed to be linear. A 2nd order polynomial fitted the interval before the previous milking. The other variables, i.e. protein % of the milk sample, interval before sampling, milk amount of sample and milk amount of the previous milking were described by a 3rd order polynomial. For all variables except fat % of the sample higher order polynomials were found significant. This however was caused by the large amount of data and no longer a possible biological effect since it also had no effect on the accuracy of the estimation.

The effect of time of sampling showed a large amount of variability over time. Using a polynomial to fit the data was therefore difficult. Estimation of the effect by hourly intervals was a good alternative as is shown in Figure 2. Lactation stage had mainly an effect in the first 50 days of lactation as is shown by Figure 3. A 3rd order polynomial fitted the data properly.
[[File:Imagefig2.png|center|thumb|''Figure 2. Average residual per class for time of sampling (minutes after midnight).'']]
[[File:Imagefig33.png|center|thumb|''Figure 3. Average residual per class for lactation stage (days).'']]

The effects of parity and month of milk sampling were both considered as class variables. For parity the effects of parity 1 to 6 and 7 or higher were considered. Table 2 shows that mainly for the lower parities the estimated 24-hour fat % was overestimated. Also the months May to October, usually the pasture period, showed an overestimation of 24-hour fat %.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" |'''''Table 2. Effect of parity and month of sampling on estimated 24-hour fat % (*100).'''''
|-
|'''Parity'''
|'''Estimate'''
|'''Month of sampling'''
|'''Estimate'''
|-
|1
|<nowiki>-6.58</nowiki>
|January
|<nowiki>-0.24</nowiki>
|-
|2
|<nowiki>-3.56</nowiki>
|February
|<nowiki>-0.28</nowiki>
|-
|3
|<nowiki>-1.42</nowiki>
|June
|<nowiki>-0.54</nowiki>
|-
|4
|<nowiki>-0.48</nowiki>
|April
|<nowiki>-0.27</nowiki>
|-
|5
|<nowiki>-0.35</nowiki>
|May
|<nowiki>-2.07</nowiki>
|-
|6
|<nowiki>-0.35</nowiki>
|June
|<nowiki>-3.36</nowiki>
|-
|7+
|<nowiki>-0.00</nowiki>
|July
|<nowiki>-4.32</nowiki>
|-
|
|
|August
|<nowiki>-5.52</nowiki>
|-
|
|
|September
|<nowiki>-4.74</nowiki>
|-
|
|
|October
|<nowiki>-2.24</nowiki>
|-
|
|
|November
|<nowiki>-0.97</nowiki>
|-
|
|
|December
|<nowiki>-0.00</nowiki>
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" |'''''Table 3. Statistics of the difference between true and estimated 24-hour fat % for six regression formulas (current, re-estimated + five steps), each also including preceding steps.'''''
|-
|style="text-align: left;"|'''Regression'''
|'''Std.'''
|'''Min'''
|'''Max'''
|'''Cor'''
|'''b-factor'''
|-
|style="text-align: left;"|Current, re-estimated
|0.2856
|<nowiki>-1.840</nowiki>
|2.224
|0.898
|0.807
|-
|style="text-align: left;"|Non-linearity
|0.2820
|<nowiki>-1.890 </nowiki>
|2.198
|0.901
|0.812
|-
|style="text-align: left;"|Time of sampling
|0.2817
|<nowiki>-1.877 </nowiki>
|2.211
|0.901
|0.813
|-
|style="text-align: left;"|Lactation stage
|0.2803
|<nowiki>-1.883 </nowiki>
|2.196
|0.902
|0.814
|-
|style="text-align: left;"|Parity
|0.2794
|<nowiki>-1.887 </nowiki>
|2.179
|0.903
|0.816
|-
|style="text-align: left;"|Month of sampling
|0.2788
|<nowiki>-1.868 </nowiki>
|2.175
|0.903
|0.817
|}
</center>

Table 3 shows some statistics of the difference between the true and estimated 24-hour fat % based on dataset 2 (validation) of the different regression formulas. Each of the five changes to the regression formula had a (minor) positive effect on either the standard deviation of the difference between the true and estimated 24-hour fat % (Std.), the correlation (Cor) between the two fat %s, the b-factor of the linear regression between the two fat %s or a combination of the these. All changes together reduced the standard deviation with 2.4% from 0.2856 to 0.2788, increased the correlation from 0.898 to 0.903 and increased the b-factor from 0.807 to 0.817.

=== Conclusions ===
The regression formula to estimate the 24-hour fat % based on one milk sample was improved. Improvements were first of all considering non-linearity of the variables by using polynomials for protein % of the milk sample (3rd order), interval before sampling (3rd order), milk amount of sample (3rd order), milk amount of previous milking (3rd order) and interval before the previous milking (2nd order). Secondly, adding the effects of time of sampling (class variable), lactation stage (3rd order polynomial), parity (class variable) and month of sampling (class variable) gave a further reduction of the difference between true and estimated 24-hour fat %. The total reduction in standard deviation of the difference between true and estimated 24-hour fat % is 2.4% (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

== Appendix 3 - A unified Python implementation of standardized 305 day yield calculation methods ==
The ICAR guideline is translated into an open-source Python package that can serve as a reference implementation for 305-day yield calculation. In addition to implementing the methods described in the original guideline (with the exception of the multi-trait method, which will be added in future work), the package incorporates 14 lactation-curve models, including traditional parametric models, Bayesian fitting approaches, and an AI-based model. The package also provides tools to derive biologically relevant lactation characteristics such as time to peak, peak yield, cumulative yield, and persistency. The package is publicly available through PyPI and can be installed directly using pip install lactationcurve (van Leerdam et al., 2026). Extensive documentation was developed alongside the package to improve transparency and reproducibility [https://bovi-analytics.github.io/bovi/lactationcurve.html https://bovi-analytics.github.io/bovi/lactationcurve.html.]

Through a companioning website (https://tools.bovi-analytics.org<nowiki/>/), users can upload milk-recording data in CSV format, fit and visualize the implemented lactation-curve models, and compare different cumulative milk-yield methodologies on both test-day and fully daily-recorded lactations using metrics such as RMSE, Pearson correlation, MAPE, and MAE. Reference datasets are provided to allow organizations to benchmark their own calculations against alternative methodologies. In addition, downloadable PDF reports summarize the results through detailed statistics and scatterplots, both overall and stratified by parity.
</div>
</div>

Section 02 – Cattle Milk Recording

2026-07-22T17:50:46Z

Cmosconi: /* Procedure 1: Computing 24-hour Yields */

= Overview =
<div class="mw-collapsible mw-collapsed">
<div>
== Introduction ==
Information about milk production traits is very important for managing and breeding dairy herds. The milk recording process starts with the collection of animal identification, a calving date of milking cows, the amount of milk given and the date with time or time frame of a day. A milk sample may be taken. The obtained milk sample is analysed for milk constituents. The results of the analysis plus the data about milk yield and time of milking are stored in a database. Subsequently a number of parameters, cumulative yields and indices are calculated and stored in the database and, finally, reported to the farmer

This Section 2 of the ICAR Guidelines focuses on the milk recording process for dairy cattle.

== Scope ==
Figure 1 gives a pictorial summary of the main elements of this guideline.

In summary, this section of the ICAR Guidelines covers the milk recording process from the enrolment of a herd for milk recording, through to the delivery of information which a herd owner can use to assist in a range of decisions.
[[File:Scope of Section 2 - Dairy cattle milk recording..png|thumb|Figure 1. Scope of Section 2 -Dairy cattle milk recording.|center|524x524px]]

Not covered in this section are:
# Standards and guidelines for ICAR approval of milk recording devices. Please consult [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices|Section 11]] for this subject.
# Standards and guidelines for ICAR approval of ID devices. Please consult [[Section 10 – Identification Device Certification|Section 10]] for this subject.
# Standards and guidelines for preparation of milk samples and for quality assurance of milk analysis. Please consult [[Section 12 – Milk Analysis|Section 12]] for this subject.
# Standards and guidelines for in-line milk analysis on the farm. Please consult [[Section 13 – On-farm Milk Analysis|Section 13]] for this subject.

== Enrolment ==

Enrolment of new herds in the recording process should involve an agreement between the farmer and the recording organisation regarding technical and financial questions such as:

# General information about the recording programme itself, i.e.
#* Herd and cow identification.
#* Scope of recorded data, including database setup as required by the user.
#* Scheduling recording.
#* Data capture and processing.
#* Recording methods and intervals.
#* Milk measuring and meters.
#* Sampling and sample transport.
#* Reports (outcomes) and supporting decisions.
# Definition of supervision scheme and other quality assurance and plausibility checking steps.
# Fee structure and invoicing.
# Approval of technicians by milk recording organisations (MROs) so as to give them free access to farms for all recording and supervision actions.

In cases where the owner of the recorded cows or his employees carry out the recording itself, it is up to the organisation to decide upon, and provide for, any necessary training.

== Standard and Guidelines for Milk Recording ==
These standards and guidelines for milk recording are valid for all milking systems, including AMS where applicable.
====General Standards and Guidelines for milk recording====
#ICAR-approved (electronic) milk meters and sampling devices must be used on the recording day (see [https://wiki.icar.org/index.php/Section_11_%E2%80%93_Testing,_Approval_and_Checking_of_Measuring,_Recording_and_Sampling_Devices#Procedure_1:_Procedure_for_Application_for_Testing_of_Measuring,_Recording_and_Sampling_Devices_or_Sensor_Systems Procedure 1 of Section 11 - Guidelines for Testing, Approval and Checking of Milk Recording Devices]). The list of approved milk meters, jars and AMS and automatic milk sampler/tray combinations sampling devices can be found on the [https://www.icar.org/index.php/certifications/icar-certifications-for-milk-meters-for-cow-sheep-goats/ ICAR web page].
#Milk weights are recorded for each milking of the recording period. The measurement may be done using any of the ICAR approved recording devices, or by weighing. The minimum accuracy of the measurement is 0.2 kg.
#Where milk constituents are analysed, the equipment used must meet ICAR standards for accuracy. Please consult [[Section 12 – Milk Analysis|Sections 12]] and [[Section 13 – On-farm Milk Analysis|Section 13]] of the Guidelines for details.
#The accuracy of the equipment used for milk recording and sampling must be checked by an agency approved by the member organisations, on a regular and systematic basis using methods approved by ICAR. The list of methods is given in [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices#Procedure 6: Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices|Procedure 6 of Section 11]] - Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices.
#All analyses of the constituents of a milk sample must be carried out on the same milk sample.
#These samples should ideally represent the 24-hour milking period.
#If milk samples do not represent a 24-hour period, the results of milk analyses must be corrected to a 24-hour period by a method approved by ICAR (see [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]).
#In cases where the duration of recording deviates from 24 hours, the results must be converted into 24-hour yields. Only approved 24-hour yield calculation methods can be used. The appropriate methodology is described in [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]
#As date of recording, we recommend to use the date on which the last sample was taken. As alternative, the date of the first sample can be used.
#Calculation methods
##The quantities of milk and milk constituents shall be calculated according to one of the methods outlined in this section of the ICAR Guidelines (see [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Standard methods for calculating 24 hour yields]).
##Member organisations should keep the ICAR Secretariat informed about the calculation methods being used by the records processing operations in their organisation or country and shall be responsible for ensuring that the records are corrected and calculated as specified in this section of the ICAR Guidelines.
====Standards and Guidelines for milk recording using AMS====
This subsection covers systems where milk weights, milk quality or other traits of the cows are monitored constantly and automatically. This can be done in both automatic and manually operated milking systems.

Requirements:
*Animal identification is automatic and reliable. Farm transponders can also be used for automatic identification if they are linked to the cow’s official identification in farm software.
*All individual milkings must be recorded from all AMSs in the farm and transmitted to the recording database for calculation, interrupted milkings included.
*For official milk recording purposes, the data file obtained from electronic milk meters must contain the following: 1) Cow ID, 2) Milking time stamp, 3) Milk weight and 4) Sampling stamp to mark the milking where the sample comes from.
*All milkings within the recording period may be sampled, and in this case the samples should be analysed separately. Alternatively, a one-milking sample can be taken for each cow, followed by fat correction calculation.
*All cows in milk on the recording day have to be sampled. The sampling device must remain in operation until all cows are sampled. When the number of available sampling devices is smaller than the number of AMS units, sampling may need to be prolonged beyond one day to allow complete sampling of all cows. In that case, the sampling device has to be moved between AMS units.
*During sampling, the automatic sampler must be monitored to make sure there are vials left for the next cows.
*24-hour yield calculations must be carried out by a MRO, independently of the AMS manufacturer. This is done in order to guarantee harmonisation of calculation methods between the different brands of equipment and software.
*Data of all milkings over a given time period must be collected for the 24-hour milk yield calculation. A 96-hour data collection period is recommended.
Recommendations:
#Ideally, data of all milkings should be collected and used to compute lactation yield.
#Description of formats to exchange data recorded by an AMS can be requested from the manufacturer or the ICAR ADE data exchange standard for milking data can be used.
#In the case of milk recording method B (see [[Section 02 – Cattle Milk Recording#Recording|chapter 1.4 "Recording]]") with AMS, the milk recording organization should make sure that the farmer knows how to load or transfer data.
#Data can be extracted by: 1) manual operation by MRO Technician’s or Farmer (file extraction), 2) automated system and data transfer through an Application Programming Interface (API), 3) another data transfer and exchange system.
#Raw milk recording data from the AMS must be easily accessible for MRO data processing.
#For official milk recording purposes, the data file obtained from electronic milk meters may also contain the following: 1) Vial ID (this is obligatory with M sampling scheme), 2) Milking duration, 3) Milking speed, 4) Incomplete milking in automatic milking systems and 5) Other relevant data measured or reported by the equipment.
#Individual milkings should be tested for milk secretion rate in order to detect interrupted and unrecorded milkings, which in turn have an effect on the calculated 24-hour yields. If there is an interrupted milking or a milking that follows an interrupted milking at the beginning of the recording period, these two milkings must be excluded from the calculations. During the recording period they can be excluded but do not need to be.
#It is recommended to individually sample all milkings within the 24-hour recording period for 24-hour fat content calculation due to the high variability of milking frequency and milk fat content. In cases where sampling all milkings is not possible, please consult Chapter 2 of [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 - Computing 24-hour Yields] (for approved correction calculation methods).
#It is recommended to sample only milkings with a preceding interval longer than 4 hours.
====Authorisation to record====
It is recommended that professional milk recording technicians are trained and certified before they carry out recordings on their own. Ideally, such training includes a period of supervised work with a certified technician. Where such a certification system is in place, it is not allowed to record without an authorisation.

It is also recommended that frequent training is given to milk recording technicians on new technologies and equipment, safety instructions and data quality issues.

In B and C recording, farmers or their employees doing the practical recording need to be capable of operating the recording equipment correctly (e.g. milk meters, data capture tools) and are familiar with recording techniques.

It is recommended to have a conformation test from a certified recording agency and that frequent training take place.
====Cows to be recorded====
In a recorded herd, all milk-producing cows must be recorded. If a herd is divided into groups, all animals in the group have to be recorded on the same recording scheme. If different recording schemes are practiced on the farm all cows must be recorded according to the standards for recording and sampling intervals in table 3.

Acceptable reasons for missing data are discussed below, in 5.5. Missing results and/or abnormal intervals are reported [[Section 02 – Cattle Milk Recording#Missing results|here]].

===Identification (ID)===
====Herd ID====
Each herd in milk recording must be allocated a unique permanent identification number.
====Animal ID====
An official milk recording system must be based on a clearly identifiable and unique animal ID. It is recommended that one identification scheme for the whole country is used. Animal identification must also be in accordance with national and international regulation (e.g. EU member countries with EU legislation - 1760/2000 for cattle), and with relevant parts of currently valid ICAR Guidelines. The animal must be marked with an ICAR approved identification device or system. If the ID of imported animals is changed, the connection to the original ID must be maintained. Management numbers for cows can be used aside the official ID.
====Identification of the sample vial====
The sample, the milk weight and the cow ID must be linked at the milking.

Vials can be identified according to:
#Vial placement in the sampling unit.
#Cow or sample ID written on the vials.
#Barcoded vial with printed cow ID.
#Barcoded vial with cow ID registered at the milking.
#RFID vial with cow ID registered at the milking.
=====Sample identification without electronic equipment=====
Samples are identified according to their placement in the sampling unit. Additionally, sample or cow numbers can be written on the vials with a waterproof marker. If this marking is not done, there must be a sure and efficient way to identify sample No. 1 (e.g. different colour) and the sequence of other samples.

Each sampling unit must be connected to a list of samples where cow ID is given for each sample. Each transportation box also has to carry the relevant herd ID’s and, preferably, the sampling dates.
=====Barcoded vials=====
Samples are identified according to the barcode on the vial label.

If the label contains cow and/or herd ID, no electronic equipment is needed at the recording. The samples can be sent to the laboratory without accompanying sample lists or herd ID markings on the box.

If the label contains a random sample ID number, the cow ID must be connected with it on the farm. This is done with a barcode reader and computer programmes making the connection possible.
=====Vials with RFID=====
Samples are identified according to the RFID chip in the vial. This system requires the use of RFID readers and specific computer programmes creating a file where the cow and vial ID’s are connected.
=====Automatic sampling systems=====
In automatic milking systems (AMS), ICAR approved automatic samplers have to be used. Sample identification in these systems can be based on vial placement, barcode or RFID. The file with corresponding cow ID is in the management programme of the milking system. Data transfer is carried out with specific software and via a specific interface from the AMS to the MRO.
=====Sample ID in the laboratory=====
For impartiality and better quality, it is recommended that the samples are identified without cow ID and sent to the laboratory anonymously and the analysis results are merged afterwards in the data processing centre.
====Connection of the sample to milking and 24 h yield====
=====Sample and milk weight from the same milking=====
The ideal situation is that the sample and milk weight represent the same milking.
=====Sample from one milking, milk weight from two=====
A corrected analysis is routinely attached to the 24-hour yield.
=====Sample from one milking, milk weight from two or more, corrected by intervals=====
In this case, a 24-hour-yield is also combined with a one-milking sample, but the 24‑hour yield is obtained by correcting the recorded milkings according to the length of the preceding milking intervals. For example, if a cow has produced 20 kg milk in two milkings and the preceding intervals total 20 hours, her 24-hour yield is calculated as 20 kg * (24 h/20 h) = 24 kg. A corrected analysis is attached to this 24‑hour yield.
=====Sample from one milking or day, milk weight from several days=====
With electronic milk meters, it is possible to use the milk production from several days. This gives better accuracy of milk yield estimation; the highest accuracy with uncorrected milk weights is reached using a 4-day average. The problem is that the sample results become disconnected from the milk yield and a loss in fat and protein yield accuracy will occur. Ideally, fat and protein production should be connected to the recording day even in AMS.

In this case, there are three options to connect samples to the 24-hour yield:
#Milk weight is estimated from a longer measurement period but for fat and protein yield estimation only the milk yield on sampling day is used.
#Information only from the recording day for constituents in milk and milk yield estimation.
#Combination of multiple day milk yield with constituents from sampling. See ICAR procedures for using data from more than one day (Lazenby ''et al''., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>, estimation of fat and protein yield (Galesloot and Peeters , 2000)<ref name=":1">Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>.
The analysis data are merged with milk weights in the laboratory or data processing centre and the date of the analysis must be known.

=== Traits to be recorded ===

==== Definition of milking speed and box time ====

===== Introduction =====
Automated Milking Systems (AMS) do measure many traits. The definition of these traits might be different per brand of AMS. Data of these traits is often used by e.g. milk recording organisations, herdbooks or management software providers. When organisations store these data in their databases and use for certain services, it is important to know how these traits are defined.

These definitions could be used by milk recording organisations etc. to take into account differences between traits measured by different brands of AMS. These definitions could also be used by manufacturers of AMS to take into account for product development, to get more alignment in trait definitions between different brands of AMS.

Aim of this document is to propose a harmonized definition of some traits measured by AMS.

At this stage, the traits milking speed and box time are taken into account. Traits related to teat coordinates are described in Section 5 (Conformatoin Recording) of the ICAR guidelines.

==== Average milking speed ====
Definition = AverageMilkingSpeed (gr/min) = {TotalMilkYield / TotalMilkingTime}

* Total milk yield (kg) = Sum of all quarter level milk yields (kg)
* Total milking time = Last Take-off time (of any teat) - Begin of milk flow (of any teat)

Recommendations for manufacturers:

* Exclude any pre-treatment time from milking time.
* Provide take-off settings (threshold in gr/min at take-off, user-defined or default) and settings for the beginning of the measurement period, as milking time will be influenced by take-off settings and by the definition of the beginning of the milk flow.

Recommendations for data users:

* Don't report milking sessions with kick-off´s, interrupted and re-attached milkings because milking time will vary for these milkings.

==== Box time ====
Different types of box time:

* Milking
* Feed-only
* Pass-through
* Selection
* Training

Definition = {End box time - Begin box time} (HH:MM:SS)

* Begin box time = datetime of recognition of animal
* End box time = datetime when cow has exited the box (which might be different from opening of the gate), best to detect when cow has actually left the box

Additional data is needed to understand the status and completeness of the milking visit (Wethal and Heringstad, 2019). Registered issues during the milking are e.g.

* ff: at least 1 teat cup kicked off
* TeatNotFound: unable to find at least 1 of the teats for milking
* IncompleteMilking/FailedMilking: Minimum of 1 teat was registered as incompletely milked.
* The expected milk yield for a milking session depends on previous milkings. Settings like yield less than 80% of expectation for a teat, the milking session would be recorded as having an incompletely milked teat.
* Manual interaction like teat manually attached or milking finished manually.

Recommendations for manufacturers:

* Make the codes available that express if a milking was successful and the cause if the milking was not successful.
* Uniform names and definitions for interrupted, incomplete or failed milkings as well.

Recommendations for data users:

* Check the availability of a code that expresses if a milking was successful and the cause if the milking was not successful. The meaning of the code can be used to consider if the box time record has to be used for the intended purpose or not.
* To check if there is any extra box time due to feeding concentrates, e.g. through user specific settings such as 'PriorityFeeding'.

=== Traits to be recorded ===
In official milk recording, the following data have to be recorded, wherever available:

# Identification of each cow in the herd, even if they remain in the herd for a very short time.
# Birth date, sex, breed and parents of each animal when known.
# All services and embryo flushings and transfers: date, recipient, sire, dam of the embryo.
# All animal deaths and movements between farms and owners.
# Recording dates and locations.
# Milk yields for each cow and recording date.
# Fat content in milk for each cow and sampling date.

It is recommended to record also the following:

# Protein content in milk for each cow and sampling date.
# Milk somatic cell count for each cow and sampling date.
# Other results obtained from milk analysis.
# Milking duration and milking speed where possible.
# Milking times during recording.
# Recording methods and respective symbols used in records.
# Information about cow during the rearing period.

=== Recording method ===
The recording method for the herd consists of using five different symbols for:

# Responsibility for the practical recording.
# Sampling scheme.
# Recording interval.
# Sampling interval (if different from the above).
# Number of milkings per day (especially any deviation from 2x milking).

The symbols in Table 2 should be used:<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Symbols for milk recording schemes.''
|- style="background-color:#efefef; text-align:center;"

|'''Responsibility for recording'''
|'''Sampling scheme'''
|'''Recording interval (weeks)'''
|'''Sampling interval (weeks)'''
|'''Number of milkings per day'''
|-
| style="text-align:center;" | A
| style="text-align:center;" | P
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | B
| style="text-align:center;" | E
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | C
| style="text-align:center;" | Z
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" |
| style="text-align:center;" | T
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" |
| style="text-align:center;" | M
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:center;" | R x
|-
| style="text-align:center;" |
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | S x
|}
</center>

As an example: Recording method is CP36, 2x means that this is a recording where records/ samples are taken partly by the owner (farmer), and partly by a technician from the MRO, where the recording frequency is every 3 weeks, where the sampling frequency is every 6 weeks, and where the number of milkings per day is 2. If a national nomenclature system is used, it should be possible to transfer this system into ICAR nomenclature.

The reference milk recording method is by a representative of the recording organisation, measuring and sampling every four weeks, with proportional sampling and two milkings per day (AP44, 2x).

Recording other than by the reference method must be indicated using the appropriate symbols.

It is recommended that a limit is set for changing the recording method e.g. so that normally it is only possible to change the method twice per year.

It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

In the next sections the symbols are explained:
====Responsibility for the recording====
This symbol indicates who is responsible for measuring the milk yields and taking samples in the herd.
#Representative of the MRO (Method A; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Farmer or his/her representative (Method B; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Mixed responsibility (Method C; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
====ICAR Standards for sampling schemes====
=====Proportional sampling (P)=====
Samples and milk weights are taken at each milking during the recording day. The sampled amount corresponds to the milk yield of each milking. This is achieved by the use of a pipette in equal number of pipetting at each milking or of a specially designed tool which ensures proportional sampling to create one mixed sample. This is the default sampling scheme with no necessary correction to the analysis results, all other schemes must be reported.
=====Equal measure sampling (E)=====
Samples and milk weights are taken at each milking during the recording day. The amount of the sample is measured to be equal at each milking and mixed into one sample. The analysis results for fat should be corrected if one of the milking intervals is shorter than 10 or longer than 14 hours.
=====Multiple sampling (M)=====
Samples are taken at more than one milking during the recording day while milk weights are taken at each milking or over several days. Samples from different milkings are not mixed but they are kept in distinct vials so that each cow has at least two samples. The analysis results must be corrected to correspond to the 24-hour fat and protein yields. For example: a cow is milked 3x during 24 hours and 2 or 3 separate samples are taken, kept and analysed in different vials. This is the gold standard for AMS. It produces the most accurate results but is more expensive.
=====One-milking sampling with milk weights from more than one milking (Z)=====
Samples are taken from one milking during the recording day while milk weights are taken at each milking or over several days. The analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Alternated one-milking recording (T)=====
Samples and milk weights are taken during one milking, alternating between morning and evening milkings. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Constant one-milking recording (C)=====
Samples and milk weights are taken during one milking, constantly during morning or evening milking. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====In-line analysis recording (I)=====
Milk is not sampled but its constituents are continuously analysed by a stationary analyser.
====ICAR Standards for recording and sampling intervals====

<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Standards for recording and sampling intervals.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| rowspan="2" style="text-align:center;" |'''Recording or sampling interval (weeks)'''
| rowspan="2" style="text-align:center;" |'''Minimum number of recordings or samplings per year'''
| colspan="2" style="text-align:center;" |'''Interval between recordings or samplings (days)'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| rowspan="10" style="text-align:center;" |Reference method
| style="text-align:center;" |1
| style="text-align:center;" |44
| style="text-align:center;" |4
| style="text-align:center;" |10
|-
| style="text-align:center;" |2
| style="text-align:center;" |22
| style="text-align:center;" |10
| style="text-align:center;" |18
|-
| style="text-align:center;" |3
| style="text-align:center;" |15
| style="text-align:center;" |16
| style="text-align:center;" |26
|-
| style="text-align:center;" |4
| style="text-align:center;" |11
| style="text-align:center;" |22
| style="text-align:center;" |37
|-
| style="text-align:center;" |5
| style="text-align:center;" |9
| style="text-align:center;" |32
| style="text-align:center;" |46
|-
| style="text-align:center;" |6
| style="text-align:center;" |8
| style="text-align:center;" |38
| style="text-align:center;" |53
|-
| style="text-align:center;" |7
| style="text-align:center;" |7
| style="text-align:center;" |44
| style="text-align:center;" |60
|-
| style="text-align:center;" |8
| style="text-align:center;" |6
| style="text-align:center;" |50
| style="text-align:center;" |70
|-
| style="text-align:center;" |9
| style="text-align:center;" |5
| style="text-align:center;" |55
| style="text-align:center;" |75
|-
| style="text-align:center;" |Daily
| style="text-align:center;" |310
| style="text-align:center;" |1
| style="text-align:center;" |3
|}
</center>

====ICAR standards for number of milkings per day====

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 3. Symbols for number of milkings per day.''
|- style="background-color:#efefef; text-align:center;"
|'''Number of milkings per day'''
|'''Symbol'''
|-
| style="text-align:center;" | Once per day milking
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | Two milkings
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | Three milkings
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" | Four milkings
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" | Continuous milking (e.g. AMS)
| style="text-align:center;" | R x
|-
| style="text-align:center;" | Regular milkings not at the same times on each day (e.g. 10 milkings per week)
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" | Shown as the average number of milkings per day.
| style="text-align:center;" |
|-
| style="text-align:center;" | Animals that are both milked and suckled. (Number of times milked to prefix the S)
| style="text-align:center;" | S x
|}
</center>

Where a herd is dry for a period of the year, the minimum number of recordings should be adjusted proportionately to the production period.

Minimum number of herd recordings should be at least 85% of the normal number of recordings.

=== Missing results and/or abnormal intervals ===
{{anchor|Missing_results}}A recorded 24-hour yield is the best estimate of the yield and the constituents of the milk, weighed, sampled and recorded within 24 hours on the day of recording.
#When herds are normally milked at intervals such that the recording day is other than 24 hours, the yields shall be adjusted to a 24-hour interval using the following procedure (or other procedures approved by the ICAR):
#*Divide 24 by the interval, then multiply by the yield. For example:
#**For a 25 hour interval (24/25) x 35 kg = 33.6 kg
#**For a 20 hour interval (24/20) x 35 kg = 42.0 kg
#A recording is a set of daily test values for a given animal on a given day of recording, one or some or all of them can be missed (missing values)
#Missing values can be due to:
#*Out of range.
#*Sickness.
#*Disaster.
#*No sample analysis results.
#The number of the official and complete (milk, fat and protein) recordings in the lactation or other accumulated yield should be reported.
#Permitted range of the daily recorded values is given in Table 5. Outside of these ranges, the daily recorded<ref>'''Note:''' High fat breeds have breed average higher than 5.0 for fat %.</ref> value will be considered as a missing value.

<center>
{| class="wikitable"
! colspan="7" style="text-align:left;" | ''Table 5. Permitted range of the daily recorded values.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| colspan="2" style="text-align:center;" |'''Milk (kg)'''
| colspan="2" style="text-align:center;" |'''Fat %'''
| colspan="2" style="text-align:center;" |'''Protein %'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| style="text-align:center;" | Main Dairy Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 1.5
| style="text-align:center;" | 9.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 7.0
|-
| style="text-align:center;" | High Fat1 Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 2.0
| style="text-align:center;" | 12.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 9.0
|}
</center>1Note: High fat breeds have breed average higher than 5.0 for fat %The true daily recorded values collected from animals labelled by the farmer as sick, injured or under treatment must be used in the computation of the lactation record unless the milk yield is less than 50% of the previous milk yield or less than 60% of the predicted yield. In such a case, the whole set of daily recorded values may be considered as missing.

Estimates of the missing values of a daily recording can be computed by using interpolation procedures or by more sophisticated procedures approved by ICAR

== Samples ==

=== Representative sample ===
The milk sample has to represent the complete milking linked to it. This is achieved by mixing the milk thoroughly or pouring it into another vessel right before sampling.

Sampling scheme P requires using a pipette for making the sample proportional between different milkings.

With sampling scheme E, it is advisable to use a measuring cup to make sure the sample parts actually are equal.

Immediately after sampling, the vials have to be preserved, capped, shaken and marked. Samples should be stored cool and dark.

=== Transport ===
Samples should be transported for analysis to a laboratory as soon as possible after sampling.

The samples need to be packed for transport and handled during transport in a manner that guarantees that sample IDs are not compromised or mixed. It is also recommended to protect the packages from external interference.

The packing material must be clean and disposable or easy to clean.

During transportation, it is recommended that the temperature of the samples stays below +10°C.

== Database ==
Storing the recorded data in a milk recording database is an indispensable part of the recording. It is recommended to use the quickest possible means to store the data in the database in order to ensure up-to-date breeding values and management applications. Where computerised data capture is possible, it should not take more than five days after the recording to have the complete recording data set in the database.

The application of the Guidelines in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield], together with other parts of the Guidelines, ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

The guidelines on storage of data collected by the milk recording process are:

# For every recording, cow identification (ID), 24-hour milk yield or individual milk yields with a minimum of 0.2 kg (or the equivalent thereof) milk accuracy and recording date have to be stored.
# Where possible, it is advisable to store each milking separately. The data stored can include milk yield, time and date of milking, and milking scheme.
# Analysed results of the milk sample are stored, namely: sample ID, fat content (or percentage), sample status, sample type. Optional data can be stored on protein and/or lactose content, somatic cell count and additional analyses.
# Analysis results can be linked to one or more milkings of the cow.
# In case of storage or performance problems it might be necessary to remove old data of individual cow milkings from the database.
# Recording day information is the yield over 24 hours and should at least be kept in the database for the current lactation and the previous lactation.
# If recording day information is changed after batch processing it should be marked with a user-ID and time stamp.
# Yields are stored in kg or lbs or, in the case of fat and protein contents, in percent units.

The necessary additional information about how the results have been obtained include:

# Who did the recording (certified technician, farmer etc.).
# Herd and/or cow milking frequency.
# How many milkings were measured.
# How many milkings were sampled.
# Sampling scheme when sampling.
# Daily yield calculation method used.
# Recording and sampling intervals.
# It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

Basic checks for recording data:

# Farm (herd) ID: identified by a unique key.
# Animal ID: has to be unique in database.
# Format of animal ID: compliant to international standards of identification and registration.
# Recording date: less than or equal to today, greater than last recording date.
# Milk yield: stored with one decimal.
# 24 hour milk yield within range ( Table 5).
# Fat and protein content: e.g. within a range of +/- 3 standard deviation of population average (Table 5).
# Calving date: greater than birthday of cow (e.g. greater than birthday of cow + 20 months).
# Calving date: less than or equal to today.
# Sample analysis

This section of the ICAR Guidelines examines how observations are performed on farms and how data are collected, analysed and reported back to farmers. It forms an integral part with other sections of the ICAR Guidelines. It ensures that samples are analysed to the relevant degree of accuracy for the purposes of milk recording, breeding value prediction and other areas of usage. ICAR members operate in a range of situations, ranging from places with almost fully automated recording systems to areas with no roads and electricity. Therefore, the guidelines only demand standards that can be followed, irrespective of production situations and recommend more advanced options, where possible or required. Under the guidelines some practices might not be permitted while other practices are tolerated but not recommended.

== Yield calculations ==
This section covers 24-hour yields and accumulated yields for milk, fat, protein and somatic cells. It also describes the procedure for acceptance of new methods not previously mentioned in the guidelines.

The basic requirements for all calculation methods are that rounding shall only take place at the last step of the computation.

=== Lactation period ===

==== Commencement of the lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, is considered to commence is:

# The day that the cow calves (calving date), or
# In the absence of a calving date, the best estimate of the day that the cow commenced milk production.

A (valid) calving is defined as a parturition taking place:

# After the mid-point of the gestation period if a service has been recorded, or,
# After at least 75% of the normal gestation period has elapsed since the previous calving recorded if no service event has been recorded.

Any parturition falling outside the above definition shall be recorded as an abortion and shall not start a new lactation period.

For cows of dairy breeds the normal gestation length shall be deemed to be 280 days unless more specific breed information is available for use.

If the first recording is done on the calving date or within the first 4 days after calving, the milk yield and constituents at the first recording should not form part of the official lactation record, especially for automated milking systems (AMS) with multiple recorded days.

==== Completion of lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, has been completed is or:

# The day that the cow ceases to give milk (goes dry) or
# The day the cow gives less than 3.0 kg/day or 1.0 kg/milking in a recording (unless recorded sick) or
# When it is common practice not to record the dry-off date, the day of the midpoint between the last recording with the cow in milk and the first recording day with the animal dry may be assumed to be the dry-off date.

The lactation period ends on whichever date above occurs first.

Cows may be recorded as absent or sick on the recording day, without the lactation period being defined as terminated.

=== Production period ===
In the case where yield records are calculated on the basis of a period of production, usually a year, the record should be expressed as a ‘production period record‘ (symbol PP).

The production period begins the day after the end of the previous production period and ends as defined by the length (in days) of the production period.

=== Additional notes ===
For any ICAR method the interval between two consecutive recordings must routinely fulfil the value for the acceptable range on the herd level.

If the first recording occurs within 14 days from calving, then no adjustment is required to the first recorded value when computing the accumulated record. If the first recording occurs 15 to 95 days from calving, then an adjustment procedure may be applied.

If the 305th day of a lactation falls before the last recording, the interpolation method should be used also for the last period to compute the yields.

=== Standard methods for calculating 24 hour yields ===
The ICAR approved methods are presented in '''[https://www.icar.org/Guidelines/02-Procedure-1-Computing-24-Hour-Yield.pdf Procedure 1 of Section 2]'''. They include:

1. Methods for calculating daily yields from AM/PM milkings:

# Method of Delorenzo and Wiggans (1986)<ref>Delorenzo, M.A., and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. [https://www.journalofdairyscience.org/article/S0022-0302(86)80678-6/pdf J Dairy Sci 69; 2386]</ref>
# Method of Liu et al. (2019). Please note that in 2022 the method of Liu et al. (2000)<ref name=":0">Liu, Z., R. Reents, F. Reinhardt and K. Kuwan. 2000. Approaches to Estimating Daily Yield from Single Milk Testing Schemes and Use of a.m.-p.m. Records in Test-Day Model Genetic Evaluation in Dairy Cattle. [https://www.journalofdairyscience.org/article/S0022-0302(00)75161-7/pdf J. Dairy Sci. 83:2672-2682].</ref> has been updated to the method of Liu et al. (2019). We recommend to organisations that currently have implemented the method of Liu et al. (2000)<ref name=":0" /> to update to method of Liu et al. (2019).
# Method of Kyntäjä et al. (2021)<ref name=":3">1. Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. [https://www.icar.org/Documents/technical_series/ICAR-Technical-Series-no-25-Virtual-Meeting/Kyntaja.pdf ICAR Technical Series no. 25: 171-175.]</ref>

2. Methods to estimate 24h yield from Automatic Milking Systems:

# Using data on more than one day (Lazenby et al., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Using data on 1 day (Bouloc et al., 2002)<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Estimation of fat and protein yield (Galesloot and Peeters, 2000)<ref>Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>
# Sampling period (Hand et al., 2004<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D.F. 2004. Comparison of Protocols to Estimate 24 Hour Percent Fat and Protein. Presented at 34th ICAR session, Sousse, Tunisia, June, 2004. Proceedings of the 34th ICAR Meeting EAAP Publication No. 113:219-224</ref>; Bouloc et al., 2004)

3. Standard methods to estimate 24h yield from electronic milk meters:

# Estimation of 24-hour milk yield
# Using data on more than one day (Hand et al., 2006)<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. [https://doi.org/10.3168/jds.S0022-0302(06)72240-8 J. Dairy Sci. 89:1723-1726]</ref>
# Estimation of 24-hour fat and protein yield

=== Standard methods for calculating accumulated yields ===
The ICAR approved methods are presented in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_2_%E2%80%93_Computing_of_Accumulated_Lactation_Yield Procedure 2 of Section 2]. They include:

# Test Interval Method (TIM) (Sargent, 1968)<ref>Sargent, F.D., V.H. Lyton, and O.G. Wall, Jr . 1968. Test interval method of calculating Dairy Herd Improvement Association records. [https://doi.org/10.3168/jds.S0022-0302(68)86943-7 J. Dairy Sci. 51:170].</ref>
# Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987)<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. [https://doi.org/10.1016/0301-6226(87)90049-2 Livest. Prod. Sci. 17:l].</ref>
# Best prediction (VanRaden, 1997)<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. [https://doi.org/10.3168/jds.S0022-0302(97)76268-4 J. Dairy Sci. 80:3015-3022].</ref>
# Multiple-Trait Procedure (MTP) (Schaeffer and Jamrozik, 1996)<ref>Schaeffer, L.R. and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. [https://doi.org/10.3168/jds.S0022-0302(96)76578-5 J. Dairy Sci. 79:2044-2055.]</ref>

=== Procedure to approve new methods ===

# All parties interested in seeking approval for any new accumulated yield calculation method will notify the ICAR Secretariat and provide a description of the proposed method.
# These parties will provide a detailed report including statistical details, scientific references and other relevant data to the ICAR Dairy Cattle Milk Recording Working Group.
# The ICAR Dairy Cattle Milk Recording Working Group will then consider the proposal and recommend that it be conditionally approved, approved or rejected.
# The final steps will consist of approval by the General Assembly and publication in the guidelines. .

== Reporting ==
This subsection covers reports, data files, statistics and calculated key figures provided to farmers for breeding and management purposes.

It is recommended that farmers are given reports after each recording and at the end of the recording year or another longer recording period. These reports should contain data on both cow and herd level. In bigger herds, it is also advisable to present results by management groups or otherwise chosen cow groups within the herd. The reporting may be done on paper, through web pages and/or in the form of data files or electronic reports.

Where data files are distributed or direct access given to the results in the database, care must be taken that data ownership is clearly defined. This also includes defining who has access to data and how this access can be authorised.

ICAR members are advised to prepare annual statistics in a reasonable timeframe after closing the recording year. The minimum data requirements are what is needed for the ICAR [https://my.icar.org/stats/list Dairy Cattle Yearly Enquiry on-line database].

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 5. Examples of key figures for herd to be used by farmers and other users.''
|- style="background-color:#efefef; text-align:center;"
|style="text-align:left |'''Key figure'''
|style="text-align:left |'''Explanation'''
|-
| style="text-align:left;" | 12-month rolling average yield
| style="text-align:center;" | Total milk, fat and protein produced during the 365 (366) days preceding the recording divided by the average number of cows for the same period.
|-
| style="text-align:left;" | Average 305-day yield
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations finished during the reporting period divided with the number of finished 305-day lactations.
|-
| style="text-align:left;" | Average 305-day yield within a period
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations during the reporting period divided with the average number of cows on a 305-day lactation within the reporting period.
|-
| style="text-align:left;" | Average annual yield
| style="text-align:center;" | Total milk, fat and protein produced during the recording year divided by the average number of cows for the same recording year.
|-
| style="text-align:left;" | Average calving interval
| style="text-align:center;" | The average preceding intervals of all calvings second and more during the reporting period.
|-
| style="text-align:left;" | Average fat, protein or lactose contents in milk
| style="text-align:center;" | Total fat, protein and lactose yields divided by the total milk yield, usually expressed with two decimals.
|-
| style="text-align:left;" | Average lactation yield
| style="text-align:center;" | Total milk, fat and protein produced within lactations of any length finished during the reporting period divided with the number of finished lactations.
|-
| style="text-align:left;" | Average lactation yield within a period
| style="text-align:center;" | Total milk, fat and protein produced during the reporting period divided with the average number of cows in milk within the reporting period.
|-
| style="text-align:left;" | Average number of cows
| style="text-align:center;" | Average number of cows in the herd (or group) on a given day during the reporting period. Usually expressed with one decimal.
|-
| style="text-align:left;" | Average somatic cell count
| style="text-align:center;" | The average of all individual cow somatic cell counts weighted for individual milk yields.
|-
| style="text-align:left;" | Daily milk, fat and protein yields
| style="text-align:center;" | 1) Total daily milk, fat and protein yields divided by number of cows, or 2) Total daily milk, fat and protein yields divided by number of cows in milk.
|-
| style="text-align:left;" | Energy Corrected Milk (ECM)
| style="text-align:center;" | Calculated according to a national standard.
Example from the Nordic countries:

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + milk yield, kg * 0.7832)/3.14

or, if lactose has been analysed

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + lactose yield * 16.54 + milk yield, kg * 0.0207)/3.14.

From solids expressed as %:

ECM = [(fat content, % * 383 + protein content, % * 242 + 783.2)/3140]* milk yield, kg

or, if lactose has been analysed

ECM = [(fat content, % * 383 + protein content, % * 242 + lactose content, % * 165.4 + 20.7)/3140]* milk yield, kg.
|-
| style="text-align:left;" | Number of lactations
| style="text-align:center;" | Total number of finished lactations in the herd (or group) during the reporting period.
|-
| style="text-align:left;" | Reporting period
| style="text-align:center;" | The period presented in the given report. The most usual options are: one day, one recording interval, lactation, rolling 365 days, recording or calendar year, and the cow’s lifetime.
|}
</center>

== Decisions ==

As a result of the recording process and reports prepared on the basis of its results, decisions can be made on one or more of the following:

=== Short term impact: day-to-day management decisions taken on farms ===

# Decisions about bulk milk quality.
# Feeding decisions - daily diet based on group or individual performance.
# Pasture management decisions.
# Grouping decisions - placing cows in different management or feeding groups.
# Culling decisions - decisions on the sale or slaughter of cattle.
# Mating decisions.
# Decisions regarding programmes of certification for milk and milk products.
# Decisions based on data flow from MRO’s to farms and vice versa.

=== Medium-term impact ===

# Farmers’ decisions based on advisory services, veterinarians, independent experts and other services.
# Decisions about production planning on farms (herd development).

=== Long-term impact ===
# Breeding programme and selection decisions - breeding partners informed by genetic evaluation ([[Section 09 – Dairy Cattle Genetic Evaluation|Section 9)]] based on milk recording results.
# Decisions based on herd book and breeder association activities and deciding on business actions related to breeding animals, i.e. in some countries animal recording data are required for international trade with breeding animals.

=== Strategic decisions ===
# Research programmes concerning management, recording and breeding.
# Political decisions about possible subsidies in dairy cattle breeding at the governmental level and implementing measurements according to agriculture policy.

== Quality control ==
This Section together with other parts of the Guidelines ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

=== Bulk tank data comparison ===
It is a recommended practice to compare milk recording data with dairy deliveries and bulk tank milk contents. This can be done on the recording day or over a longer period of time. The calculation is done as follows:

# Comparison ratio = Total recorded milk yield, kg /Total milk produced, kg. This comparison is used where there is a reliable estimate of the farm use of milk.
# Quick comparison ratio = Total recorded milk yield, kg/ Total milk delivered, kg. This comparison is used where farm use of milk is not estimated.
# Content comparison = Recorded average fat / Bulk tank average fat
# Comparison ratio for fat = Total recorded fat yield, kg/ Total fat produced, kg
# Total recorded milk yield, kg = Ʃ (Individual milk yield, kg)
# Total milk delivered, kg = Total milk delivered, litres * milk density kg/litre
# Total milk produced, kg = (Total milk delivered, litres + Milk used or discarded on the farm, litres) * milk density kg/litre
# Total fat produced, kg = Total milk produced, kg x (Bulk tank fat percent/100)
# Recorded average fat = Ʃ [Individual milk yield kg x (Individual fat percent/100)]/Ʃ (Individual milk yield, kg)

The recommended acceptable range for comparison ratios is 0.95 - 1.05, and for quick comparison ratios 0.90 - 1.00, with due regard to herd size.

=== One day bulk tank data comparison ===
Milk yields and fat yields or contents are compared on the recording day. Comparing the contents is routinely possible where every delivery is sampled or by taking a bulk tank sample (see point [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Bulk_tank_data_comparison 1.10] above for how the comparison is done.)

=== Bulk tank data comparison over a longer period ===
Milk yields and fat yields or contents are compared over a longer period of time, e.g. 4 months or 12 months. This option requires a routine to obtain the applicable data from the dairies or milk buyers. Farm use of milk may be taken into account where applicable.

=== Bulk tank sample ===
Bulk tank samples can be used to verify the milk contents analysis obtained in milk recording. A sample is taken from a well-mixed bulk tank on the recording day. It must represent the milk of the whole 24-hour period. Bulk tank fat and protein contents are then compared to the weighted averages of the fat and protein percent obtained from milk recording. Normally, the difference between the values should not be more than 5%.

=== Supervised or repeated recording ===
Supervised recording is a tool designed to verify that individual cow records are reliable. It is based on repeating the herd recording as soon as possible after the original recording, and the obtained results are compared with the original recording. It is obligatory for ICAR Certificate of Quality (CoQ) holders to practice regular supervision, irrespective of recording methods used.

It is recommended that the supervised recording will follow immediately after the original recording, but for a good reason it can be postponed for up to 7 days.

The farmer and any other staff doing the original recording must not know that a supervised recording will follow. The technician who performs the supervised recording should not be the same person who did the original recording.

Usually supervised recording is done by recording the whole herd again, using the same sampling scheme and recording method (or a reference method) as in the previous recording. When herd size exceeds 200 cows, it is also allowed to do a supervised recording to selected, or randomised groups of animals in the herd.

Choosing the herds for supervised recording may be random or based on preselection. Traits for this preselection may include high yield, great increase in yield, presence of bull dams in the herd, and general suspicions about the correctness of herd results.

The traits compared in supervised recording must include milk and fat. Comparing protein is also recommended.

=== Supervision - example of comparison calculations ===

# Milk, fat and protein yields per cow are calculated for both the original and the supervised milking.
# Individual cow records where results between supervised recording and the original recording differ outside the norms might be excused where a good explanation can be given for exclusion (illness, heat, missed milking)
# Deviations (%) are calculated for each cow and yield constituent according to the formula: deviation = (supervised yield/unsupervised yield)*100-100
# Herd averages of the absolute values for each yield constituent are calculated.
# If the supervised recording occurs within 2 days of the original recording, the acceptable difference in herd averages are 7% for milk and protein and 9% for fat.
# If the supervised recording occurs between 3 and 7 days after the original recording, the acceptable difference of the aforementioned herd averages are 9% for milk and protein and 12% for fat.

The limits mentioned in these examples are typically applied by some of the member organisations, and are not meant to be understood as exact norms. Such norms should be laid down by each member organisation.

=== Evaluation of recording data ===
It is recommended that data quality is evaluated for each herd recording day. When such an evaluation is applied, the following features of the data have to be included:

# Person responsible for the recording.
# ICAR approval and calibration status of the recording equipment if owned by the farmer.
# Number of herd recordings per time period and/or recording interval.
# Number of herd samplings per time period and/or sampling interval.

The following features are also recommended to be included if possible:

# Deviation of milk and fat yields from dairy deliveries.
# Deviation of milk and fat yields from previous or predicted yields.
# Standard deviation of individual cow records.
# Number of recorded and/or sampled milkings within the recording day.
# Number of cows missed or not recorded in the recording.
</div>
</div>
= Procedures =
== Procedure 1: Computing 24-hour Yields ==

=== Methods to calculate 24-hour yield for milk yield and fat percentage from a single milking ===

==== Method of Delorenzo & Wiggans (1986)<ref>Delorenzo, M.A. and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. J. Dairy Sci. 69: 2386-2394.</ref> ====
Daily milk (DMY) and fat yield (DFY) estimates are based on measured yield and milking frequency. An adjustment factor accounts for differences in the average milking interval (expressed in decimal hours) between the preceding milking and the measured milking, and the time of day of the measured milking (started in a.m. or p.m.). For 2X milking, an additional adjustment is applied to milk yield for the interaction between milking interval and stage of lactation, with mid lactation (158 DIM) set to zero. Milking interval does not affect protein and solids non fat (SNF) percentages and so the percentages for the sampled milking are used for test-day estimates. Protein yield is calculated from the measured percentage and the adjusted milk yield.

The prediction of DMY and DFY from single milking on morning or evening in herds milked twice a day requires factors, that are the reciprocal of the proportion of total yield expected from single milkings in relation to the milking interval.

We propose to derive these coefficients (intercept, slope, etc.) for each country separately.

===== Adjustment of milking interval =====
The milking interval is the interval between milking time for the observed milking and the milking time preceding the observed milking. The milking interval is divided into 15-minutes classes. Factors for milk and fat yields may be calculated to each class using Equation 1:

''Equation 1. Factors for milk and fat yields.''
[[File:Equation 1.png|none|thumb|397x397px]]

===== Adjustment of lactation stage =====
Because the lactation stage of the cow has an influence on the effect of different milking intervals on milk production a second adjustment is made for every interval class through a covariate of days in milk as addition:

Covariate x (days in milk - 158)

===== Estimating sample day yields =====
Formulas for prediction sample day yields and percentages in herds with two milkings are:

''Equation 2. Equation for predicting 24-hour milk yield.''
[[File:Equation2.png|none|thumb|428x428px]]

''Equation 3. Equation for predicting 24-hour fat percentage.''
[[File:Equation3.png|none|thumb|431x431px]]

''Equation 4. Equation for predicting 24-hour fat yield.''
[[File:Equation4.png|none|thumb]]

''Equation 5. Equation for predicting 24-hour protein yield.''
[[File:Equation5.png|none|thumb|316x316px]]

===== Calculation examples =====

====== Practical Application ======
Two sets of factors are available for estimating DMY from a single milking, each for morning or evening milking sampling. The factors are calculated from the formula as described above and given in Table 1.
<center>
{| class="wikitable"
| colspan="5" align="left" |'''''Table 1. Factor of milk yield and covariate for herds milked twice a day.'''''
|- style="background-color:#efefef;"
| rowspan="2" align="center" |'''Length of milking interval in hours (minutes in decimal)'''
| colspan="2" align="center" |'''Morning milking'''
| colspan="2" align="center" |'''Evening milking'''
|- style="background-color:#efefef;"
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
|-
| align="center" |< 9.00
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.594
| align="center" |0.00378
|-
| align="center" |9.00-9.24
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.534
| align="center" |0.00485
|-
| align="center" |9.25-9.49
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.477
| align="center" |0.00486
|-
| align="center" |9.50-9.74
| align="center" |2.411
| align="center" |0.00716
| align="center" |2.423
| align="center" |0.00511
|-
| align="center" |9.75-9.99
| align="center" |2.359
| align="center" |0.00726
| align="center" |2.370
| align="center" |0.00473
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |10.00-10.24
| align="center" |2.310
| align="center" |0.00458
| align="center" |2.321
| align="center" |0.00337
|-
| align="center" |10.25-10.49
| align="center" |2.262
| align="center" |0.00399
| align="center" |2.273
| align="center" |0.00214
|-
| align="center" |10.50-10.74
| align="center" |2.217
| align="center" |0.00294
| align="center" |2.227
| align="center" |0.00000
|-
| align="center" |10.75-10.99
| align="center" |2.173
| align="center" |0.00223
| align="center" |2.183
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |11.00-11.24
| align="center" |2.131
| align="center" |0.00000
| align="center" |2.140
| align="center" |0.00000
|-
| align="center" |11.25-11.49
| align="center" |2.091
| align="center" |0.00000
| align="center" |2.099
| align="center" |0.00000
|-
| align="center" |11.50-11.74
| align="center" |2.052
| align="center" |0.00000
| align="center" |2.060
| align="center" |0.00000
|-
| align="center" |11.75-11.99
| align="center" |2.014
| align="center" |0.00000
| align="center" |2.022
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |12.00
| align="center" |2.000
| align="center" |0.00000
| align="center" |2.000
| align="center" |0.00000
|-
| align="center" |12.01-12.24
| align="center" |1.978
| align="center" |0.00000
| align="center" |1.986
| align="center" |0.00000
|-
| align="center" |12.25-12.49
| align="center" |1.943
| align="center" |0.00000
| align="center" |1.951
| align="center" |0.00000
|-
| align="center" |12.50-12.74
| align="center" |1.910
| align="center" |0.00000
| align="center" |1.917
| align="center" |0.00000
|-
| align="center" |12.75-12.99
| align="center" |1.877
| align="center" |0.00000
| align="center" |1.884
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |13.00-13.24
| align="center" |1.846
| align="center" |0.00000
| align="center" |1.852
| align="center" |-0.00190
|-
| align="center" |13.25-13.49
| align="center" |1.815
| align="center" |0.00000
| align="center" |1.822
| align="center" |-0.00231
|-
| align="center" |13.50-13.74
| align="center" |1.786
| align="center" |-0.00167
| align="center" |1.792
| align="center" |-0.00308
|-
| align="center" |13.75-13.99
| align="center" |1.757
| align="center" |-0.00258
| align="center" |1.763
| align="center" |-0.00339
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |14.00-14.24
| align="center" |1.730
| align="center" |-0.00347
| align="center" |1.736
| align="center" |-0.00509
|-
| align="center" |14.25-14.49
| align="center" |1.703
| align="center" |-0.00363
| align="center" |1.709
| align="center" |-0.00471
|-
| align="center" |14.50-14.74
| align="center" |1.677
| align="center" |-0.00332
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |14.75-14.99
| align="center" |1.652
| align="center" |-0.00316
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |≥ 15.00
| align="center" |1.628
| align="center" |-0.00235
| align="center" |1.683
| align="center" |-0.00454
|}
</center>

For estimating daily fat percentage there is only one table independent of morning or evening sampling – refer to Table 2.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" |'''''Table 2. Factor of fat percentage for herds milked twice a day.'''''
|- style="background-color:#efefef;"
|'''Length of milking'''

'''interval in hours'''
|'''Fat (percentage'''

'''factor)'''
|-
|< 9.00
|0.919
|-
|9.00-9.24
|0.927
|-
|9.25-9.49
|0.934
|-
|9.50-9.74
|0.941
|-
|9.75-9.99
|0.948
|-
|
|
|-
|10.00-10.24
|0.955
|-
|10.25-10.49
|0.961
|-
|10.50-10.74
|0.968
|-
|10.75-10.99
|0.974
|-
|
|
|-
|11.00-11.24
|0.980
|-
|11.25-11.49
|0.986
|-
|11.50-11.74
|0.992
|-
|11.75-11.99
|0.997
|-
|
|
|-
|12.00
|1.000
|-
|12.01-12.24
|1.003
|-
|12.25-12.49
|1.008
|-
|12.50-12.74
|1.013
|-
|12.75-12.99
|1.018
|-
|
|
|-
|13.00-13.24
|1.023
|-
|13.25-13.49
|1.028
|-
|13.50-13.74
|1.033
|-
|13.75-13.99
|1.037
|-
|
|
|-
|14.00-14.24
|1.042
|-
|14.25-14.49
|1.046
|-
|14.50-14.74
|1.050
|-
|14.75-14.99
|1.054
|-
|≥ 15.00
|1.058
|}
</center>

Milking-interval factors are calculated using Equation 1, where the intercept and slope are as in Table 3.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 3. Slope and intercept for milk yield and fat yield.'''''
|- style="background-color:#efefef;"
| rowspan="2" |'''Trait'''
| colspan="2" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started in a.m.'''
|'''For measured milking started in p.m.'''
|-
|Milk yield
|0.0654
|0.0634
|0.0363
|-
|Fat yield
|0.1965
|0.1939
|0.0254
|}
</center>
The milking interval has no significant influence on protein percentage. Therefore, the protein percentage of the sampled milking is used as the daily protein percentage.

====== Calculation of daily yields from morning milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Data for a cow from morning milking.'''''
|-
|Begin of recording:
|6:15
|(Morning milking)
|-
|Start of preceding milking:
|17:25
|
|-
|Length of milking interval:
|12 hours 50 minutes
|(Expressed as decimal 12.83)
|-
|Milk results at morning:
|12,0
|Milk-kg
|-
|
|4,12
|Fat-percentage
|-
|
|3,45
|Protein-percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 5. Factors for morning milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.877
|-
|The covariate is
|0
|-
|The factor for fat percentage from Table 2 is
|1.018
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 6. Example calculations for morning milking.'''''
|-
|The sample-day milk yield:
|1.877 x 12,0 kg + 0 x (120 - 158) = 22,5 kg
|-
|The sample-day fat percentage:
|1.018 x 4,12 = 4,19
|-
|The sample-day fat yield:
|22,5 kg x 0,0419 = 0,94 kg
|-
|The sample-day protein yield:
|22,5 kg x 0,0345 = 0,78 kg
|}
</center>

====== Calculation of daily yields from evening milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 7. Data for a cow from evening milking.'''''
|-
|Begin of recording:
|16:48
|Evening milking
|-
|Start of preceding milking:
|6:35
|
|-
|Length of milking interval:
|13 hours 47 minutes
|Expressed as decimal 13.78
|-
|Milk results at evening:
|14,0
|Milk kg
|-
|
|4,00
|Fat percentage
|-
|
|3,40
|Protein percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 8. Factors for evening milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.763
|-
|The covariate is
|<nowiki>-0,00339</nowiki>
|-
|The factor for fat percentage from Table 2 is
|1.037
|}
{| class="wikitable"
| colspan="2" |'''''Table 9. Example calculations for evening milking.'''''
|-
|The sample-day milk yield:
|1.763 x 14,0 kg - 0,00339 x (120 - 158) = 24,8 kg
|-
|The sample-day fat percentage:
|1.037 x 4,00 = 4,15
|-
|The sample-day fat yield:
|24,8 kg x 0,0415 = 1,03 kg
|-
|The sample-day protein yield:
|24,8 kg x 0,0340 = 0,84 kg
|}
</center>

====== Alternate recording of components and milk yield at both milkings ======
For this plan only the sample-day fat yield has to be calculated with regard to milking interval. The milk yield is the sum of evening and morning milk results.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 10. Example data for a cow from both milkings.'''''
|-
|Begin of recording evening:
|17:25
|
|-
|Milk results at evening:
|10:00
|Milk kg (only milking-yield)
|-
|Begin of recording morning:
|6:15
|
|-
|Milk results at morning:
|12:00
|Milk kg
|-
|
|4:20
|Fat percentage
|-
|
|3:50
|Protein percentage
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 11. Factor for fat percentage.'''''
|-
|Length of milking interval:
|12 hours 50 minutes (expressed

as decimal 12.83)
|-
|The factor for fat percentage from Table 2 is
|1.018.
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 12. Example calculation of daily yields.'''''
|-
|The sample-day milk yield:
|10,0 kg + 12,0 kg = 22,0 kg
|-
|The sample-day fat percentage:
|1.018 x 4,20 = 4,28
|-
|The sample-day fat yield:
|22,0 kg x 0,0428 = 0,94 kg
|-
|The sample-day protein yield:
|22,0 kg x 0,0350 = 0,77 kg
|}
</center>

====== Calculation for 3X Milking ======
For 3X herds, a single milking or two consecutive milkings may be weighed. The sample may be collected at one or both of these milkings. Stage of lactation × milking interval adjustments are not used for greater than 2× milking. These AM/PM factors for estimating daily yields in 3X herds should not be confused with factors that adjust 3X records to a 2X basis. Milking-interval factors are calculated using the same formula with the intercept and slope as in Table 13.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" align = "left" |'''''Table 13. Slope and intercept factors for 3X milking.'''''
|- style="background-color:#efefef;"
| rowspan="2" | '''Trait'''
| colspan="3" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started between 2 a.m. and 9:59 a.m.'''
|'''For measured milking started between 10 a.m. and 5:59 p.m.'''
|'''For measured milking started between 6:00 p.m. and 1:59 a.m.'''
|-
|Milk yield
|0.077
|0.068
|0.066
|0.0329
|-
|Fat yield
|0.186
|0.186
|0.182
|0.0186
|}
</center>
When two milkings are included for sampling, the intercepts and intervals for both milkings are included in determining a factor for calculated estimated milk yield that is applied to the total yield from both milkings as in Equation 6.

''Equation 6. Milking interval factor for 3X milking.''
[[File:Equation6.png|none|thumb|536x536px]]
Milk and fat percent factors are calculated separately based on the number of milkings weighed or sampled.

====== Calculation for 4X - 6X Milking ======
The intercept terms for calculating 3X factors (0.077, 0.068, and 0.066) are multiplied by the factor [3 / (milkings per day)] for use in calculating factors for milking frequencies greater than 3X.

==== Method of Liu et al. (2019) ====
A multiple regression method (MRM) is used for estimating 24-hour daily milk yield (DMY), daily fat yield (DFY) and daily protein yield (DPY) based on partial yields from either morning (AM) or evening (PM) milking. Fat percentage (DFP) or protein percentage (DPP) on a 24-hour daily basis are then derived using the estimated 24-hour daily yields. The MRM can be used as a reference method for estimating daily yields and component percentages.

The method of Liu et al. (2019) is an updated version of the method of Liu et al. (2000). The model is only used for farms with 2 time milkings during 24 hours.

The following formula is used to estimate DMY, DFY, DPY based on partial yields (PMY, PFY,PPY) from either morning (AM) or evening (PM) milking:

''Equation 7. Model for predicting 24-hour yield.''

''yijk = a + bijk * xijk''

where:

yijk is the estimated 24-hour daily yield (DMY, DFY or DPY);

xijk is AM or PM partial daily yield on a test day (PMY, PFY, or PPY).

Subscript '''''i''''' represents class of parity effect with 2 levels: first and higher parities.

Subscript '''''j''''' represents class of length of preceding milking interval with 8 levels for AM milking: < 720 minutes, < 740 minutes, < 760 minutes, < 780 minutes, < 800 minutes, < 820 minutes, < 840 minutes, >= 840 minutes and 8 levels for PM milking: < 600 minutes, < 620 minutes, < 640 minutes, < 660 minutes, < 680 minutes, < 700 minutes, < 720 minutes, >= 720 minutes.

Subscript '''''k''''' represents class of lactation stage with 7 classes: < 60 days, < 120 days, < 180 days, < 240 days, < 300 days, < 360 days, >= 360 days.

'''''a''''' is the estimated intercept for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

'''''b'''''ijk is the estimated slope for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

The factors for '''''a''''' and '''''b'''''ijk can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Appendix_1_-_Adjustment_factors_to_calculate_24-hour_yields_using_the_Liu_method Appendix 1].

For a given yield trait a total number of 112 formulae are to be estimated for calculating 24-hour daily yield based on partial yield from either AM or PM milking. Component percentage for fat (DFP) and protein (DPP), on a 24-hour basis is calculated by dividing estimated fat or protein yield by estimated daily milk yield:[[File:Imagefinal.png|center|thumb|339x339px]]

===== Calculation example with method of Liu et al. (2019) =====
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" align = "left" |'''''Table 14. Data from an evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="6" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="6" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="6" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow'''

'''ID'''
|'''Calving date'''
|'''Lactation number'''
| colspan="2" |'''Milk yield (kg)'''
|'''Fat content (%)'''
|'''Protein content (%)'''
|'''Fat yield (kg)'''
|'''Protein yield (kg)'''
|'''Index1'''
|-
|A
|01.01.2020
|1
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1132
|-
|B
|01.01.2020
|2
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1232
|-
|C
|27.03.2020
|1
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1131
|-
|D
|27.03.2020
|2
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1231
|-
|
|
|
|
|
|
|
|
|
|
|}
'''1''' Index is marked in the Appendix table.
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 15. Calculation of 24-hour daily yield and components for evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="3" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="3" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="3" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow ID'''
|'''DMY (kg)'''
|'''DFY (kg)'''
| colspan="2" |'''DPY (kg)'''
|'''DFP (%)'''
|'''DPP (%)'''
|-
|A
|3,47396+25,0

<nowiki>*</nowiki> 1,98268 = 53,0401 ≈ '''53,0'''
|0,2135+0,995

<nowiki>*</nowiki> 1,68050 = 1,8855975
| colspan="2" |0,10471+0,8325* 1,99092 = 1,7621509
|1,8855975 / 53,04096*100

≈ '''3,55'''
|1,7621509 / 53,04096*100

≈ '''3,32'''
|-
|B
|4,15080+25,0* 1,98520 = 53,7808 ≈ '''53,8'''
|0,3635+0,995

<nowiki>*</nowiki> 1,47515 = 1,8312743
| colspan="2" |0,13952+0,8325* 1,97074 = 1,7801611
|1,8312743 / 53,7808*100

≈ '''3,41'''
|1,7801611 / 53,7808*100

≈ '''3,31'''
|-
|C
|2,80244+33,1

<nowiki>*</nowiki> 2,02183 = 69,72501 ≈ '''69,7'''
|0,17663+1,3339 * 1,72438 = 2,4767805
| colspan="2" |0,11078+1,1122 * 1,96422 = 2,2953855
|2,4767805 / 69,725013*100

≈ '''3,55'''
|2,2953855 / 69,725013*100

≈ '''3,29'''
|-
|D
|3,85525+33,1 * 2,00429 = 70,19725 ≈ '''70,2'''
|0,27991+1,3339 * 1,62403 = 2,4462036
| colspan="2" |0,12863+1,1122* 1,98973 = 2,3416077
|2,4462036 / 70,7197249*100 ≈ '''3,48'''
|2,3416077 / 70,7197249*100 ≈ '''''3,34'''''
|-
|
|
|
|
|
|
|
|}
</center>
'''Note''' that intercepts and slopes of the applied regression formulae are underscored.

===== Fat correction for equal measure sampling =====
With Equal measure sampling, it is advisable to use Equation 8 (or the like) to correct fat contents:

Equation 8. Fat correction for equal measure sampling.

Fat, % = Analysed fat, % + 0.69 – 1.3 x (morning milk/ 24-hour milk)

The relation of morning milk to 24-hour milk is to be calculated to at least four decimals.

==== 1.1 Method of Kyntäjä & Nokka (2021)<ref name=":3" />: 24-hour correction factors for fat percentage ====
This method can be applied to calculate 24-hour correction factors for fat percentage, in case the milk recording is based on two milkings, with at least one known milk yield and one sample. A 24-hour recording day is assumed.

The conventional way to calculate correction factors is based on a data set where all milkings have been recorded and analysed separately. This approach requires a lot of effort and extra analysis, and is not cheap to organise. Organisations that have access to a large number of records may be able to use those data to calculate correction factors even if they have no extra analysis.

Requirements for the data set:

# The data set has to be large enough. Every single factor needs to be based on at least 10,000 or, even better, 100,000 observations.
# Each individual data set must contain at least one preceding milking interval, milk weight, and analysed sample. If it contains more milk weights, intervals etc. that is even better. It is also good to include breed, lactation number, days in milk and other data that may have an effect on the factors.

===== Calculation example of the method of Kyntäjä & Nokka (2021)<ref>Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. ICAR Technical Series no. 25: 171-175.</ref> =====

====== The accumulated data set ======
Since 2003, Finland had accumulated a data set of 7.5 million recordings with data on the time of the sampled and preceding milking as reported by the farmer, the lab analysis results, and the 24-hour milk yield. Grouped according to the preceding interval, the analysed fat content gives a nice sigmoid curve with the highest fat content found after a 540 to 630 minutes’ interval (9 to 10.5 hours) and the lowest at 810 to 930 minutes (13.5 to 15.5 hours).
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 16. Average analysed milk fat percentage by preceding interval class, 2003 – 2020.'''''
|- style="background-color:#efefef;"
|'''Interval before'''

'''Sampling (minutes)'''
|'''Number of samples'''
|'''Median interval in the class'''
|'''Average fat content analysed (%)'''
|-
|<510
|93,577
|495
|4.20
|-
|510-539
|19,523
|525
|4.70
|-
|540-569
|111,268
|555
|4.79
|-
|570-599
|253,807
|585
|4.83
|-
|600-629
|1,461,587
|615
|4.75
|-
|630-659
|919,968
|645
|4.66
|-
|660-689
|1,168,683
|675
|4.56
|-
|690-719
|223,877
|705
|4.42
|-
|720-749
|517,447
|735
|4.28
|-
|750-779
|212,428
|765
|4.16
|-
|780-809
|924,014
|795
|4.12
|-
|810-839
|698,463
|825
|4.09
|-
|840-869
|1,104,778
|855
|4.07
|-
|870-899
|154,561
|885
|4.05
|-
|900-929
|77,024
|915
|4.07
|-
|>929
|26,977
|945
|4.13
|}
</center>

The results were also divided into subgroups according to lactation number, phase of lactation, and breed. The effect of the preceding milk interval on milk fat seems to be bigger with older cows and in the beginning of lactation. It was also bigger with Ayrshire cows as compared with Holsteins. At this point, however, the decision was made not to take these factors into account when calculating new correction factors.

====== Calculation of new factors ======
The results above were turned into a simple set of correction factors, dependent solely on the preceding interval. In order to do this, two assumptions were made:

# A 24-hour recording day was assumed. This way, we can deduce the second milking interval from the one we know and mirror the fat percent for that milking.
# Milk secretion rate was assumed to be constant around the 24-hour period. This allows us to deduce the share of the 24-hour yield produced at each milking.

These assumptions allow us to create the new correction factors by mirroring the milk yield and milk fat content in the milking whose actual data we have not got. This way, we get the following formula:

Equation 9. Correction factor.
[[File:Equation9.png|none|thumb|545x545px]]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left" |'''''Table 17. Calculation of the mirrored milking and the correction factors'''''
|- style="background-color:#efefef;"
|'''Interval before sampling (minutes)'''
|'''Average fat in the sampled milking (%)'''
|'''Share of 24-hour milk in the sampled milking'''
|'''Mirrored interval (minutes)'''
|'''Average fat in the mirrored milking (%)'''
|'''Calculated 24-hour average fat(%)'''
|'''Correction factor'''
|-
|<510
|4.21
|0.34
|>929
|4.14
|4.16
|0.989
|-
|510-539
|4.77
|0.36
|900-929
|4.08
|4.33
|0.907
|-
|540-569
|4.82
|0.39
|870-899
|4.05
|4.35
|0.903
|-
|570-599
|4.84
|0.41
|840-869
|4.07
|4.38
|0.906
|-
|600-629
|4.76
|0.43
|810-839
|4.09
|4.37
|0.919
|-
|630-659
|4.66
|0.45
|780-809
|4.12
|4.36
|0.936
|-
|660-689
|4.56
|0.47
|750-779
|4.16
|4.35
|0.953
|-
|690-719
|4.43
|0.49
|720-749
|4.29
|4.36
|0.984
|-
|720-749
|4.29
|0.51
|690-719
|4.43
|4.36
|1.016
|-
|750-779
|4.16
|0.53
|660-689
|4.56
|4.35
|1.046
|-
|780-809
|4.12
|0.55
|630-659
|4.66
|4.36
|1.059
|-
|810-839
|4.09
|0.57
|600-629
|4.76
|4.37
|1.070
|-
|840-869
|4.07
|0.59
|570-599
|4.84
|4.38
|1.076
|-
|870-899
|4.05
|0.61
|540-569
|4.82
|4.35
|1.073
|-
|900-929
|4.08
|0.64
|510-539
|4.77
|4.33
|1.062
|-
|>929
|4.14
|0.66
|<510
|4.21
|4.16
|1.006
|}
</center>

=== Methods to calculate 24-hour yields in Automatic Milking Systems ===

==== General remarks about calculation of 24-hour milk yield ====
It is characteristic for AMS systems that individual cows set their own milking rhythm, thus making it largely irrelevant to use the traditional model of measuring milk yields and sampling at all milkings in the herd during the recording day. In order to determine how much an individual cow’s real 24-hour milk, fat and protein yield is, more complex calculations are required, especially with milk fat that varies considerably from milking to milking. For protein content and cell counts, no correction is needed for a one-milking sample.

The basic idea with calculating a 24-hour milk yield from AMS data is that milk yields per milking are converted into milk yield per time unit (minute or hour) during the preceding interval. This milk yield per time unit is then converted into milk yield in 24 hours. In order to do this, the data set must also contain time stamps for each milking.

How many milkings or how long a measurement period is used for creating 24-hour yields depends on the milk recording organisation. The fewer milkings are used the more random variance there will be in the individual cow milk yields. The absolute minimum is two milkings with preceding intervals, while a measuring period of 96 hours is recommended.

The sampled milking must always be inside the milk yield measurement period. For the calculation of fat and protein yields, it is recommended to use only those milk yields that are from the same period or day. With Z sampling, the 24-hour fat and protein yields may be calculated based on a shorter measurement period than what is used for calculating the 24-hour milk yields.

==== Calculation of milk yield using data of several days (Lazenby ''et al''., 2002<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Automatic Milking Systems (AMS). The average of most recent milk weights can be calculated using a number of preceding milkings or a number of preceding days. If number of milkings is used, the optimal estimate of the milking rate is obtained using an average of current milking together with the 12 most recent milkings back in time. The optimal estimate is the maximum value of the difference curve at which the correlation with the ‘true’ 24-hour milk yield is greatest and the variance across milkings is minimized. If number of days is used, the optimal estimate of the milking rate is obtained using an average of all milkings occurred in the last 96 hours (4 most recent days). In Table 18 the percent of maximum difference for various number of milkings and days is reported. The optimal estimate is independent from stage of lactation and parity.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 18. Percent maximum for different number of days and milkings.'''''
|- style="background-color:#efefef;"
|'''Days'''
|'''Percent Max.'''
|'''Current milking'''

'''+ most recent milkings'''
|'''Percent max.'''
|-
|1
|49.38
|10
|97.85
|-
|2
|77.26
|11
|99.08
|-
|3
|92.34
|12
|99.70
|-
|4
|98.91
|13
|99.81
|-
|5
|98.50
|14
|99.40
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table19.png|center|thumb|911x911px]]
Therefore, 24-hour yield estimation using most recent milkings (1+12) is computed using Equation 10.

''Equation 10. 24-hour yield estimation using 12 previous milkings from AMS.''
[[File:Equation10.png|none|thumb|527x527px]]
and, 24-hour yield estimation using all milkings occurred in the last 96 hours (most recent 4 days), all milking in the last 4 days are included is computed using Equation 11.

''Equation 11. 24 hours yield estimation using milkings from the last 96 hours from AMS''
[[File:Equation11.png|none|thumb|534x534px]]

===== Advantages and disadvantages of this method =====
In terms of Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between milk weights and contents may arise if contents are recorded on one day only. Moreover, some cows may begin or finish their lactation during the period of recording. In this case the computation of milk yield must be adapted. The number of data that need to be validated is higher (for instance, contents have short interval between two milkings).

==== Calculation of milk yield using data on 1 day (Bouloc ''et al''., 2002<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
When the number of milkings is reduced to milkings obtained during one day only, the accuracy of the estimation of the true performance is the same as classical milk recording methods with the same interval between two test days. For instance, Milk Yield estimated from all the milkings recorded during 24 hours, and with an interval between two test days of four weeks has the same accuracy as A4.

==== Calculation of fat and protein yield (Galesloot & Peeters, 2000<ref name=":1" />) ====
Calculation of fat and protein percent must be based on milk weights at time of sampling. The 24-hour protein percentage can be predicted by the protein percentage of the sample without adjustment. However, the 24-hour fat percentage is more difficult to predict, as levels of fat percent are inversely proportional to the amount of milk yield. It is important then to have a close connection between time of samples and actual milk yields.

The Peeters and Galesloot method is a multiple linear regression model for estimating 24-hour fat percent and yields from one-sampled milking during the AMS sampling period. Six different statistical models were tested. This method takes into account fat percent, protein percent, milk weight and milking interval of the sampled milking, milking interval and milk weight of the previous milking (simple model). Another model, based on six different classification of variables (Ca - Cf) such as, time of sampled milking, interval preceding the sampled milking, ratio of fat to protein percent, parity, lactation stage, can be applied (complex model).

===== Simple model =====
24-hour Fat% = b0 + b1* Fat%(n) + b2* Prot%(n) + b3* Int(n) + b4* Int(n-1) + b5* Milk(n) + b6* Milk (n-1) + e

b0= Intercept, b1 to b6 = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, e = Residual effect.

===== Complex model =====
24-hour Fat%i = b0i + b1i* Fat%(n) + b2i* Prot%(n) + b3i* Int(n) + b4i* Int(n-1) + b5i* Milk(n) + b6i* Milk(n-1) + ei

b0i = Intercept, b1i to b6i = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, ei = Residual effect

i = subclass of classification for class variables Cx for x = a, b, c, d, e, f

Ca = Day Time of sampled milking (h) 0-5.59, 6.00-11.59, 12.00-17.59, 18.00-23.59

Cb = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440

Cc = Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

Cd = Parity 1, 2, ≥ 3

Ce = Lactation stage 1-99, 100-199, ≥200

Cf = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440 and Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

The best prediction of 24-hour fat percent and 24-hour fat yields from this method, includes fat percent, protein percent, milk weight and milking interval of the sampled milking, milk weight and milking interval of the preceding milking and the interaction between milking interval, the ratio of fat to protein percent of the sampled milking (complex model corresponding to Cf classification).

The Peeters and Galesloot method has been updated by Roelofs et al. (2006)<ref>Peeters, R. and P. J. B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. J Dairy Sci. 85:682-688.</ref>. The Roelofs method is described in [[Section 02 – Cattle Milk Recording#Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme|Appendix 2]] of this Section.

N.B. This method has been developed by CRV. CRV has available a set of parameters, estimated with this method. For more information about costs and advice on application of this method, please contact CRV. ICAR has no benefit from the application of this method or any other method described in these guidelines.

==== Calculation example of 24-hour fat and protein yields with sampling scheme M ====
With this method, all milkings in a 24-hour recording period must be sampled. The obtained separate analysis results are then used to compute a 24-hour yield of milk solids, and a weighted average of their content.

Individual milkings (last 96 hours) and recording day contents:
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left" |'''''Table 20. Calculation of 24-hour fat and protein contents with sampling scheme M.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY/MM/DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat%'''
|'''Protein%'''
|-
|1
|2021/09/09
|20:45
|525
|13.7
|26.1
|
|
|-
|2
|2021/09/10
|5:30
|617
|16.0
|25.9
|
|
|-
|3
|2021/09/10
|15:47
|720
|18.7
|26.0
|
|
|-
|4
|2021/09/11
|3:25
|645
|16.8
|26.0
|
|
|-
|5
|2021/09/11
|14:10
|899
|18.3
|20.3
|
|
|-
|6
|2021/09/11
|23:27
|557
|14.6
|26.2
|
|
|-
|7
|2021/09/12
|10:51
|684
|17.4
|25.4
|4.53
|3.17
|-
|8
|2021/09/12
|19:44
|533
|14.1
|26.5
|4.92
|3.18
|-
|9
|2021/09/13
|1:35
|351
|9.9
|28.2
|5.92
|3.07
|}
</center>

For example, calculation of fat% on recording day:

24-hour Fat% = (9.9 kg milk x 5.92% fat + 14.1 kg milk x 4.92 % fat + 17.4 kg milk x 4.53 % fat) / (9.9 + 14.1 + 17.4) kg milk = 5.00 %

To calculate the 24-hour fat yield, the calculated 24-hour milk yield is multiplied by the fat content thus obtained (5.00 %).

The same method is used for protein, somatic cell count, urea, lactose and other milk constituents.

Estimation of milk contents: It is recommended to set the robot not to take samples if the preceding milking of the individual cow is not more than 4 hours earlier. If such milkings occur the milk sampled from them is not suitable for 24-hour fat calculation.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left"|'''''Table 21. Calculation of 24-hour fat and protein contents with sampling scheme M where one milking interval was shorter than 4 hours.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY-MM-DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat %'''
|'''Protein%'''
|-
|1
|2021/11/12
|20:05
|590
|15.4
|26.4
|
|
|-
|2
|2021/11/13
|6:31
|626
|16.3
|26.0
|
|
|-
|3
|2021/11/13
|17:12
|641
|17.1
|26.7
|
|
|-
|4
|2021/11/14
|4:40
|688
|17.5
|25.4
|
|
|-
|5
|2021/11/14
|15:11
|631
|16.4
|26.0
|
|
|-
|6
|2021/11/15
|2:25
|674
|16.5
|24.5
|
|
|-
|7
|2021/11/15
|9:47
|452
|10.8
|23.9
|
|
|-
|8
|2021/11/15
|18:30
|523
|13.6
|26.0
|4.71
|3.36
|-
|9
|2021/11/15
|21:15
|165
|3.1
|18.8
|5.161
|3.481
|-
|10
|2021/11/16
|7:49
|634
|16.5
|26.0
|4.47
|3.21
|}
1 Time between two consecutive milkings shorter than 4 hours, data not taken into account for calculation of milk contents.
</center>

Calculation of the fat content of milk during the recording day:

24-hour Fat% = (16.5 kg milk x 4.47 % fat + 13.6 kg milk x 4.71 % fat) / (16.5 kg + 13.6 kg) = 4.57 %

The same method is used for protein, somatic cells, urea, lactose and other milk constituents.

=== Methods to calculate 24-hour yields from electronic milk meters ===

==== Using data on more than one day (Hand ''et al''., 2006<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. J. Dairy Sci. 89:1723–1726.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Electronic Milk Meters. The average of most recent milk weights can be calculated using a number of preceding days. Table 22 reports the concordance correlations for a range of multiple-day averages. As soon as at least the 3 preceding days are used in the calculation, the concordance correlation reaches a high value of at least 0.981. There are no significant differences between 3, 4, 5, 6 and 7-day averages. The correlations are independent from stage of lactation and parity. Thus, 24-hour yields can be the average of from 3 to 7 daily milkings previous to the test day when fat and protein samples were taken.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 22. Concordance correlations for different multiple-day averages.'''''
|- style="background-color:#efefef;"
|'''Multiple-day average'''
|'''Concordance correlation'''
|-
|1
|0.957
|-
|2
|0.975
|-
|3
|0.981
|-
|4
|0.981
|-
|5
|0.982
|-
|6
|0.981
|-
|7
|0.981
|-
|10
|0.979
|-
|14
|0.977
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table20.png|center|thumb|923x923px]]

Therefore, 24-hour yield estimation averaging over 5 days is given by Equation 12.

''Equation 12. 24-hour yield estimation averaging over 5 days.''
[[File:Equation12.png|center|thumb|601x601px]]

===== Advantages and disadvantages of this method =====
Concerning Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between Milk weights and contents have been shown. The estimation bias increases proportionally to the number of days use to compute the 24-hour average. Thus, this method is recommended only if milk weight is the only variable of interest. If milk contents are of interest then the milk weight should be calculated using the milkings from the same day of sampling.

==== Estimation of 24-hour fat and protein yield ====
Fat and protein yields should be determined from the 24-hour yield on the day of sampling, and not the averaged value.

=== Calculation of daily fat percentage from single samples by Gerke et al., 2025 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Gerke.xlsx here]

Constant access to the automatic milking system (AMS) leads to varying milking frequency of cows and subsequently varying milking interval lengths (MI) and milk yield (MY) of single milkings. This influences milk production and can result in variable milk composition in individual milkings during the day. Therefore, the fat percentage from one sampled milking must be adjusted before it can be used as a daily value. The method described specifies the data required and the calculation procedure for deriving a corrected 24 h milk fat percentage from a single sample on test day (TD) in AMS herds.

==== Model specification ====
The multiple linear regression includes transformation, interaction, and polynomial parameters to model non-linearity and thereby improve prediction accuracy. Beside F% of a single milking (''m'') on TD, the model focused on lactation characteristics and milk recording data of up to 4 preceding milkings. With milking intervals ranging between 4 and 20 hours, the method can be applied to milk recording samples from cows with 2 or 3 milkings whose milking intervals lengths (MI) before sampling accumulate to less than 24 h.

The functional form of the model described below specifies the data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample:[[File:Image A.png|center|thumb|636x636px|'''Data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample''']]
</div>where:

DF% = estimated 24 h fat percentage on TD

''m'' = sampled milking on TD

''m-x'' = x milkings before the milking where the sample was taken (x: 1-3)

F% = fat percentage of the sampled milking ''m''

MY(''m'') = milk yield (kg) of ''m''

MI(''m'') = length of time interval (min) preceding the sampled milking ''m''

MY(''m''-x) = milk yields of the 1-3 preceding milkings of ''m''

MI(''m''-x) = milking interval length corresponding to MY(''m''-x)

DIM = days in milk on TD ranging between 5 and 330 d

Parity = parity class (e.g primiparous = 1 and multiparous = 0)

Daytime = time-of-day group of ''m'' (e.g. morning/noon/evening)

e = residual error

The method and its implementation are described in detail by Gerke et al. (2025).

==== Calculation and examples ====
The mathematical notation, with the corresponding regression coefficients in Table 1 for calculating the daily fat percentage (DF%):[[File:Calculating the daily fat percentage (DF%).jpg|center|Calculating the daily fat percentage (DF%)|thumb|511x511px]][[File:Calculating the daily fat percentage (DF%) 2.jpg|center|frame|'''Table 1. Coefficients for regression formula.''']]
</div>
[[File:Example data required for estimating 24 h fat percentage (DF%).jpg|alt=Example data required for estimating 24 h fat percentage (DF%)|center|frame|'''Table 2.''' '''Example data required for estimating 24 h fat percentage (DF%)''']]
Based on the data assembled on TD (Table 2), the corrected 24 h fat percentage (DF%) can be calculated using the mathematical formula und its corresponding coefficients listed in Table 1 as shown in the following examples:
[[File:Corrected 24 h fat percentage.jpg|alt=Corrected 24 h fat percentage|center|thumb|661x661px|'''Corrected 24 h fat percentage''']]

=== Reference ===
Gerke, J. S., Kammer, M., Werner, A., Köstler, R., Piepenburg, J., Mayerhofer, M., … Duda, J. (2025). Estimating daily fat percentage from single samples in herds with automatic milking system using a regression model. ''Livestock Science'', ''293'', 105649. doi: 10.1016/j.livsci.2025.105649

=== Calculation of daily fat percentage from single samples by Jenko et al., 2008, 2010 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Jenko.xlsx here]

This method estimates daily milk yield (DMY), daily fat yield (DFY), and daily protein yield (DPY) in the alternate one-milking recording (T) scheme. Daily fat percentage (DFP) and daily protein percentage (DPP) are then derived from the daily yield (DY) estimates. Utilizing this method allows us to remove the risk of underestimating high and overestimating low DY and contents.

The following formula is used to estimate the DY from the partial yield (PY) and the estimated PY/DY ratio (y):

DY=PYi/yi

where the subscript i is either morning (a.m.) or evening (p.m.).

The value of y is calculated based on the milking interval in minutes (MI), estimated intercept (µ) and regression coefficients (b1 and b2) for yield traits in a.m. or p.m. milking using the following equations for DMY and DPY:

'''Equation 1. Model for milk yield and protein yield.'''

yi = µ + b1 × MI

and for DFY

'''Equation 2. Model for fat yield.'''

yi = µ + b1 × MI + b2 × MI2

The intercept and regression coefficients can be either estimated from the data with records from both a.m. and p.m. milking or the estimates from Table 1 can be applied.

'''Table 1. Intercept and regression coefficients for calculation of daily yield.'''
{| class="wikitable"
|'''Daily yield'''
|'''Milking'''
|'''µ'''
|'''b1'''
|'''b2'''
|-
|DMY
|a.m.
|0,1081000000
|0,0005503000
|
|-
|
|p.m.
|0,0884200000
|0,0005683000
|
|-
|DPY
|a.m.
|0,1124000000
|0,0005419000
|
|-
|
|p.m.
|0,0966400000
|0,0005593000
|
|-
|DFY .
|a.m.
|0,5903000000
|<nowiki>-0,0005093000</nowiki>
|0,0000005377
|-
|
|p.m.
|0,1574000000
|0,0006705000
|<nowiki>-0,0000002744</nowiki>
|}
Finally, daily fat percentage (DFP) and daily protein percentage (DPP) are calculated from the estimated DY:

DFP=DFY/DMY × 100

DPP=DPY/DMY × 100

==== Calulation example with method of Jenko et al. (2008, 2010) ====
Example of the calculations of daily yields from morning milking and evening milking is presented in tables 3 and 4. Data from the Delorenzo and Wiggans method is used in the calculations (Table 2).

'''Table 2. Data for morning and evening milking.'''
{| class="wikitable"
|'''Milking'''
|'''a.m.'''
|'''p.m.'''
|-
|Beginning of recording
|06:15
|20:22
|-
|Start of preceding milking
|17:25
|06:35
|-
|Milking interval (min)
|770
|827
|-
|'''Milking results'''
|
|
|-
|Milk (kg)
|12,00
|14,00
|-
|Protein (%)
|3,45
|3,40
|-
|Fat (%)
|4,12
|4,00
|}

'''Table 3. Calculation of partial yield (PY) and calculation of y value.'''
{| class="wikitable"
|Trait
|Milking
|PY (%)
|PY (kg)
|y
|-
|Milk
|a.m.
|
|12,00
|0,1081000000 + 0,0005503000 x 770 = 0,531831
|-
|
|p.m.
|
|14,00
|0,0884200000 + 0,0005683000 x 827 = 0,558404
|-
|Protein
|a.m.
|3,45
|12,00 / 3,45 = 0,41
|0,1124000000 + 0,0005419000 x 770 = 0,529663
|-
|
|p.m.
|3,40
|14,00 / 3,40 = 0,48
|0,0966400000 + 0,0005593000 x 827 = 0,559181
|-
|Fat
|a.m.
|

4,12
|12,00 / 4,12 = 0,49
|0,5903000000 -0,0005093000 x 770 + 0,0000005377 x 7702 = 0,516941
|-
|
|p.m.
|

4,00
|12,00 / 4,00 = 0,56
|0,1574000000 +0,0006705000 x 827 - 0,0000002744 x 8272 = 0,524233
|}

'''Table 4. Calculation of daily yield (DY, kg) and daily components (DY, %).'''
{| class="wikitable"
|Trait
|DY
|Milking
|DY (kg)
|DY (%)
|-
|Milk
|DMY
|a.m.
|12,00 / 0,531831 = 22,56356
|
|-
|
|
|p.m.
|14,00 / 0,531831 = 25,07145
|
|-
|Protein
|DPY
|a.m.
|0,41 / 0,529663 = 0,781629
|(0,781629 / 22,56356) x 100 = 3,46
|-
|
|
|p.m.
|0,48 / 0,559181 = 0,851245
|(0,851245 / 25,07145) x 100 = 3,40
|-
|Fat
|DFY
|a.m.
|0,49 / 0,516941 = 0,956395
|(0,956395 / 22,56356) x 100 = 4,24
|-
|
|
|p.m.
|0,56 / 0,524233 = 1,068227
|(1,068227 / 25,07145) x 100 = 4,26
|}

==== References ====

* Jenko, J., Perpar, T., Logar, B., Sadar, M., Ivanovič, B., Jeretina, J., Verbič, J., Podgoršek, P. 2008. Comparison of different models for estimating daily yields from a.m./p.m. milkings in Slovenian dairy scheme. Presented at the 36th ICAR Session, Niagara Falls, New York, United States, June 16-20, 2008.
* Jenko, J., Perpar, T., Gorjanc G., Babnik, D. 2010. Evaluation of different approaches for the estimation of daily yield from single milk testing scheme in cattle, J. Dairy Res., 77 (2010), pp. 137-143; DOI: 10.1017/S0022029909990586

== Procedure 2 – Computing of Accumulated Lactation Yield ==
<div class="mw-collapsible mw-collapsed">
<div>
=== The Test Interval Method (TIM) (Sargent, 1968<ref>Sargent, F. D., V. H. Lyton, and 0. G. Wall, J r . 1968. Test interval method of calculating Dairy Herd Improvement Association records. J. Dairy Sci. 51:170.</ref>) ===
Test Interval Method is the reference method for calculating accumulated yields. Another adaptation of the method is the Centering Date Method where the yields from the preceding recording are used until the mid point of the recording interval and then substituted by the yields from the following recording.

The following equations are used to compute the lactation record for milk yield (MY), for fat (and protein) yield (FY), and for fat (and protein) percent (FP).
[[File:Equation1111.png|none|thumb|653x653px]]
Where:
M1, M2, Mn are the weights in kilograms, given to one decimal place, of the milk yielded in the 24 hours of the recording day.

F1, F2, Fn are the fat yields estimated by multiplying the milk yield and the fat percent (given to at least two decimal places) collected on the recording day.

I1, I2, In-1 are the intervals, in days, between recording dates.

I0 is the interval, in days, between the lactation period start date and the first recording date.

In is the interval, in days, between the last recording date and the end of the lactation period.

The equation applied for fat yield and percentage must be applied for any other milk components such as protein and lactose.

Details of how to apply the formulae are shown in Table 3 using the example data in Table 1, below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" align = "left" |'''''Table 1. Raw data used in example (TIM).'''''
|- style="background-color:#efefef;"
| colspan="6" align = "left"|'''Data:'''

'''Calving March 25'''
|- style="background-color:#efefef;"
|
|'''Date of'''

'''recording'''
|'''Number'''

'''of days'''
|'''Quantity of milk'''

'''weighed in kg'''
|'''Fat'''

'''percentage'''
|'''Fat'''

'''in grams'''
|-
|April
|8
|14
|28.2
|3.65
|1 029
|-
|May
|6
|28
|24.8
|3.45
|856
|-
|June
|5
|30
|26.6
|3.40
|904
|-
|July
|7
|32
|23.2
|3.55
|824
|-
|August
|2
|26
|20.2
|3.85
|778
|-
|August
|30
|28
|17.8
|4.05
|721
|-
|September
|25
|26
|13.2
|4.45
|587
|-
|October
|27
|32
|9.6
|4.65
|446
|-
|November
|22
|26
|5.8
|4.95
|287
|-
|December
|20
|28
|4.4
|5.25
|231
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left"|'''''Table 2. Lactation period summary (TIM).'''''
|-
|Beginning of lactation:
|March 26
|-
|End of lactation:
|January 3
|-
|Duration of lactation period:
|284 days
|-
|Number of testings (weighings):
|10
|}
</center>
<center>
{| class="wikitable"
| colspan="8" |'''''Table 3. Computations using Test Interval Method.'''''
|- style="background-color:#efefef;"
| colspan="3" rowspan="2" |'''Interval'''

'''both days included'''
|
| colspan="2" |'''Daily production'''
| colspan="2" |'''Sum'''
|- style="background-color:#efefef;"
|'''Days'''
|'''Kg milk'''
|'''Grams of fat'''
|'''Kg milk'''
|'''Kg fat'''
|-
|Mar 26
|<nowiki>-</nowiki>
|Apr 8
|14
|28.2
|1 029
|395
|14.410
|-
|Apr 9
|<nowiki>-</nowiki>
|May 6
|28
|(28.2+24.8)/2
|(1 029+856) /2
|742
|26.389
|-
|May 7
|<nowiki>-</nowiki>
|June 5
|30
|(24.8+26.6) /2
|(856+904) /2
|771
|26.400
|-
|June 6
|<nowiki>-</nowiki>
|July 7
|32
|(26.6+23.2) /2
|(904+824) /2
|797
|27.648
|-
|July 8
|<nowiki>-</nowiki>
|Aug. 2
|26
|(23.2+20.2) /2
|(824+778) /2
|564
|20.817
|-
|Aug. 3
|<nowiki>-</nowiki>
|Aug 30
|28
|(20.2+17.8) /2
|(778+721) /2
|532
|20.980
|-
|Aug 31
|<nowiki>-</nowiki>
|Sept. 25
|26
|(17.8+13.2) /2
|(721+587) /2
|403
|17.008
|-
|Sept. 26
|<nowiki>-</nowiki>
|Oct. 27
|32
|(13.2+9.6) /2
|(587+446) /2
|365
|16.541
|-
|Oct. 28
|<nowiki>-</nowiki>
|Nov. 22
|26
|(9.6+5.8) /2
|(446+287) /2
|200
|9.536
|-
|Nov. 23
|<nowiki>-</nowiki>
|Dec. 20
|28
|(5.8+4.4) /2
|(287+231) /2
|143
|7.253
|-
|Dec. 21
|<nowiki>-</nowiki>
|Jan. 3
|14
|4.4
|231
|62
|3.234
|-
|
|
|
|284
|
|
|4973
|190.216
|-
| colspan="8" |
|-
| colspan="8" |Total quantity of milk: 4 973. kg
|-
| colspan="8" |Total quantity of fat: 190 kg
|-
| colspan="8" |Average fat percentage (190.216 / 4973) x 100 = 3.82%
|}
</center>

=== Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. Livest. Prod. Sci. 17:l.</ref>) ===
With the method 'Interpolation using Standard Lactation Curves' missing test day yields and 305 day projections are predicted. The method makes use of separate standard lactation curves representing the expected course of the lactation, for a certain herd production level, age at calving and season of calving and yield trait. By interpolation using standard lactation curves, the fact that after calving milk yield generally increases and subsequently decreases is taken into account. The daily yields are predicted for fixed days of the lactation: day 0, 10, 30, 50 etc.

The cumulative yield is calculated as follows in :
[[File:Equation2222222.png|none|thumb|474x474px]]
where:

yi = the i-th daily yield;

INTi = the interval in days between the daily yields yi and yi+1;

''n'' = total number of daily yields (measured daily yields and predicted daily yields).

The next example illustrates the calculation of a record in progress. The cow was tested at day 35 and day 65 of the lactation. To determine the lactation yield, daily milk yields are determined for day 0, 10, 30 and 50 of the lactation, by means of the standard lactation curves. The daily yields are in Table 4.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Measured and derived daily yields, used to calculate the record in progress in the example (ISLC).'''''
|- style="background-color:#efefef;"
|'''Day of lactation'''
|'''Milk (kg)'''
|'''Note'''
|-
|0
|25.9
|Predicted
|-
|10
|27.8
|Predicted
|-
|30
|31.7
|Predicted
|-
|35
|31.8
|Measured
|-
|50
|32.9
|Interpolated using standard lactation curve
|-
|65
|33.0
|Measured
|}
</center>

Next, the record in progress can be calculated by means of the formula for a cumulative yield as follows:

[(10 - 1) * 25.9 + (10+1) * 27.8] / 2 +

[(20 - 1) * 27.8 + (20+1) * 31.7] / 2 +

[(5 - 1) * 31.7 + (5+1) * 31.8] / 2 +

[(15 - 1) * 31.8 + (15+1) * 32.9] / 2 +

[(15 - 1) * 32.9 + (15+1) * 33.0] / 2 = 2005.3 kg.

This corresponds to the surface below the line through the predicted and measured daily yields (see Figure 1).
[[File:Figure1.png|center|thumb|621x621px|''Figure 1. Example of calculation of record in progress.'']]

=== Best prediction (BP) (VanRaden, 1997<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. J. Dairy Sci. 80:3015-3022.</ref>) ===
Recorded milk weights are combined into a lactation record using standard selection index methods. Let vector y contain M1, M2, to Mn and let E('''y''') contain corresponding the expected values for each recorded day. The E(y) are obtained from standard lactation curves for the population or for the herd and should account for the cow's age and other environmental factors such as season, milking frequency, etc. The yields in '''y''' covary as a function of the recording interval between them (I). Diagonal elements in Var(y) are the population or herd variance for that recording day and off diagonals are obtained from autoregressive or similar functions such as Corr(M1, M2)=0.995I for first lactations or 0.992I for later lactations. Covariances of one observation with the lactation yield, for example Cov(M1, MY), are the sum of 305 individual covariances. E(MY) is the sum of 305 daily expected values. Lactation milk yield is then predicted as Equation 3:
[[File:Equation333333.png|none|thumb|640x640px]]
With best prediction, predicted milk yields have less variance than true milk yields. With TIM, estimated yields have more variance than true yields. The reason is that predicted yields are regressed toward the mean unless all 305 daily yields are observed. With best prediction, the predicted MY for a lactation without any observed yields is E(MY) which is the population or herd mean for a cow of that age and season. With TIM, the estimated MY is undefined if no daily yields are recorded.

Milk, fat, and protein yields can be processed separately using single-trait best prediction or jointly using multi-trait best prediction. Replacement of M1, M2, to Mn with F1, F2, to Fn or P1, P2, to Pn gives the single-trait predictions for fat or for protein. Multi-trait predictions require larger vectors and matrices but similar algebra. Products of trait correlations and autoregressive correlations, for example, may provide the needed covariances.

=== Multiple-Trait Procedure (MTP) (Schaeffer & Jamrozik, 1996<ref>Schaeffer, L.R., and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. J. Dairy Sci. 79:2044-2055.</ref>) ===
The Multiple-Trait Procedure predicts 305-d lactation yields for milk, fat, protein and SCS, incorporating information about standard lactation curves and covariances between milk, fat, and protein yields and SCS. Test day yields are weighted by their relative variances, and standard lactation curves of cows of similar breed, region, lactation number, age, and season of calving are used in the estimation of lactation curve parameters for each cow. The multiple-trait procedure can handle long intervals between test days, test days with milk only recorded, and can make 305-d predictions on the basis of just one test day record per cow. The procedure also lends itself to the calculation of peak yield, day of peak yield, yield persistency, and expected test-day yields, which could be useful management tools for a producer on a milk recording program.

The MTP method is based upon Wilmink's model in conjunction with an approach incorporating standard curve parameters for cows with the same production characteristics. Wilmink's function for one trait is given by Equation 4.

Equation 4. Wilmink function for one trait (MTP).

y = A + B''t'' ± C''exp'' (-0.05''t'') + ''e''

where y is yield on day t of lactation, A, B, and C are related to the shape of the lactation curve.

The parameters A, B, and C need to be estimated for each yield trait. The yield traits have high phenotypic correlations, and MTP would incorporate these correlations. Use of MTP would allow for the prediction of yields even if data were not available on each test day for a cow.

The vector of parameters to be estimated for one cow are designated:
[[File:Vectro.png|center|thumb]]
where M, F, and P represent milk, fat, and protein, respectively, and S represents somatic cell score. The vector c is to be estimated from the available test-day records. Let c0 represent the corresponding parameters estimated across all cows with the same production characteristics as the cow in question.

Let
[[File:Vector2.png|center|thumb]]

be the vector of yield traits and somatic cell scores on test ''k'' at day ''t'' of the lactation.

The incidence matrix, ''Xk'', is constructed as follows:
[[File:Vector3.png|center|thumb|558x558px]]

The MTP equations are:
[[File:Equation55555.png|none|thumb|560x560px]]
and ''n'' is the number of tests for that cow. ''Rk'' is a matrix of order 4 that contains the variances and covariances among the yields on ''kth'' test at day ''t'' of lactation. The elements of this matrix were derived from regression formulas based on fitting phenotypic variances and covariances of yields to models with ''t'' and ''t2'' as covariables. Thus, element ''ij'' of ''Rk'' would be determined by

rij(t) = ß0ij + ß1ij (t) + ß2ij (t2)

G is a 12 x 12 matrix containing variances and covariances among the parameters in '''ĉ''' and represents the cow to cow variation in these parameters, which includes genetic and permanent environmental effects, but ignores genetic covariances between cows. The parameters for '''''G''''' and '''''Rk''''' vary depending on the breed, but must be known. Initially, these matrices were allowed to vary by region of Canada in addition to breed, but this meant that there could exist two cows with identical production records on the same days in milk, but because one cow was in one region and the other cow was in another region, then the accuracy of their predictions would be different. This was considered to be too confusing for dairy producers, so that regional differences in variance-covariance matrices were ignored and one set of parameters would be used for all regions for a particular breed. Estimation of G is described later.

If a cow has a test, but only milk yield is reported, then

y’k(Mk 0 0 0)

and
[[File:And.png|center|thumb|540x540px]]

The inverse of '''''Rk''''' is the regular inverse of the nonzero submatrix within '''''Rk''''', ignoring the zero rows and columns. Thus, missing yields can be accommodated in MTP.

Accuracy of predicted 305-d lactation totals depends on the number of test-day records during the lactation and DIM associated with each test. Thus, any prediction procedure will require reliability figures to be reported with all predictions, especially if fewer tests at very irregular intervals are going to be frequent in milk recording. At the moment, an approximate procedure is applied that uses the inverse elements of '''(X’R-1X + G-1) -1.'''

==== 1.1 Example calculations ====
Four test day records on a 25 month old, Holstein cow calving in June from Ontario are given in the Table 5 below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 5. Example test day data for a cow (MTP).'''''
|- style="background-color:#efefef;"
|'''Test no.'''
|'''DIM=''t'''''
|'''Exp(-0.05''t'')'''
|'''Milk (kg)'''
|'''Fat (kg)'''
|'''Protein (kg)'''
|'''SCS'''
|-
|1
|15
|0.47237
|28.8
|
|
|3.130
|-
|2
|54
|0.06721
|29.2
|1.12
|0.87
|2.463
|-
|3
|188
|0.000083
|23.7
|0.97
|0.78
|2.157
|-
|4
|250
|0.0000037
|20.8
|
|
|2.619
|}
</center>

Notice that two tests do not have fat and protein yields, and that intervals between tests are irregular and large. The vector of standard curve parameters based on all available comparable cow, is
[[File:Vector4.png|center|thumb]]
The R^(-1)_k matrices for each test day need to be constructed. These matrices are derived from regression equations. The equations for Holsteins were:
<center>
{| class="wikitable" style="text-align: center;"
|''rMM(t) =''
|71.0752 - 0.281201''t'' + 0.0004977''t2''
|-
|''rMF(t) =''
|2.4365 - 0.013274''t'' + 0.0000302''t2''
|-
|''rMP(t) =''
|2.0504 - 0.008286''t'' + 0.0000163''t2''
|-
|''rMS(t) =''
|<nowiki>-1.7993 + 0.013209</nowiki>''t'' - 0.000056''t2''
|-
|''rFF(t) =''
|0.1312 - 0.000725''t'' + 0.000001586''t2''
|-
|''rFP(t) =''
|0.0739 - 0.000386''t'' + 0.000000926''t2''
|-
|''rFS(t) =''
|<nowiki>- 0.0386 + 0.000292</nowiki>''t'' - 0.000001796''t2''
|-
|''rPP(t) =''
|0.066 - 0.000267''t'' + 0.0000005636''t2''
|-
|''rPS(t) =''
|<nowiki>- 0.0404 + 0.000369</nowiki>''t'' - 0.000001743''t2''
|-
|''rSS(t) =''
|3.0404 - 0.000083''t'' - 0.000006105''t2''
|}
</center>

The inverses of the residual variance-covariance matrices for yields for the four test days are as follows:
<center>
{| class="wikitable" style="text-align: center;"
|
|0.0151259
|0
|0
|0.0080354
|-
|'''R^(-1)_1''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0080354
|0
|0
|0.3334553
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.1685584
|0.345947
|<nowiki>-4.851935</nowiki>
|0.0254775
|-
|'''R^(-1)_2''' = =
|<nowiki>-0.345947</nowiki>
|26.830915
|<nowiki>-17.40281</nowiki>
|<nowiki>-0.041445</nowiki>
|-
|
|<nowiki>-4.851935</nowiki>
|<nowiki>-17.40281</nowiki>
|187.18579
|<nowiki>-0.584885</nowiki>
|-
|
|0.0254775
|<nowiki>-0.041445</nowiki>
|<nowiki>-0.584885</nowiki>
|0.3365425
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.2620161
|0.1479068
|<nowiki>-7.943903</nowiki>
|0.0316069
|-
|'''R^(-1)_3''' = =
|0.1479068
|54.446977
|<nowiki>-56.01333</nowiki>
|0.3306741
|-
|
|<nowiki>-7.943903</nowiki>
|<nowiki>-56.01333</nowiki>
|317.9609
|<nowiki>-0.92601</nowiki>
|-
|
|0.0316069
|0.3306741
|<nowiki>-0.92601</nowiki>
|0.3654369
|}
{| class="wikitable" style="text-align: center;"
|

|0.0329465
|0
|0
|0.0251039
|-
|'''R^(-1)_4''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0251039
|0
|0
|0.3981981
|}

Inverse matrix G^(-1) of order 12 is the same for all cows of the same breed:

[[File:Left 6x6.jpg|center|thumb|600x600px|Inverse matrix G^(-1) of order 12]]

</center>
Note that many covariances between different parameters of the lactation curves have been set to zero. When all covariances were included, the prediction errors for individual cows were very large, possibly because the covariances were highly correlated to each other within and between traits. Including only covariances between the same parameter among traits gave much smaller prediction errors.

The elements of the MTP equations of order 12 for this cow are shown in partitioned format also:

'''X’R-1X ='''
<center>[[File:Elements of the MTP equations of order 12.jpg|center|thumb|600x600px|Elements of the MTP equations of order 12]]
</center>
[[File:Equation7.png|center|thumb|632x632px]]

The solution vector for this cow is
[[File:Equation6666.png|center|thumb]]

To predict 305-day yields, Y305
[[File:Equation7777.png|none|thumb|551x551px]]
Equation 6 is used separately for each trait (milk, fat, protein, and SCS). The results for this cow were 7456 kg milk, 301 kg fat, and 239 kg protein. The result for SCS is divided by 305 to give an average daily SCS of 2.477.
</div>
</div>

= Appendices =
== Appendix 1 - Adjustment factors to calculate 24-hour yields using the Liu method ==
<div class="mw-collapsible mw-collapsed">
<div>
In Table 6 the adjustment factors to calculate 24-hour yields, using the Liu method, can be found. The description of the Liu method can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2.]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" |'''''Table 1. Adjustment factors to calculate 24-hour yields using the Liu method. Milking time (MT) is either 1 (PM) or 2 (AM), i = parity class, j= milking interval class and k = stage of lactation class.'''''
|- style="background-color:#efefef;"
|'''MT'''
|'''i'''
|'''j'''
|'''k'''
| colspan="2" |'''Milk yield (DMY)'''
| colspan="2" |'''Fat yield (DFY)'''
| colspan="2" |'''Protein yield (DPY)'''
|-
| colspan="4" |
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|-
|1
|1
|1
|1
|5.29333
|1.83283
|0.30911
|1.43518
|0.18984
|1.77461
|-
|1
|1
|1
|2
|4.17676
|1.97447
|0.2803
|1.56914
|0.12246
|2.00568
|-
|1
|1
|1
|3
|4.26476
|1.95945
|0.18826
|1.82468
|0.12624
|2.0137
|-
|1
|1
|1
|4
|3.41282
|2.01814
|0.25025
|1.64707
|0.12519
|1.99629
|-
|1
|1
|1
|5
|1.79548
|2.22665
|0.06578
|2.09515
|0.05249
|2.24065
|-
|1
|1
|1
|6
|3.7751
|1.95508
|0.12854
|1.93892
|0.11936
|2.00979
|-
|1
|1
|1
|7
|1.544
|2.1478
|0.06425
|2.06779
|0.0569
|2.13851
|-
|1
|1
|2
|1
|5.8584
|1.79409
|0.33193
|1.42953
|0.20756
|1.7288
|-
|1
|1
|2
|2
|5.45524
|1.84258
|0.32877
|1.43235
|0.21332
|1.74001
|-
|1
|1
|2
|3
|4.64052
|1.86706
|0.27155
|1.57017
|0.16439
|1.84539
|-
|1
|1
|2
|4
|2.86835
|2.06209
|0.18647
|1.79403
|0.10803
|2.0193
|-
|1
|1
|2
|5
|2.11336
|2.12055
|0.10435
|1.97206
|0.07193
|2.10651
|-
|1
|1
|2
|6
|2.00673
|2.0636
|0.1386
|1.83336
|0.06892
|2.06532
|-
|1
|1
|2
|7
|1.71752
|2.11269
|0.06501
|2.0379
|0.05569
|2.12881
|-
|1
|1
|3
|1
|2.80244
|2.02183
|0.17663
|1.72438
|0.11078
|1.96422
|-
|1
|1
|3
|2
|3.47396
|1.98268
|0.2135
|1.6805
|0.10471
|1.99092
|-
|1
|1
|3
|3
|2.81702
|2.04348
|0.20754
|1.71868
|0.1127
|1.98403
|-
|1
|1
|3
|4
|3.1989
|1.998
|0.21578
|1.6991
|0.10802
|1.99517
|-
|1
|1
|3
|5
|2.47055
|2.04826
|0.15418
|1.83151
|0.07492
|2.07547
|-
|1
|1
|3
|6
|1.923
|2.07728
|0.11783
|1.89678
|0.06457
|2.08391
|-
|1
|1
|3
|7
|1.85264
|2.0873
|0.13047
|1.86711
|0.071
|2.06917
|-
|1
|1
|4
|1
|2.75042
|1.96631
|0.24794
|1.61741
|0.09248
|1.95376
|-
|1
|1
|4
|2
|2.97505
|1.96711
|0.20029
|1.71842
|0.09381
|1.97081
|-
|1
|1
|4
|3
|2.33365
|2.02986
|0.17021
|1.79996
|0.07631
|2.03167
|-
|1
|1
|4
|4
|3.41505
|1.94107
|0.1845
|1.76799
|0.10989
|1.95456
|-
|1
|1
|4
|5
|2.67488
|1.97797
|0.13433
|1.85893
|0.09432
|1.97755
|-
|1
|1
|4
|6
|1.89907
|2.04841
|0.08715
|1.96251
|0.07132
|2.04225
|-
|1
|1
|4
|7
|1.80326
|2.03554
|0.1251
|1.86477
|0.06072
|2.04747
|-
|1
|1
|5
|1
|2.76763
|1.92863
|0.15754
|1.72474
|0.10187
|1.88749
|-
|1
|1
|5
|2
|3.36896
|1.92048
|0.2236
|1.64149
|0.12369
|1.8823
|-
|1
|1
|5
|3
|2.22763
|2.00452
|0.17614
|1.7474
|0.08019
|1.9782
|-
|1
|1
|5
|4
|2.44625
|1.97049
|0.17217
|1.74753
|0.0889
|1.94647
|-
|1
|1
|5
|5
|2.379
|1.97307
|0.15965
|1.76134
|0.0896
|1.94575
|-
|1
|1
|5
|6
|1.62948
|2.02491
|0.11021
|1.85546
|0.0852
|1.94593
|-
|1
|1
|5
|7
|1.45651
|2.0254
|0.07479
|1.92789
|0.05846
|2.00196
|-
|1
|1
|6
|1
|2.01088
|1.9497
|0.16548
|1.68143
|0.101
|1.85846
|-
|1
|1
|6
|2
|2.96605
|1.93064
|0.25841
|1.52566
|0.12097
|1.86061
|-
|1
|1
|6
|3
|2.2281
|1.96085
|0.19036
|1.69013
|0.08032
|1.9375
|-
|1
|1
|6
|4
|2.39473
|1.952
|0.17854
|1.72423
|0.06863
|1.97582
|-
|1
|1
|6
|5
|2.37955
|1.94127
|0.19579
|1.66419
|0.08447
|1.93156
|-
|1
|1
|6
|6
|0.36203
|2.12393
|0.14291
|1.75822
|0.03845
|2.04562
|-
|1
|1
|6
|7
|1.5702
|1.96794
|0.1336
|1.76796
|0.06449
|1.94829
|-
|1
|1
|7
|1
|3.93654
|1.82772
|0.2359
|1.61894
|0.15032
|1.76054
|-
|1
|1
|7
|2
|4.39662
|1.81581
|0.24969
|1.5881
|0.16909
|1.74794
|-
|1
|1
|7
|3
|3.78325
|1.82778
|0.19228
|1.71802
|0.12368
|1.8268
|-
|1
|1
|7
|4
|3.39116
|1.86302
|0.1969
|1.71838
|0.12282
|1.848
|-
|1
|1
|7
|5
|3.20111
|1.83255
|0.09893
|1.86309
|0.1044
|1.84257
|-
|1
|1
|7
|6
|3.75639
|1.78665
|0.25205
|1.56174
|0.14105
|1.76802
|-
|1
|1
|7
|7
|1.42153
|1.95649
|0.09226
|1.85882
|0.04636
|1.96245
|-
|1
|1
|8
|1
|2.3454
|1.90436
|0.14321
|1.77423
|0.10703
|1.82306
|-
|1
|1
|8
|2
|3.97557
|1.82746
|0.26651
|1.58374
|0.15298
|1.76385
|-
|1
|1
|8
|3
|4.26939
|1.80503
|0.22918
|1.64925
|0.12924
|1.81061
|-
|1
|1
|8
|4
|2.90779
|1.89861
|0.18578
|1.73968
|0.13948
|1.79679
|-
|1
|1
|8
|5
|2.8265
|1.87632
|0.19374
|1.67929
|0.12377
|1.80944
|-
|1
|1
|8
|6
|2.26312
|1.87397
|0.09917
|1.82528
|0.08819
|1.84453
|-
|1
|1
|8
|7
|0.31382
|2.04402
|0.05049
|1.95773
|0.02612
|1.99012
|-
|1
|2
|1
|1
|4.63752
|1.99615
|0.31102
|1.58962
|0.16637
|1.96686
|-
|1
|2
|1
|2
|5.56226
|1.91521
|0.26761
|1.64342
|0.16973
|1.94145
|-
|1
|2
|1
|3
|4.51983
|1.96962
|0.26221
|1.65088
|0.12245
|2.03857
|-
|1
|2
|1
|4
|4.51563
|1.93033
|0.18468
|1.80715
|0.15252
|1.94807
|-
|1
|2
|1
|5
|2.60334
|2.07338
|0.16011
|1.81257
|0.09892
|2.05493
|-
|1
|2
|1
|6
|2.86068
|1.98457
|0.15381
|1.79197
|0.08619
|2.04046
|-
|1
|2
|1
|7
|1.6596
|2.11753
|0.13089
|1.83687
|0.09908
|1.96479
|-
|1
|2
|2
|1
|3.94656
|2.03607
|0.23716
|1.6988
|0.19559
|1.88765
|-
|1
|2
|2
|2
|4.20525
|1.98621
|0.3553
|1.46663
|0.1657
|1.92175
|-
|1
|2
|2
|3
|3.31729
|2.04589
|0.29682
|1.57761
|0.12491
|2.00945
|-
|1
|2
|2
|4
|1.95977
|2.13926
|0.16059
|1.79846
|0.06713
|2.12835
|-
|1
|2
|2
|5
|1.49014
|2.14889
|0.10057
|1.90772
|0.05279
|2.14047
|-
|1
|2
|2
|6
|0.82235
|2.22517
|0.07573
|1.94963
|0.04014
|2.17549
|-
|1
|2
|2
|7
|1.53608
|2.08972
|0.11472
|1.81148
|0.0676
|2.03957
|-
|1
|2
|3
|1
|3.85525
|2.00429
|0.27991
|1.62403
|0.12863
|1.98973
|-
|1
|2
|3
|2
|4.1508
|1.9852
|0.3635
|1.47515
|0.13952
|1.97074
|-
|1
|2
|3
|3
|3.31493
|2.02332
|0.31131
|1.55183
|0.11703
|2.00696
|-
|1
|2
|3
|4
|2.47354
|2.0652
|0.20828
|1.71637
|0.09402
|2.04147
|-
|1
|2
|3
|5
|1.68517
|2.08809
|0.14418
|1.80246
|0.06917
|2.05808
|-
|1
|2
|3
|6
|1.316
|2.12714
|0.11206
|1.87179
|0.04723
|2.12486
|-
|1
|2
|3
|7
|0.4841
|2.20538
|0.04633
|2.02915
|0.02369
|2.18113
|-
|1
|2
|4
|1
|2.82623
|2.01819
|0.25826
|1.69268
|0.11251
|1.97665
|-
|1
|2
|4
|2
|3.24039
|1.9811
|0.36283
|1.50648
|0.11719
|1.96246
|-
|1
|2
|4
|3
|2.4545
|2.03386
|0.19627
|1.75339
|0.09698
|2.00807
|-
|1
|2
|4
|4
|2.46446
|2.01626
|0.17827
|1.76414
|0.08026
|2.02912
|-
|1
|2
|4
|5
|2.11339
|2.00724
|0.14884
|1.77964
|0.07749
|2.00585
|-
|1
|2
|4
|6
|1.51141
|2.04563
|0.11559
|1.82474
|0.06194
|2.02586
|-
|1
|2
|4
|7
|0.95936
|2.09963
|0.07044
|1.95281
|0.03645
|2.0993
|-
|1
|2
|5
|1
|3.36561
|1.97323
|0.2649
|1.65361
|0.13019
|1.92402
|-
|1
|2
|5
|2
|3.66222
|1.95479
|0.35065
|1.51028
|0.14652
|1.89882
|-
|1
|2
|5
|3
|3.20442
|1.96165
|0.28676
|1.58823
|0.12031
|1.93028
|-
|1
|2
|5
|4
|1.78673
|2.0426
|0.17183
|1.75198
|0.0678
|2.02025
|-
|1
|2
|5
|5
|1.61868
|2.01988
|0.11914
|1.80878
|0.06624
|1.99283
|-
|1
|2
|5
|6
|1.30123
|2.02218
|0.10515
|1.80653
|0.05345
|2.00292
|-
|1
|2
|5
|7
|0.65695
|2.08269
|0.06835
|1.89102
|0.0332
|2.0525
|-
|1
|2
|6
|1
|2.3773
|1.9669
|0.24867
|1.6336
|0.08319
|1.94741
|-
|1
|2
|6
|2
|2.82556
|1.95506
|0.31731
|1.51798
|0.12008
|1.89324
|-
|1
|2
|6
|3
|2.7235
|1.94883
|0.30621
|1.5177
|0.09365
|1.93764
|-
|1
|2
|6
|4
|1.77727
|1.98273
|0.17989
|1.69341
|0.07314
|1.95161
|-
|1
|2
|6
|5
|0.81041
|2.05295
|0.13961
|1.74391
|0.04468
|2.01091
|-
|1
|2
|6
|6
|0.72188
|2.0465
|0.09874
|1.79927
|0.03137
|2.03309
|-
|1
|2
|6
|7
|1.21598
|1.97942
|0.07065
|1.87211
|0.04484
|1.98491
|-
|1
|2
|7
|1
|3.55054
|1.89128
|0.27402
|1.61031
|0.10827
|1.89085
|-
|1
|2
|7
|2
|5.0062
|1.81574
|0.3119
|1.54857
|0.18009
|1.76865
|-
|1
|2
|7
|3
|3.95204
|1.84947
|0.30465
|1.53907
|0.16048
|1.789
|-
|1
|2
|7
|4
|2.36233
|1.9168
|0.18751
|1.70412
|0.09531
|1.88355
|-
|1
|2
|7
|5
|1.48851
|1.94443
|0.09973
|1.81041
|0.05904
|1.92497
|-
|1
|2
|7
|6
|1.22525
|1.94454
|0.06617
|1.87082
|0.05516
|1.91259
|-
|1
|2
|7
|7
|1.13847
|1.93756
|0.08109
|1.83388
|0.04706
|1.93165
|-
|1
|2
|8
|1
|4.09874
|1.87708
|0.20312
|1.73434
|0.15506
|1.83083
|-
|1
|2
|8
|2
|4.66403
|1.84302
|0.31808
|1.56093
|0.18049
|1.78288
|-
|1
|2
|8
|3
|3.24375
|1.89351
|0.2827
|1.59546
|0.13583
|1.83427
|-
|1
|2
|8
|4
|2.24175
|1.92084
|0.17795
|1.72611
|0.09636
|1.87438
|-
|1
|2
|8
|5
|1.63783
|1.93625
|0.1225
|1.78642
|0.0659
|1.90934
|-
|1
|2
|8
|6
|2.01753
|1.89095
|0.13742
|1.74752
|0.08289
|1.86553
|-
|1
|2
|8
|7
|0.97568
|1.97215
|0.05926
|1.88807
|0.04057
|1.95672
|-
|2
|1
|1
|1
|3.44076
|1.73133
|0.27759
|1.55037
|0.13323
|1.68913
|-
|2
|1
|1
|2
|4.99596
|1.64527
|0.2322
|1.58033
|0.17533
|1.62422
|-
|2
|1
|1
|3
|3.83372
|1.68144
|0.25087
|1.52033
|0.14525
|1.66706
|-
|2
|1
|1
|4
|3.87034
|1.68102
|0.20979
|1.60153
|0.13627
|1.68885
|-
|2
|1
|1
|5
|1.76134
|1.80424
|0.15241
|1.70485
|0.06231
|1.81524
|-
|2
|1
|1
|6
|0.79304
|1.89072
|0.09906
|1.80312
|0.03277
|1.89435
|-
|2
|1
|1
|7
|1.43535
|1.80614
|0.0593
|1.81589
|0.0407
|1.85002
|-
|2
|1
|2
|1
|3.72284
|1.68499
|0.19226
|1.66567
|0.1237
|1.66453
|-
|2
|1
|2
|2
|4.42667
|1.66508
|0.24314
|1.55652
|0.14361
|1.66251
|-
|2
|1
|2
|3
|2.7019
|1.75871
|0.32717
|1.38452
|0.11056
|1.72312
|-
|2
|1
|2
|4
|2.41538
|1.75937
|0.14575
|1.68355
|0.09038
|1.74138
|-
|2
|1
|2
|5
|1.65412
|1.81649
|0.13926
|1.70623
|0.0597
|1.81378
|-
|2
|1
|2
|6
|2.0843
|1.7735
|0.21052
|1.57508
|0.07244
|1.78566
|-
|2
|1
|2
|7
|1.43238
|1.80651
|0.08031
|1.78712
|0.05269
|1.81727
|-
|2
|1
|3
|1
|2.45314
|1.77068
|0.18152
|1.73443
|0.07657
|1.78025
|-
|2
|1
|3
|2
|3.01217
|1.70966
|0.19388
|1.66175
|0.05624
|1.80606
|-
|2
|1
|3
|3
|2.09997
|1.74945
|0.14493
|1.68277
|0.05446
|1.7922
|-
|2
|1
|3
|4
|2.36683
|1.71741
|0.12244
|1.71407
|0.06775
|1.75721
|-
|2
|1
|3
|5
|1.56776
|1.75755
|0.08776
|1.76946
|0.04244
|1.79675
|-
|2
|1
|3
|6
|1.63824
|1.75452
|0.09422
|1.76794
|0.04181
|1.80604
|-
|2
|1
|3
|7
|0.74114
|1.83421
|0.08039
|1.78306
|0.02347
|1.85596
|-
|2
|1
|4
|1
|1.47047
|1.78588
|0.17271
|1.69379
|0.06511
|1.74985
|-
|2
|1
|4
|2
|2.22168
|1.72985
|0.20701
|1.59429
|0.08178
|1.71455
|-
|2
|1
|4
|3
|2.50108
|1.69618
|0.16828
|1.61962
|0.08598
|1.70516
|-
|2
|1
|4
|4
|1.97141
|1.7202
|0.1446
|1.66357
|0.06856
|1.73201
|-
|2
|1
|4
|5
|1.17054
|1.75879
|0.1172
|1.69234
|0.04624
|1.75806
|-
|2
|1
|4
|6
|1.74755
|1.70968
|0.12562
|1.67603
|0.0629
|1.72333
|-
|2
|1
|4
|7
|0.52482
|1.80155
|0.07345
|1.75615
|0.02671
|1.79288
|-
|2
|1
|5
|1
|1.76464
|1.76219
|0.24301
|1.59094
|0.07156
|1.73136
|-
|2
|1
|5
|2
|1.99594
|1.73438
|0.1984
|1.5954
|0.06489
|1.73449
|-
|2
|1
|5
|3
|1.8804
|1.72362
|0.13019
|1.67977
|0.06783
|1.71916
|-
|2
|1
|5
|4
|1.83337
|1.71477
|0.11197
|1.70244
|0.05764
|1.73194
|-
|2
|1
|5
|5
|1.49752
|1.72615
|0.13128
|1.65461
|0.04656
|1.7433
|-
|2
|1
|5
|6
|1.3042
|1.7305
|0.07173
|1.75315
|0.04482
|1.7399
|-
|2
|1
|5
|7
|2.00868
|1.67669
|0.12298
|1.64761
|0.09175
|1.64669
|-
|2
|1
|6
|1
|0.84993
|1.75972
|0.12918
|1.74026
|0.0328
|1.74802
|-
|2
|1
|6
|2
|1.93666
|1.67406
|0.16606
|1.59943
|0.04535
|1.7106
|-
|2
|1
|6
|3
|2.12115
|1.64964
|0.19988
|1.50821
|0.05229
|1.68986
|-
|2
|1
|6
|4
|0.68831
|1.73901
|0.09674
|1.6838
|0.01696
|1.75787
|-
|2
|1
|6
|5
|1.13081
|1.69479
|0.06413
|1.72559
|0.04936
|1.67757
|-
|2
|1
|6
|6
|0.5893
|1.72537
|0.02598
|1.80138
|0.01591
|1.74082
|-
|2
|1
|6
|7
|0.72519
|1.71955
|0.03157
|1.78405
|0.02889
|1.71972
|-
|2
|1
|7
|1
|1.85937
|1.66064
|0.2416
|1.49676
|0.06807
|1.63599
|-
|2
|1
|7
|2
|1.8527
|1.64892
|0.2374
|1.43845
|0.06336
|1.6431
|-
|2
|1
|7
|3
|1.56905
|1.66084
|0.15434
|1.55598
|0.04336
|1.68109
|-
|2
|1
|7
|4
|0.74968
|1.69857
|0.13496
|1.56636
|0.02871
|1.6933
|-
|2
|1
|7
|5
|1.08222
|1.65925
|0.10847
|1.613
|0.03305
|1.67829
|-
|2
|1
|7
|6
|1.1124
|1.68059
|0.14267
|1.57525
|0.04416
|1.6776
|-
|2
|1
|7
|7
|0.88031
|1.6751
|0.10534
|1.60483
|0.04216
|1.66444
|-
|2
|1
|8
|1
|0.62802
|1.72402
|0.19225
|1.54631
|0.03247
|1.69368
|-
|2
|1
|8
|2
|0.83902
|1.68303
|0.15492
|1.53421
|0.05922
|1.61411
|-
|2
|1
|8
|3
|1.33727
|1.63407
|0.19835
|1.43309
|0.05874
|1.61141
|-
|2
|1
|8
|4
|1.06381
|1.64762
|0.11026
|1.58762
|0.04019
|1.64574
|-
|2
|1
|8
|5
|1.13714
|1.61716
|0.13322
|1.53166
|0.05648
|1.59149
|-
|2
|1
|8
|6
|1.19134
|1.60463
|0.11089
|1.54864
|0.06258
|1.56912
|-
|2
|1
|8
|7
|1.58872
|1.60204
|0.066
|1.64659
|0.04748
|1.63282
|-
|2
|2
|1
|1
|3.46775
|1.78609
|0.28956
|1.68515
|0.15003
|1.72171
|-
|2
|2
|1
|2
|5.69879
|1.67614
|0.3725
|1.5045
|0.19774
|1.64659
|-
|2
|2
|1
|3
|5.18985
|1.66571
|0.40124
|1.40574
|0.17828
|1.65793
|-
|2
|2
|1
|4
|3.43435
|1.74182
|0.20332
|1.66994
|0.11075
|1.76221
|-
|2
|2
|1
|5
|2.48643
|1.76219
|0.13714
|1.7396
|0.09636
|1.75624
|-
|2
|2
|1
|6
|1.41151
|1.82292
|0.15415
|1.6725
|0.06549
|1.80013
|-
|2
|2
|1
|7
|0.9096
|1.8409
|0.08811
|1.7823
|0.03467
|1.85275
|-
|2
|2
|2
|1
|1.85358
|1.83615
|0.28355
|1.64765
|0.06055
|1.83138
|-
|2
|2
|2
|2
|3.81188
|1.74978
|0.25972
|1.62799
|0.11238
|1.7646
|-
|2
|2
|2
|3
|3.16717
|1.76679
|0.29832
|1.53409
|0.09407
|1.78959
|-
|2
|2
|2
|4
|2.33664
|1.78934
|0.22694
|1.60101
|0.07273
|1.80371
|-
|2
|2
|2
|5
|2.01675
|1.79303
|0.10664
|1.79792
|0.06062
|1.8184
|-
|2
|2
|2
|6
|1.80809
|1.80081
|0.13659
|1.70935
|0.07335
|1.79213
|-
|2
|2
|2
|7
|1.01661
|1.8295
|0.0548
|1.84688
|0.03414
|1.84213
|-
|2
|2
|3
|1
|2.01474
|1.8142
|0.21867
|1.74325
|0.05359
|1.83088
|-
|2
|2
|3
|2
|3.53989
|1.71985
|0.28196
|1.60868
|0.10823
|1.73763
|-
|2
|2
|3
|3
|3.38412
|1.69907
|0.27409
|1.56164
|0.11042
|1.71397
|-
|2
|2
|3
|4
|2.2171
|1.74622
|0.16076
|1.70107
|0.07372
|1.75906
|-
|2
|2
|3
|5
|1.11799
|1.80944
|0.11087
|1.75678
|0.03792
|1.81891
|-
|2
|2
|3
|6
|1.40464
|1.76033
|0.10048
|1.72933
|0.05342
|1.75745
|-
|2
|2
|3
|7
|0.11328
|1.8972
|0.04052
|1.87101
|0.00787
|1.88753
|-
|2
|2
|4
|1
|2.59777
|1.74476
|0.28154
|1.66509
|0.10763
|1.71072
|-
|2
|2
|4
|2
|3.53853
|1.69511
|0.38311
|1.46839
|0.13243
|1.66523
|-
|2
|2
|4
|3
|2.80538
|1.70587
|0.26686
|1.55787
|0.1126
|1.68024
|-
|2
|2
|4
|4
|2.18191
|1.72068
|0.18333
|1.65612
|0.085
|1.71029
|-
|2
|2
|4
|5
|1.23383
|1.7716
|0.12824
|1.71179
|0.04845
|1.76628
|-
|2
|2
|4
|6
|0.85652
|1.79279
|0.0763
|1.79314
|0.03563
|1.78528
|-
|2
|2
|4
|7
|0.97995
|1.77178
|0.0797
|1.7577
|0.03846
|1.77043
|-
|2
|2
|5
|1
|2.47016
|1.74985
|0.32061
|1.60073
|0.10455
|1.71058
|-
|2
|2
|5
|2
|3.76194
|1.68979
|0.32787
|1.54675
|0.11781
|1.69109
|-
|2
|2
|5
|3
|2.61421
|1.70766
|0.20307
|1.64866
|0.08315
|1.71378
|-
|2
|2
|5
|4
|1.6809
|1.74028
|0.16795
|1.66491
|0.06202
|1.73305
|-
|2
|2
|5
|5
|1.31241
|1.75722
|0.14383
|1.68302
|0.05338
|1.74562
|-
|2
|2
|5
|6
|1.66563
|1.71781
|0.12721
|1.69231
|0.06147
|1.72101
|-
|2
|2
|5
|7
|0.87471
|1.74991
|0.07882
|1.71706
|0.04173
|1.73246
|-
|2
|2
|6
|1
|1.70055
|1.72832
|0.20839
|1.67759
|0.06001
|1.71779
|-
|2
|2
|6
|2
|3.20558
|1.65143
|0.33676
|1.47797
|0.09642
|1.6546
|-
|2
|2
|6
|3
|1.5827
|1.71538
|0.19719
|1.62038
|0.05324
|1.71254
|-
|2
|2
|6
|4
|1.7692
|1.69473
|0.14854
|1.66225
|0.05758
|1.69946
|-
|2
|2
|6
|5
|1.33003
|1.70542
|0.10726
|1.69398
|0.04565
|1.7096
|-
|2
|2
|6
|6
|1.01266
|1.71155
|0.09376
|1.70285
|0.04005
|1.70822
|-
|2
|2
|6
|7
|0.9856
|1.70091
|0.06454
|1.73063
|0.0394
|1.69796
|-
|2
|2
|7
|1
|2.02441
|1.67788
|0.30435
|1.5407
|0.08673
|1.63673
|-
|2
|2
|7
|2
|1.43949
|1.71143
|0.30098
|1.47963
|0.06527
|1.67295
|-
|2
|2
|7
|3
|1.68946
|1.66442
|0.24777
|1.47116
|0.06594
|1.64834
|-
|2
|2
|7
|4
|1.10967
|1.68591
|0.15663
|1.60109
|0.04949
|1.67069
|-
|2
|2
|7
|5
|0.77866
|1.70882
|0.11248
|1.64389
|0.03402
|1.70215
|-
|2
|2
|7
|6
|0.67502
|1.69719
|0.10289
|1.62419
|0.03507
|1.67744
|-
|2
|2
|7
|7
|0.65216
|1.70336
|0.05545
|1.73388
|0.02233
|1.72102
|-
|2
|2
|8
|1
|1.33877
|1.67358
|0.18369
|1.64385
|0.06055
|1.63818
|-
|2
|2
|8
|2
|0.71697
|1.71038
|0.25461
|1.49037
|0.04798
|1.66397
|-
|2
|2
|8
|3
|2.13197
|1.62429
|0.2393
|1.47673
|0.08136
|1.6065
|-
|2
|2
|8
|4
|1.16932
|1.66188
|0.13759
|1.60108
|0.0463
|1.64856
|-
|2
|2
|8
|5
|1.48369
|1.62387
|0.12547
|1.58988
|0.06919
|1.5925
|-
|2
|2
|8
|6
|1.18879
|1.65442
|0.10031
|1.62813
|0.07392
|1.58846
|-
|2
|2
|8
|7
|0.58052
|1.68546
|0.02696
|1.7382
|0.01982
|1.70519
|}
</center>
</div>
</div>

== Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme ==
<div class="mw-collapsible mw-collapsed">
<div>
=== Abstract ===
Based on comments on imprecision of the estimation method for 24-hour fat % in AM/PM milk recording schemes the regression formula was extended and re-estimated. Non-linearity for the existing effects of protein % of the milk sample, interval before sampling, milk amount of sample, milk amount of previous milking and interval before the previous milking was incorporated by using polynomials. Extensions were made by adding the effects of time of sampling, parity and month of sampling as class variables and lactation stage as polynomial. In total a reduction of the standard deviation of the difference between true and estimated 24-hour fat % of 2.4% was reached (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

'''''Keywords''''': estimation, fat %, AM/PM.

=== Introduction ===
The AM/PM milk recording routine is based on only one morning (a.m.) or evening (p.m.) milk sample which are collected in an alternating way. A condition to take part in this AM/PM milk recording in The Netherlands is that on farm electronic milk measurements (EMM) are available. EMM-data consists of time of milking and milk quantity of every milking. Based on one milk sample and the EMM-data the 24-hour fat % is estimated (Peeters & Galesloot, 2002<ref name=":2">Peeters, R. and P. Galesloot, 2002.Estimating daily fat yield from a single milking on test day for herds with a robotic milking system. J. Dairy Sci. 85, 682-688.</ref>). Also for farms with an automatic milking system (AMS) this estimation is used when only one milk sample is available for analysis on milk composition.

Based on comments from farmers on fluctuations in 24-hour fat % preliminary research was conducted. This showed that the current estimation caused an underestimation of 24-hour fat % based on an a.m.-sample of 0.09% while the estimate based on a p.m.-sample was overestimated by 0.05%. Possible causes for this fluctuation are differences in milk-fat synthesis between day- and night-time as was shown by Gilbert et al. (1972) <ref>Gilbert, G.R., G.L. Hargrove and M. Kroger, 1972. Diurnal variations in milk yield, fat yield, milk fat % and milk protein % by the test interval method. J. Dairy Sci. 56, 409-410.</ref>and Lee & Wardorp (1984)<ref>Lee, A.J. and Wardorp, 1984. Predicting daily milk yield, fat percent, and protein percent from morning or afternoon tests. J. Dairy Sci. 67, 351-360.</ref>. Other factors of imprecision in the current estimation can be caused by lactation stage and parity, two factors that are accounted for in the method of Liu et al. (2000)<ref>Liu, Z., R. Reents, F. Reinhardt and K Kuwan, 2000. Approaches to estimating daily yield from single milk testing schemes and use of a.m.-p.m. records in test-day model genetic evaluation in dairy cattle. J. Dairy Sci. 83, 2672-2682.</ref>.

The objective of this research is to re-estimate the regression formula which is used to estimate the 24-hour fat %s in AM/PM milk recording and AMS recordings with only one sample. By testing for non-linearity of current effects and introducing new explanatory variables the aim is to increase the accuracy of the estimated 24-hour fat %.

=== Material and Methods ===
The data needed for the objective had to meet a number of criteria. The most important criteria were that the data comprised:

* differences in interval between milking times;
* different milking times;
* multiple samples per cow per herd test date;
* milking time and quantity of all milkings;

Only data of farms that use an AMS met all of these criteria. Therefore the research was conducted on data of all farms that used an AMS from January 20th 2001 until July 1st 2004. Records with only one sample per herd test date were excluded from the analysis.

In order to estimate as well as validate the new regression formula the each herd test date was assigned at random into two separate datasets. Dataset 1 was used for estimation and contained 371.528 samplings on 50.591 cows on 537 farms. Dataset 2 was used for validation and contained 371.885 milkings on 50.643 cows on 538 farms. Some characteristics of variables of both datasets are presented in Table 1.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" |'''''Table 1. Characteristics of variables in dataset 1 (estimation) and dataset 2 (validation).'''''
|-
| rowspan="2" |'''Variable'''
| colspan="2" |'''Dataset 1 (estimation)'''
| colspan="2" |'''Dataset 2 (validation)'''
|-
|'''Mean'''
|'''Std'''
|'''Mean'''
|'''Std'''
|-
|Sample milk amount (kg)
|10.1
|3.1
|10.1
|3.1
|-
|Sample fat (%)
|4.40
|0.76
|4.41
|0.76
|-
|Sample protein (%)
|3.49
|0.35
|3.49
|0.35
|-
|Time at sampling
|12.29
|7.24
|12.31
|7.24
|-
|Interval before sample (min)
|520
|154
|521
|155
|-
|Interval before prev. milking (min)
|526
|158
|527
|159
|}
</center>

=== Methods ===
The analysis started with the currently used regression formula which uses the effects: fat %, protein %, milk amount of sampling, interval before sampling, milk amount of the previous milking and interval before the previous milking (Peeters & Galesloot, 2002<ref name=":2" />). All these effects are considered to be linear. As an extra check of the data this regression formula was re-estimated and compared to the currently used regression formula. In order to estimate the regression formula first of all the 24-hour fat % was determined by using a weighted average of all milk samples for that cow on that herd test date.

Subsequently, a number of changes to the regression formula were tested for their effect on the accuracy of the 24-hour fat %. The changes that are tested are:

# non-linearity of the current effects;
# effect of time at sampling;
# effect of lactation stage;
# effect of parity;
# month of milk recording;

The effects were all tested in a similar way by plotting the residuals of the regression formula without the effect that is tested to the tested effect. Based on this plot a possible relation between residual and effect becomes clear and the best way of incorporating the effect is shown. The conclusion if an effect had a positive effect on the accuracy of the regression formula was based on the standard deviation of the difference between estimated and true 24-hour fat %. Also the correlation between the two fat %s and the b-factor (regression coefficient) of the linear regression between the two fat %s were considered.

=== Results ===
The regression coefficients of the re-estimated regression formula differed slightly from the estimates by Peeters & Galesloot (2002)<ref name=":1" />, probably due to the different dataset.

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %.
[[File:Imagefig1.png|center|thumb|''Figure 1a: Average residual per class for the variables sample fat %'']]
[[File:Imagefig1b.png|center|thumb|''Figure 1b: Sample protein %'' ]]
[[File:Imagefig1c.png|center|thumb|''Figure 1c : Interval before sampling'']]
[[File:Imagefig1d.png|center|thumb|''Figure 1d : Interval before previous milking'']]
[[File:Imagefig1e.png|center|thumb|''Figure 1e : Sample milk amount'']]
[[File:Imagefig1f.png|center|thumb|''Figure 1f: Milk amount before sampling'']]

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %. Of all variables, only fat % of the milk sample (Figure 1a) seemed to be linear. A 2nd order polynomial fitted the interval before the previous milking. The other variables, i.e. protein % of the milk sample, interval before sampling, milk amount of sample and milk amount of the previous milking were described by a 3rd order polynomial. For all variables except fat % of the sample higher order polynomials were found significant. This however was caused by the large amount of data and no longer a possible biological effect since it also had no effect on the accuracy of the estimation.

The effect of time of sampling showed a large amount of variability over time. Using a polynomial to fit the data was therefore difficult. Estimation of the effect by hourly intervals was a good alternative as is shown in Figure 2. Lactation stage had mainly an effect in the first 50 days of lactation as is shown by Figure 3. A 3rd order polynomial fitted the data properly.
[[File:Imagefig2.png|center|thumb|''Figure 2. Average residual per class for time of sampling (minutes after midnight).'']]
[[File:Imagefig33.png|center|thumb|''Figure 3. Average residual per class for lactation stage (days).'']]

The effects of parity and month of milk sampling were both considered as class variables. For parity the effects of parity 1 to 6 and 7 or higher were considered. Table 2 shows that mainly for the lower parities the estimated 24-hour fat % was overestimated. Also the months May to October, usually the pasture period, showed an overestimation of 24-hour fat %.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" |'''''Table 2. Effect of parity and month of sampling on estimated 24-hour fat % (*100).'''''
|-
|'''Parity'''
|'''Estimate'''
|'''Month of sampling'''
|'''Estimate'''
|-
|1
|<nowiki>-6.58</nowiki>
|January
|<nowiki>-0.24</nowiki>
|-
|2
|<nowiki>-3.56</nowiki>
|February
|<nowiki>-0.28</nowiki>
|-
|3
|<nowiki>-1.42</nowiki>
|June
|<nowiki>-0.54</nowiki>
|-
|4
|<nowiki>-0.48</nowiki>
|April
|<nowiki>-0.27</nowiki>
|-
|5
|<nowiki>-0.35</nowiki>
|May
|<nowiki>-2.07</nowiki>
|-
|6
|<nowiki>-0.35</nowiki>
|June
|<nowiki>-3.36</nowiki>
|-
|7+
|<nowiki>-0.00</nowiki>
|July
|<nowiki>-4.32</nowiki>
|-
|
|
|August
|<nowiki>-5.52</nowiki>
|-
|
|
|September
|<nowiki>-4.74</nowiki>
|-
|
|
|October
|<nowiki>-2.24</nowiki>
|-
|
|
|November
|<nowiki>-0.97</nowiki>
|-
|
|
|December
|<nowiki>-0.00</nowiki>
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" |'''''Table 3. Statistics of the difference between true and estimated 24-hour fat % for six regression formulas (current, re-estimated + five steps), each also including preceding steps.'''''
|-
|style="text-align: left;"|'''Regression'''
|'''Std.'''
|'''Min'''
|'''Max'''
|'''Cor'''
|'''b-factor'''
|-
|style="text-align: left;"|Current, re-estimated
|0.2856
|<nowiki>-1.840</nowiki>
|2.224
|0.898
|0.807
|-
|style="text-align: left;"|Non-linearity
|0.2820
|<nowiki>-1.890 </nowiki>
|2.198
|0.901
|0.812
|-
|style="text-align: left;"|Time of sampling
|0.2817
|<nowiki>-1.877 </nowiki>
|2.211
|0.901
|0.813
|-
|style="text-align: left;"|Lactation stage
|0.2803
|<nowiki>-1.883 </nowiki>
|2.196
|0.902
|0.814
|-
|style="text-align: left;"|Parity
|0.2794
|<nowiki>-1.887 </nowiki>
|2.179
|0.903
|0.816
|-
|style="text-align: left;"|Month of sampling
|0.2788
|<nowiki>-1.868 </nowiki>
|2.175
|0.903
|0.817
|}
</center>

Table 3 shows some statistics of the difference between the true and estimated 24-hour fat % based on dataset 2 (validation) of the different regression formulas. Each of the five changes to the regression formula had a (minor) positive effect on either the standard deviation of the difference between the true and estimated 24-hour fat % (Std.), the correlation (Cor) between the two fat %s, the b-factor of the linear regression between the two fat %s or a combination of the these. All changes together reduced the standard deviation with 2.4% from 0.2856 to 0.2788, increased the correlation from 0.898 to 0.903 and increased the b-factor from 0.807 to 0.817.

=== Conclusions ===
The regression formula to estimate the 24-hour fat % based on one milk sample was improved. Improvements were first of all considering non-linearity of the variables by using polynomials for protein % of the milk sample (3rd order), interval before sampling (3rd order), milk amount of sample (3rd order), milk amount of previous milking (3rd order) and interval before the previous milking (2nd order). Secondly, adding the effects of time of sampling (class variable), lactation stage (3rd order polynomial), parity (class variable) and month of sampling (class variable) gave a further reduction of the difference between true and estimated 24-hour fat %. The total reduction in standard deviation of the difference between true and estimated 24-hour fat % is 2.4% (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

== Appendix 3 - A unified Python implementation of standardized 305 day yield calculation methods ==
The ICAR guideline is translated into an open-source Python package that can serve as a reference implementation for 305-day yield calculation. In addition to implementing the methods described in the original guideline (with the exception of the multi-trait method, which will be added in future work), the package incorporates 14 lactation-curve models, including traditional parametric models, Bayesian fitting approaches, and an AI-based model. The package also provides tools to derive biologically relevant lactation characteristics such as time to peak, peak yield, cumulative yield, and persistency. The package is publicly available through PyPI and can be installed directly using pip install lactationcurve (van Leerdam et al., 2026). Extensive documentation was developed alongside the package to improve transparency and reproducibility [https://bovi-analytics.github.io/bovi/lactationcurve.html https://bovi-analytics.github.io/bovi/lactationcurve.html.]

Through a companioning website (https://tools.bovi-analytics.org<nowiki/>/), users can upload milk-recording data in CSV format, fit and visualize the implemented lactation-curve models, and compare different cumulative milk-yield methodologies on both test-day and fully daily-recorded lactations using metrics such as RMSE, Pearson correlation, MAPE, and MAE. Reference datasets are provided to allow organizations to benchmark their own calculations against alternative methodologies. In addition, downloadable PDF reports summarize the results through detailed statistics and scatterplots, both overall and stratified by parity.
</div>
</div>

Section 02 – Cattle Milk Recording

2026-07-22T17:41:44Z

Cmosconi: /* Procedure 1: Computing 24-hour Yields */

= Overview =
<div class="mw-collapsible mw-collapsed">
<div>
== Introduction ==
Information about milk production traits is very important for managing and breeding dairy herds. The milk recording process starts with the collection of animal identification, a calving date of milking cows, the amount of milk given and the date with time or time frame of a day. A milk sample may be taken. The obtained milk sample is analysed for milk constituents. The results of the analysis plus the data about milk yield and time of milking are stored in a database. Subsequently a number of parameters, cumulative yields and indices are calculated and stored in the database and, finally, reported to the farmer

This Section 2 of the ICAR Guidelines focuses on the milk recording process for dairy cattle.

== Scope ==
Figure 1 gives a pictorial summary of the main elements of this guideline.

In summary, this section of the ICAR Guidelines covers the milk recording process from the enrolment of a herd for milk recording, through to the delivery of information which a herd owner can use to assist in a range of decisions.
[[File:Scope of Section 2 - Dairy cattle milk recording..png|thumb|Figure 1. Scope of Section 2 -Dairy cattle milk recording.|center|524x524px]]

Not covered in this section are:
# Standards and guidelines for ICAR approval of milk recording devices. Please consult [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices|Section 11]] for this subject.
# Standards and guidelines for ICAR approval of ID devices. Please consult [[Section 10 – Identification Device Certification|Section 10]] for this subject.
# Standards and guidelines for preparation of milk samples and for quality assurance of milk analysis. Please consult [[Section 12 – Milk Analysis|Section 12]] for this subject.
# Standards and guidelines for in-line milk analysis on the farm. Please consult [[Section 13 – On-farm Milk Analysis|Section 13]] for this subject.

== Enrolment ==

Enrolment of new herds in the recording process should involve an agreement between the farmer and the recording organisation regarding technical and financial questions such as:

# General information about the recording programme itself, i.e.
#* Herd and cow identification.
#* Scope of recorded data, including database setup as required by the user.
#* Scheduling recording.
#* Data capture and processing.
#* Recording methods and intervals.
#* Milk measuring and meters.
#* Sampling and sample transport.
#* Reports (outcomes) and supporting decisions.
# Definition of supervision scheme and other quality assurance and plausibility checking steps.
# Fee structure and invoicing.
# Approval of technicians by milk recording organisations (MROs) so as to give them free access to farms for all recording and supervision actions.

In cases where the owner of the recorded cows or his employees carry out the recording itself, it is up to the organisation to decide upon, and provide for, any necessary training.

== Standard and Guidelines for Milk Recording ==
These standards and guidelines for milk recording are valid for all milking systems, including AMS where applicable.
====General Standards and Guidelines for milk recording====
#ICAR-approved (electronic) milk meters and sampling devices must be used on the recording day (see [https://wiki.icar.org/index.php/Section_11_%E2%80%93_Testing,_Approval_and_Checking_of_Measuring,_Recording_and_Sampling_Devices#Procedure_1:_Procedure_for_Application_for_Testing_of_Measuring,_Recording_and_Sampling_Devices_or_Sensor_Systems Procedure 1 of Section 11 - Guidelines for Testing, Approval and Checking of Milk Recording Devices]). The list of approved milk meters, jars and AMS and automatic milk sampler/tray combinations sampling devices can be found on the [https://www.icar.org/index.php/certifications/icar-certifications-for-milk-meters-for-cow-sheep-goats/ ICAR web page].
#Milk weights are recorded for each milking of the recording period. The measurement may be done using any of the ICAR approved recording devices, or by weighing. The minimum accuracy of the measurement is 0.2 kg.
#Where milk constituents are analysed, the equipment used must meet ICAR standards for accuracy. Please consult [[Section 12 – Milk Analysis|Sections 12]] and [[Section 13 – On-farm Milk Analysis|Section 13]] of the Guidelines for details.
#The accuracy of the equipment used for milk recording and sampling must be checked by an agency approved by the member organisations, on a regular and systematic basis using methods approved by ICAR. The list of methods is given in [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices#Procedure 6: Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices|Procedure 6 of Section 11]] - Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices.
#All analyses of the constituents of a milk sample must be carried out on the same milk sample.
#These samples should ideally represent the 24-hour milking period.
#If milk samples do not represent a 24-hour period, the results of milk analyses must be corrected to a 24-hour period by a method approved by ICAR (see [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]).
#In cases where the duration of recording deviates from 24 hours, the results must be converted into 24-hour yields. Only approved 24-hour yield calculation methods can be used. The appropriate methodology is described in [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]
#As date of recording, we recommend to use the date on which the last sample was taken. As alternative, the date of the first sample can be used.
#Calculation methods
##The quantities of milk and milk constituents shall be calculated according to one of the methods outlined in this section of the ICAR Guidelines (see [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Standard methods for calculating 24 hour yields]).
##Member organisations should keep the ICAR Secretariat informed about the calculation methods being used by the records processing operations in their organisation or country and shall be responsible for ensuring that the records are corrected and calculated as specified in this section of the ICAR Guidelines.
====Standards and Guidelines for milk recording using AMS====
This subsection covers systems where milk weights, milk quality or other traits of the cows are monitored constantly and automatically. This can be done in both automatic and manually operated milking systems.

Requirements:
*Animal identification is automatic and reliable. Farm transponders can also be used for automatic identification if they are linked to the cow’s official identification in farm software.
*All individual milkings must be recorded from all AMSs in the farm and transmitted to the recording database for calculation, interrupted milkings included.
*For official milk recording purposes, the data file obtained from electronic milk meters must contain the following: 1) Cow ID, 2) Milking time stamp, 3) Milk weight and 4) Sampling stamp to mark the milking where the sample comes from.
*All milkings within the recording period may be sampled, and in this case the samples should be analysed separately. Alternatively, a one-milking sample can be taken for each cow, followed by fat correction calculation.
*All cows in milk on the recording day have to be sampled. The sampling device must remain in operation until all cows are sampled. When the number of available sampling devices is smaller than the number of AMS units, sampling may need to be prolonged beyond one day to allow complete sampling of all cows. In that case, the sampling device has to be moved between AMS units.
*During sampling, the automatic sampler must be monitored to make sure there are vials left for the next cows.
*24-hour yield calculations must be carried out by a MRO, independently of the AMS manufacturer. This is done in order to guarantee harmonisation of calculation methods between the different brands of equipment and software.
*Data of all milkings over a given time period must be collected for the 24-hour milk yield calculation. A 96-hour data collection period is recommended.
Recommendations:
#Ideally, data of all milkings should be collected and used to compute lactation yield.
#Description of formats to exchange data recorded by an AMS can be requested from the manufacturer or the ICAR ADE data exchange standard for milking data can be used.
#In the case of milk recording method B (see [[Section 02 – Cattle Milk Recording#Recording|chapter 1.4 "Recording]]") with AMS, the milk recording organization should make sure that the farmer knows how to load or transfer data.
#Data can be extracted by: 1) manual operation by MRO Technician’s or Farmer (file extraction), 2) automated system and data transfer through an Application Programming Interface (API), 3) another data transfer and exchange system.
#Raw milk recording data from the AMS must be easily accessible for MRO data processing.
#For official milk recording purposes, the data file obtained from electronic milk meters may also contain the following: 1) Vial ID (this is obligatory with M sampling scheme), 2) Milking duration, 3) Milking speed, 4) Incomplete milking in automatic milking systems and 5) Other relevant data measured or reported by the equipment.
#Individual milkings should be tested for milk secretion rate in order to detect interrupted and unrecorded milkings, which in turn have an effect on the calculated 24-hour yields. If there is an interrupted milking or a milking that follows an interrupted milking at the beginning of the recording period, these two milkings must be excluded from the calculations. During the recording period they can be excluded but do not need to be.
#It is recommended to individually sample all milkings within the 24-hour recording period for 24-hour fat content calculation due to the high variability of milking frequency and milk fat content. In cases where sampling all milkings is not possible, please consult Chapter 2 of [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 - Computing 24-hour Yields] (for approved correction calculation methods).
#It is recommended to sample only milkings with a preceding interval longer than 4 hours.
====Authorisation to record====
It is recommended that professional milk recording technicians are trained and certified before they carry out recordings on their own. Ideally, such training includes a period of supervised work with a certified technician. Where such a certification system is in place, it is not allowed to record without an authorisation.

It is also recommended that frequent training is given to milk recording technicians on new technologies and equipment, safety instructions and data quality issues.

In B and C recording, farmers or their employees doing the practical recording need to be capable of operating the recording equipment correctly (e.g. milk meters, data capture tools) and are familiar with recording techniques.

It is recommended to have a conformation test from a certified recording agency and that frequent training take place.
====Cows to be recorded====
In a recorded herd, all milk-producing cows must be recorded. If a herd is divided into groups, all animals in the group have to be recorded on the same recording scheme. If different recording schemes are practiced on the farm all cows must be recorded according to the standards for recording and sampling intervals in table 3.

Acceptable reasons for missing data are discussed below, in 5.5. Missing results and/or abnormal intervals are reported [[Section 02 – Cattle Milk Recording#Missing results|here]].

===Identification (ID)===
====Herd ID====
Each herd in milk recording must be allocated a unique permanent identification number.
====Animal ID====
An official milk recording system must be based on a clearly identifiable and unique animal ID. It is recommended that one identification scheme for the whole country is used. Animal identification must also be in accordance with national and international regulation (e.g. EU member countries with EU legislation - 1760/2000 for cattle), and with relevant parts of currently valid ICAR Guidelines. The animal must be marked with an ICAR approved identification device or system. If the ID of imported animals is changed, the connection to the original ID must be maintained. Management numbers for cows can be used aside the official ID.
====Identification of the sample vial====
The sample, the milk weight and the cow ID must be linked at the milking.

Vials can be identified according to:
#Vial placement in the sampling unit.
#Cow or sample ID written on the vials.
#Barcoded vial with printed cow ID.
#Barcoded vial with cow ID registered at the milking.
#RFID vial with cow ID registered at the milking.
=====Sample identification without electronic equipment=====
Samples are identified according to their placement in the sampling unit. Additionally, sample or cow numbers can be written on the vials with a waterproof marker. If this marking is not done, there must be a sure and efficient way to identify sample No. 1 (e.g. different colour) and the sequence of other samples.

Each sampling unit must be connected to a list of samples where cow ID is given for each sample. Each transportation box also has to carry the relevant herd ID’s and, preferably, the sampling dates.
=====Barcoded vials=====
Samples are identified according to the barcode on the vial label.

If the label contains cow and/or herd ID, no electronic equipment is needed at the recording. The samples can be sent to the laboratory without accompanying sample lists or herd ID markings on the box.

If the label contains a random sample ID number, the cow ID must be connected with it on the farm. This is done with a barcode reader and computer programmes making the connection possible.
=====Vials with RFID=====
Samples are identified according to the RFID chip in the vial. This system requires the use of RFID readers and specific computer programmes creating a file where the cow and vial ID’s are connected.
=====Automatic sampling systems=====
In automatic milking systems (AMS), ICAR approved automatic samplers have to be used. Sample identification in these systems can be based on vial placement, barcode or RFID. The file with corresponding cow ID is in the management programme of the milking system. Data transfer is carried out with specific software and via a specific interface from the AMS to the MRO.
=====Sample ID in the laboratory=====
For impartiality and better quality, it is recommended that the samples are identified without cow ID and sent to the laboratory anonymously and the analysis results are merged afterwards in the data processing centre.
====Connection of the sample to milking and 24 h yield====
=====Sample and milk weight from the same milking=====
The ideal situation is that the sample and milk weight represent the same milking.
=====Sample from one milking, milk weight from two=====
A corrected analysis is routinely attached to the 24-hour yield.
=====Sample from one milking, milk weight from two or more, corrected by intervals=====
In this case, a 24-hour-yield is also combined with a one-milking sample, but the 24‑hour yield is obtained by correcting the recorded milkings according to the length of the preceding milking intervals. For example, if a cow has produced 20 kg milk in two milkings and the preceding intervals total 20 hours, her 24-hour yield is calculated as 20 kg * (24 h/20 h) = 24 kg. A corrected analysis is attached to this 24‑hour yield.
=====Sample from one milking or day, milk weight from several days=====
With electronic milk meters, it is possible to use the milk production from several days. This gives better accuracy of milk yield estimation; the highest accuracy with uncorrected milk weights is reached using a 4-day average. The problem is that the sample results become disconnected from the milk yield and a loss in fat and protein yield accuracy will occur. Ideally, fat and protein production should be connected to the recording day even in AMS.

In this case, there are three options to connect samples to the 24-hour yield:
#Milk weight is estimated from a longer measurement period but for fat and protein yield estimation only the milk yield on sampling day is used.
#Information only from the recording day for constituents in milk and milk yield estimation.
#Combination of multiple day milk yield with constituents from sampling. See ICAR procedures for using data from more than one day (Lazenby ''et al''., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>, estimation of fat and protein yield (Galesloot and Peeters , 2000)<ref name=":1">Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>.
The analysis data are merged with milk weights in the laboratory or data processing centre and the date of the analysis must be known.

=== Traits to be recorded ===

==== Definition of milking speed and box time ====

===== Introduction =====
Automated Milking Systems (AMS) do measure many traits. The definition of these traits might be different per brand of AMS. Data of these traits is often used by e.g. milk recording organisations, herdbooks or management software providers. When organisations store these data in their databases and use for certain services, it is important to know how these traits are defined.

These definitions could be used by milk recording organisations etc. to take into account differences between traits measured by different brands of AMS. These definitions could also be used by manufacturers of AMS to take into account for product development, to get more alignment in trait definitions between different brands of AMS.

Aim of this document is to propose a harmonized definition of some traits measured by AMS.

At this stage, the traits milking speed and box time are taken into account. Traits related to teat coordinates are described in Section 5 (Conformatoin Recording) of the ICAR guidelines.

==== Average milking speed ====
Definition = AverageMilkingSpeed (gr/min) = {TotalMilkYield / TotalMilkingTime}

* Total milk yield (kg) = Sum of all quarter level milk yields (kg)
* Total milking time = Last Take-off time (of any teat) - Begin of milk flow (of any teat)

Recommendations for manufacturers:

* Exclude any pre-treatment time from milking time.
* Provide take-off settings (threshold in gr/min at take-off, user-defined or default) and settings for the beginning of the measurement period, as milking time will be influenced by take-off settings and by the definition of the beginning of the milk flow.

Recommendations for data users:

* Don't report milking sessions with kick-off´s, interrupted and re-attached milkings because milking time will vary for these milkings.

==== Box time ====
Different types of box time:

* Milking
* Feed-only
* Pass-through
* Selection
* Training

Definition = {End box time - Begin box time} (HH:MM:SS)

* Begin box time = datetime of recognition of animal
* End box time = datetime when cow has exited the box (which might be different from opening of the gate), best to detect when cow has actually left the box

Additional data is needed to understand the status and completeness of the milking visit (Wethal and Heringstad, 2019). Registered issues during the milking are e.g.

* ff: at least 1 teat cup kicked off
* TeatNotFound: unable to find at least 1 of the teats for milking
* IncompleteMilking/FailedMilking: Minimum of 1 teat was registered as incompletely milked.
* The expected milk yield for a milking session depends on previous milkings. Settings like yield less than 80% of expectation for a teat, the milking session would be recorded as having an incompletely milked teat.
* Manual interaction like teat manually attached or milking finished manually.

Recommendations for manufacturers:

* Make the codes available that express if a milking was successful and the cause if the milking was not successful.
* Uniform names and definitions for interrupted, incomplete or failed milkings as well.

Recommendations for data users:

* Check the availability of a code that expresses if a milking was successful and the cause if the milking was not successful. The meaning of the code can be used to consider if the box time record has to be used for the intended purpose or not.
* To check if there is any extra box time due to feeding concentrates, e.g. through user specific settings such as 'PriorityFeeding'.

=== Traits to be recorded ===
In official milk recording, the following data have to be recorded, wherever available:

# Identification of each cow in the herd, even if they remain in the herd for a very short time.
# Birth date, sex, breed and parents of each animal when known.
# All services and embryo flushings and transfers: date, recipient, sire, dam of the embryo.
# All animal deaths and movements between farms and owners.
# Recording dates and locations.
# Milk yields for each cow and recording date.
# Fat content in milk for each cow and sampling date.

It is recommended to record also the following:

# Protein content in milk for each cow and sampling date.
# Milk somatic cell count for each cow and sampling date.
# Other results obtained from milk analysis.
# Milking duration and milking speed where possible.
# Milking times during recording.
# Recording methods and respective symbols used in records.
# Information about cow during the rearing period.

=== Recording method ===
The recording method for the herd consists of using five different symbols for:

# Responsibility for the practical recording.
# Sampling scheme.
# Recording interval.
# Sampling interval (if different from the above).
# Number of milkings per day (especially any deviation from 2x milking).

The symbols in Table 2 should be used:<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Symbols for milk recording schemes.''
|- style="background-color:#efefef; text-align:center;"

|'''Responsibility for recording'''
|'''Sampling scheme'''
|'''Recording interval (weeks)'''
|'''Sampling interval (weeks)'''
|'''Number of milkings per day'''
|-
| style="text-align:center;" | A
| style="text-align:center;" | P
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | B
| style="text-align:center;" | E
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | C
| style="text-align:center;" | Z
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" |
| style="text-align:center;" | T
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" |
| style="text-align:center;" | M
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:center;" | R x
|-
| style="text-align:center;" |
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | S x
|}
</center>

As an example: Recording method is CP36, 2x means that this is a recording where records/ samples are taken partly by the owner (farmer), and partly by a technician from the MRO, where the recording frequency is every 3 weeks, where the sampling frequency is every 6 weeks, and where the number of milkings per day is 2. If a national nomenclature system is used, it should be possible to transfer this system into ICAR nomenclature.

The reference milk recording method is by a representative of the recording organisation, measuring and sampling every four weeks, with proportional sampling and two milkings per day (AP44, 2x).

Recording other than by the reference method must be indicated using the appropriate symbols.

It is recommended that a limit is set for changing the recording method e.g. so that normally it is only possible to change the method twice per year.

It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

In the next sections the symbols are explained:
====Responsibility for the recording====
This symbol indicates who is responsible for measuring the milk yields and taking samples in the herd.
#Representative of the MRO (Method A; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Farmer or his/her representative (Method B; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Mixed responsibility (Method C; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
====ICAR Standards for sampling schemes====
=====Proportional sampling (P)=====
Samples and milk weights are taken at each milking during the recording day. The sampled amount corresponds to the milk yield of each milking. This is achieved by the use of a pipette in equal number of pipetting at each milking or of a specially designed tool which ensures proportional sampling to create one mixed sample. This is the default sampling scheme with no necessary correction to the analysis results, all other schemes must be reported.
=====Equal measure sampling (E)=====
Samples and milk weights are taken at each milking during the recording day. The amount of the sample is measured to be equal at each milking and mixed into one sample. The analysis results for fat should be corrected if one of the milking intervals is shorter than 10 or longer than 14 hours.
=====Multiple sampling (M)=====
Samples are taken at more than one milking during the recording day while milk weights are taken at each milking or over several days. Samples from different milkings are not mixed but they are kept in distinct vials so that each cow has at least two samples. The analysis results must be corrected to correspond to the 24-hour fat and protein yields. For example: a cow is milked 3x during 24 hours and 2 or 3 separate samples are taken, kept and analysed in different vials. This is the gold standard for AMS. It produces the most accurate results but is more expensive.
=====One-milking sampling with milk weights from more than one milking (Z)=====
Samples are taken from one milking during the recording day while milk weights are taken at each milking or over several days. The analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Alternated one-milking recording (T)=====
Samples and milk weights are taken during one milking, alternating between morning and evening milkings. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Constant one-milking recording (C)=====
Samples and milk weights are taken during one milking, constantly during morning or evening milking. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====In-line analysis recording (I)=====
Milk is not sampled but its constituents are continuously analysed by a stationary analyser.
====ICAR Standards for recording and sampling intervals====

<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Standards for recording and sampling intervals.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| rowspan="2" style="text-align:center;" |'''Recording or sampling interval (weeks)'''
| rowspan="2" style="text-align:center;" |'''Minimum number of recordings or samplings per year'''
| colspan="2" style="text-align:center;" |'''Interval between recordings or samplings (days)'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| rowspan="10" style="text-align:center;" |Reference method
| style="text-align:center;" |1
| style="text-align:center;" |44
| style="text-align:center;" |4
| style="text-align:center;" |10
|-
| style="text-align:center;" |2
| style="text-align:center;" |22
| style="text-align:center;" |10
| style="text-align:center;" |18
|-
| style="text-align:center;" |3
| style="text-align:center;" |15
| style="text-align:center;" |16
| style="text-align:center;" |26
|-
| style="text-align:center;" |4
| style="text-align:center;" |11
| style="text-align:center;" |22
| style="text-align:center;" |37
|-
| style="text-align:center;" |5
| style="text-align:center;" |9
| style="text-align:center;" |32
| style="text-align:center;" |46
|-
| style="text-align:center;" |6
| style="text-align:center;" |8
| style="text-align:center;" |38
| style="text-align:center;" |53
|-
| style="text-align:center;" |7
| style="text-align:center;" |7
| style="text-align:center;" |44
| style="text-align:center;" |60
|-
| style="text-align:center;" |8
| style="text-align:center;" |6
| style="text-align:center;" |50
| style="text-align:center;" |70
|-
| style="text-align:center;" |9
| style="text-align:center;" |5
| style="text-align:center;" |55
| style="text-align:center;" |75
|-
| style="text-align:center;" |Daily
| style="text-align:center;" |310
| style="text-align:center;" |1
| style="text-align:center;" |3
|}
</center>

====ICAR standards for number of milkings per day====

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 3. Symbols for number of milkings per day.''
|- style="background-color:#efefef; text-align:center;"
|'''Number of milkings per day'''
|'''Symbol'''
|-
| style="text-align:center;" | Once per day milking
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | Two milkings
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | Three milkings
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" | Four milkings
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" | Continuous milking (e.g. AMS)
| style="text-align:center;" | R x
|-
| style="text-align:center;" | Regular milkings not at the same times on each day (e.g. 10 milkings per week)
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" | Shown as the average number of milkings per day.
| style="text-align:center;" |
|-
| style="text-align:center;" | Animals that are both milked and suckled. (Number of times milked to prefix the S)
| style="text-align:center;" | S x
|}
</center>

Where a herd is dry for a period of the year, the minimum number of recordings should be adjusted proportionately to the production period.

Minimum number of herd recordings should be at least 85% of the normal number of recordings.

=== Missing results and/or abnormal intervals ===
{{anchor|Missing_results}}A recorded 24-hour yield is the best estimate of the yield and the constituents of the milk, weighed, sampled and recorded within 24 hours on the day of recording.
#When herds are normally milked at intervals such that the recording day is other than 24 hours, the yields shall be adjusted to a 24-hour interval using the following procedure (or other procedures approved by the ICAR):
#*Divide 24 by the interval, then multiply by the yield. For example:
#**For a 25 hour interval (24/25) x 35 kg = 33.6 kg
#**For a 20 hour interval (24/20) x 35 kg = 42.0 kg
#A recording is a set of daily test values for a given animal on a given day of recording, one or some or all of them can be missed (missing values)
#Missing values can be due to:
#*Out of range.
#*Sickness.
#*Disaster.
#*No sample analysis results.
#The number of the official and complete (milk, fat and protein) recordings in the lactation or other accumulated yield should be reported.
#Permitted range of the daily recorded values is given in Table 5. Outside of these ranges, the daily recorded<ref>'''Note:''' High fat breeds have breed average higher than 5.0 for fat %.</ref> value will be considered as a missing value.

<center>
{| class="wikitable"
! colspan="7" style="text-align:left;" | ''Table 5. Permitted range of the daily recorded values.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| colspan="2" style="text-align:center;" |'''Milk (kg)'''
| colspan="2" style="text-align:center;" |'''Fat %'''
| colspan="2" style="text-align:center;" |'''Protein %'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| style="text-align:center;" | Main Dairy Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 1.5
| style="text-align:center;" | 9.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 7.0
|-
| style="text-align:center;" | High Fat1 Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 2.0
| style="text-align:center;" | 12.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 9.0
|}
</center>1Note: High fat breeds have breed average higher than 5.0 for fat %The true daily recorded values collected from animals labelled by the farmer as sick, injured or under treatment must be used in the computation of the lactation record unless the milk yield is less than 50% of the previous milk yield or less than 60% of the predicted yield. In such a case, the whole set of daily recorded values may be considered as missing.

Estimates of the missing values of a daily recording can be computed by using interpolation procedures or by more sophisticated procedures approved by ICAR

== Samples ==

=== Representative sample ===
The milk sample has to represent the complete milking linked to it. This is achieved by mixing the milk thoroughly or pouring it into another vessel right before sampling.

Sampling scheme P requires using a pipette for making the sample proportional between different milkings.

With sampling scheme E, it is advisable to use a measuring cup to make sure the sample parts actually are equal.

Immediately after sampling, the vials have to be preserved, capped, shaken and marked. Samples should be stored cool and dark.

=== Transport ===
Samples should be transported for analysis to a laboratory as soon as possible after sampling.

The samples need to be packed for transport and handled during transport in a manner that guarantees that sample IDs are not compromised or mixed. It is also recommended to protect the packages from external interference.

The packing material must be clean and disposable or easy to clean.

During transportation, it is recommended that the temperature of the samples stays below +10°C.

== Database ==
Storing the recorded data in a milk recording database is an indispensable part of the recording. It is recommended to use the quickest possible means to store the data in the database in order to ensure up-to-date breeding values and management applications. Where computerised data capture is possible, it should not take more than five days after the recording to have the complete recording data set in the database.

The application of the Guidelines in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield], together with other parts of the Guidelines, ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

The guidelines on storage of data collected by the milk recording process are:

# For every recording, cow identification (ID), 24-hour milk yield or individual milk yields with a minimum of 0.2 kg (or the equivalent thereof) milk accuracy and recording date have to be stored.
# Where possible, it is advisable to store each milking separately. The data stored can include milk yield, time and date of milking, and milking scheme.
# Analysed results of the milk sample are stored, namely: sample ID, fat content (or percentage), sample status, sample type. Optional data can be stored on protein and/or lactose content, somatic cell count and additional analyses.
# Analysis results can be linked to one or more milkings of the cow.
# In case of storage or performance problems it might be necessary to remove old data of individual cow milkings from the database.
# Recording day information is the yield over 24 hours and should at least be kept in the database for the current lactation and the previous lactation.
# If recording day information is changed after batch processing it should be marked with a user-ID and time stamp.
# Yields are stored in kg or lbs or, in the case of fat and protein contents, in percent units.

The necessary additional information about how the results have been obtained include:

# Who did the recording (certified technician, farmer etc.).
# Herd and/or cow milking frequency.
# How many milkings were measured.
# How many milkings were sampled.
# Sampling scheme when sampling.
# Daily yield calculation method used.
# Recording and sampling intervals.
# It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

Basic checks for recording data:

# Farm (herd) ID: identified by a unique key.
# Animal ID: has to be unique in database.
# Format of animal ID: compliant to international standards of identification and registration.
# Recording date: less than or equal to today, greater than last recording date.
# Milk yield: stored with one decimal.
# 24 hour milk yield within range ( Table 5).
# Fat and protein content: e.g. within a range of +/- 3 standard deviation of population average (Table 5).
# Calving date: greater than birthday of cow (e.g. greater than birthday of cow + 20 months).
# Calving date: less than or equal to today.
# Sample analysis

This section of the ICAR Guidelines examines how observations are performed on farms and how data are collected, analysed and reported back to farmers. It forms an integral part with other sections of the ICAR Guidelines. It ensures that samples are analysed to the relevant degree of accuracy for the purposes of milk recording, breeding value prediction and other areas of usage. ICAR members operate in a range of situations, ranging from places with almost fully automated recording systems to areas with no roads and electricity. Therefore, the guidelines only demand standards that can be followed, irrespective of production situations and recommend more advanced options, where possible or required. Under the guidelines some practices might not be permitted while other practices are tolerated but not recommended.

== Yield calculations ==
This section covers 24-hour yields and accumulated yields for milk, fat, protein and somatic cells. It also describes the procedure for acceptance of new methods not previously mentioned in the guidelines.

The basic requirements for all calculation methods are that rounding shall only take place at the last step of the computation.

=== Lactation period ===

==== Commencement of the lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, is considered to commence is:

# The day that the cow calves (calving date), or
# In the absence of a calving date, the best estimate of the day that the cow commenced milk production.

A (valid) calving is defined as a parturition taking place:

# After the mid-point of the gestation period if a service has been recorded, or,
# After at least 75% of the normal gestation period has elapsed since the previous calving recorded if no service event has been recorded.

Any parturition falling outside the above definition shall be recorded as an abortion and shall not start a new lactation period.

For cows of dairy breeds the normal gestation length shall be deemed to be 280 days unless more specific breed information is available for use.

If the first recording is done on the calving date or within the first 4 days after calving, the milk yield and constituents at the first recording should not form part of the official lactation record, especially for automated milking systems (AMS) with multiple recorded days.

==== Completion of lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, has been completed is or:

# The day that the cow ceases to give milk (goes dry) or
# The day the cow gives less than 3.0 kg/day or 1.0 kg/milking in a recording (unless recorded sick) or
# When it is common practice not to record the dry-off date, the day of the midpoint between the last recording with the cow in milk and the first recording day with the animal dry may be assumed to be the dry-off date.

The lactation period ends on whichever date above occurs first.

Cows may be recorded as absent or sick on the recording day, without the lactation period being defined as terminated.

=== Production period ===
In the case where yield records are calculated on the basis of a period of production, usually a year, the record should be expressed as a ‘production period record‘ (symbol PP).

The production period begins the day after the end of the previous production period and ends as defined by the length (in days) of the production period.

=== Additional notes ===
For any ICAR method the interval between two consecutive recordings must routinely fulfil the value for the acceptable range on the herd level.

If the first recording occurs within 14 days from calving, then no adjustment is required to the first recorded value when computing the accumulated record. If the first recording occurs 15 to 95 days from calving, then an adjustment procedure may be applied.

If the 305th day of a lactation falls before the last recording, the interpolation method should be used also for the last period to compute the yields.

=== Standard methods for calculating 24 hour yields ===
The ICAR approved methods are presented in '''[https://www.icar.org/Guidelines/02-Procedure-1-Computing-24-Hour-Yield.pdf Procedure 1 of Section 2]'''. They include:

1. Methods for calculating daily yields from AM/PM milkings:

# Method of Delorenzo and Wiggans (1986)<ref>Delorenzo, M.A., and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. [https://www.journalofdairyscience.org/article/S0022-0302(86)80678-6/pdf J Dairy Sci 69; 2386]</ref>
# Method of Liu et al. (2019). Please note that in 2022 the method of Liu et al. (2000)<ref name=":0">Liu, Z., R. Reents, F. Reinhardt and K. Kuwan. 2000. Approaches to Estimating Daily Yield from Single Milk Testing Schemes and Use of a.m.-p.m. Records in Test-Day Model Genetic Evaluation in Dairy Cattle. [https://www.journalofdairyscience.org/article/S0022-0302(00)75161-7/pdf J. Dairy Sci. 83:2672-2682].</ref> has been updated to the method of Liu et al. (2019). We recommend to organisations that currently have implemented the method of Liu et al. (2000)<ref name=":0" /> to update to method of Liu et al. (2019).
# Method of Kyntäjä et al. (2021)<ref name=":3">1. Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. [https://www.icar.org/Documents/technical_series/ICAR-Technical-Series-no-25-Virtual-Meeting/Kyntaja.pdf ICAR Technical Series no. 25: 171-175.]</ref>

2. Methods to estimate 24h yield from Automatic Milking Systems:

# Using data on more than one day (Lazenby et al., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Using data on 1 day (Bouloc et al., 2002)<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Estimation of fat and protein yield (Galesloot and Peeters, 2000)<ref>Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>
# Sampling period (Hand et al., 2004<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D.F. 2004. Comparison of Protocols to Estimate 24 Hour Percent Fat and Protein. Presented at 34th ICAR session, Sousse, Tunisia, June, 2004. Proceedings of the 34th ICAR Meeting EAAP Publication No. 113:219-224</ref>; Bouloc et al., 2004)

3. Standard methods to estimate 24h yield from electronic milk meters:

# Estimation of 24-hour milk yield
# Using data on more than one day (Hand et al., 2006)<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. [https://doi.org/10.3168/jds.S0022-0302(06)72240-8 J. Dairy Sci. 89:1723-1726]</ref>
# Estimation of 24-hour fat and protein yield

=== Standard methods for calculating accumulated yields ===
The ICAR approved methods are presented in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_2_%E2%80%93_Computing_of_Accumulated_Lactation_Yield Procedure 2 of Section 2]. They include:

# Test Interval Method (TIM) (Sargent, 1968)<ref>Sargent, F.D., V.H. Lyton, and O.G. Wall, Jr . 1968. Test interval method of calculating Dairy Herd Improvement Association records. [https://doi.org/10.3168/jds.S0022-0302(68)86943-7 J. Dairy Sci. 51:170].</ref>
# Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987)<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. [https://doi.org/10.1016/0301-6226(87)90049-2 Livest. Prod. Sci. 17:l].</ref>
# Best prediction (VanRaden, 1997)<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. [https://doi.org/10.3168/jds.S0022-0302(97)76268-4 J. Dairy Sci. 80:3015-3022].</ref>
# Multiple-Trait Procedure (MTP) (Schaeffer and Jamrozik, 1996)<ref>Schaeffer, L.R. and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. [https://doi.org/10.3168/jds.S0022-0302(96)76578-5 J. Dairy Sci. 79:2044-2055.]</ref>

=== Procedure to approve new methods ===

# All parties interested in seeking approval for any new accumulated yield calculation method will notify the ICAR Secretariat and provide a description of the proposed method.
# These parties will provide a detailed report including statistical details, scientific references and other relevant data to the ICAR Dairy Cattle Milk Recording Working Group.
# The ICAR Dairy Cattle Milk Recording Working Group will then consider the proposal and recommend that it be conditionally approved, approved or rejected.
# The final steps will consist of approval by the General Assembly and publication in the guidelines. .

== Reporting ==
This subsection covers reports, data files, statistics and calculated key figures provided to farmers for breeding and management purposes.

It is recommended that farmers are given reports after each recording and at the end of the recording year or another longer recording period. These reports should contain data on both cow and herd level. In bigger herds, it is also advisable to present results by management groups or otherwise chosen cow groups within the herd. The reporting may be done on paper, through web pages and/or in the form of data files or electronic reports.

Where data files are distributed or direct access given to the results in the database, care must be taken that data ownership is clearly defined. This also includes defining who has access to data and how this access can be authorised.

ICAR members are advised to prepare annual statistics in a reasonable timeframe after closing the recording year. The minimum data requirements are what is needed for the ICAR [https://my.icar.org/stats/list Dairy Cattle Yearly Enquiry on-line database].

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 5. Examples of key figures for herd to be used by farmers and other users.''
|- style="background-color:#efefef; text-align:center;"
|style="text-align:left |'''Key figure'''
|style="text-align:left |'''Explanation'''
|-
| style="text-align:left;" | 12-month rolling average yield
| style="text-align:center;" | Total milk, fat and protein produced during the 365 (366) days preceding the recording divided by the average number of cows for the same period.
|-
| style="text-align:left;" | Average 305-day yield
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations finished during the reporting period divided with the number of finished 305-day lactations.
|-
| style="text-align:left;" | Average 305-day yield within a period
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations during the reporting period divided with the average number of cows on a 305-day lactation within the reporting period.
|-
| style="text-align:left;" | Average annual yield
| style="text-align:center;" | Total milk, fat and protein produced during the recording year divided by the average number of cows for the same recording year.
|-
| style="text-align:left;" | Average calving interval
| style="text-align:center;" | The average preceding intervals of all calvings second and more during the reporting period.
|-
| style="text-align:left;" | Average fat, protein or lactose contents in milk
| style="text-align:center;" | Total fat, protein and lactose yields divided by the total milk yield, usually expressed with two decimals.
|-
| style="text-align:left;" | Average lactation yield
| style="text-align:center;" | Total milk, fat and protein produced within lactations of any length finished during the reporting period divided with the number of finished lactations.
|-
| style="text-align:left;" | Average lactation yield within a period
| style="text-align:center;" | Total milk, fat and protein produced during the reporting period divided with the average number of cows in milk within the reporting period.
|-
| style="text-align:left;" | Average number of cows
| style="text-align:center;" | Average number of cows in the herd (or group) on a given day during the reporting period. Usually expressed with one decimal.
|-
| style="text-align:left;" | Average somatic cell count
| style="text-align:center;" | The average of all individual cow somatic cell counts weighted for individual milk yields.
|-
| style="text-align:left;" | Daily milk, fat and protein yields
| style="text-align:center;" | 1) Total daily milk, fat and protein yields divided by number of cows, or 2) Total daily milk, fat and protein yields divided by number of cows in milk.
|-
| style="text-align:left;" | Energy Corrected Milk (ECM)
| style="text-align:center;" | Calculated according to a national standard.
Example from the Nordic countries:

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + milk yield, kg * 0.7832)/3.14

or, if lactose has been analysed

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + lactose yield * 16.54 + milk yield, kg * 0.0207)/3.14.

From solids expressed as %:

ECM = [(fat content, % * 383 + protein content, % * 242 + 783.2)/3140]* milk yield, kg

or, if lactose has been analysed

ECM = [(fat content, % * 383 + protein content, % * 242 + lactose content, % * 165.4 + 20.7)/3140]* milk yield, kg.
|-
| style="text-align:left;" | Number of lactations
| style="text-align:center;" | Total number of finished lactations in the herd (or group) during the reporting period.
|-
| style="text-align:left;" | Reporting period
| style="text-align:center;" | The period presented in the given report. The most usual options are: one day, one recording interval, lactation, rolling 365 days, recording or calendar year, and the cow’s lifetime.
|}
</center>

== Decisions ==

As a result of the recording process and reports prepared on the basis of its results, decisions can be made on one or more of the following:

=== Short term impact: day-to-day management decisions taken on farms ===

# Decisions about bulk milk quality.
# Feeding decisions - daily diet based on group or individual performance.
# Pasture management decisions.
# Grouping decisions - placing cows in different management or feeding groups.
# Culling decisions - decisions on the sale or slaughter of cattle.
# Mating decisions.
# Decisions regarding programmes of certification for milk and milk products.
# Decisions based on data flow from MRO’s to farms and vice versa.

=== Medium-term impact ===

# Farmers’ decisions based on advisory services, veterinarians, independent experts and other services.
# Decisions about production planning on farms (herd development).

=== Long-term impact ===
# Breeding programme and selection decisions - breeding partners informed by genetic evaluation ([[Section 09 – Dairy Cattle Genetic Evaluation|Section 9)]] based on milk recording results.
# Decisions based on herd book and breeder association activities and deciding on business actions related to breeding animals, i.e. in some countries animal recording data are required for international trade with breeding animals.

=== Strategic decisions ===
# Research programmes concerning management, recording and breeding.
# Political decisions about possible subsidies in dairy cattle breeding at the governmental level and implementing measurements according to agriculture policy.

== Quality control ==
This Section together with other parts of the Guidelines ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

=== Bulk tank data comparison ===
It is a recommended practice to compare milk recording data with dairy deliveries and bulk tank milk contents. This can be done on the recording day or over a longer period of time. The calculation is done as follows:

# Comparison ratio = Total recorded milk yield, kg /Total milk produced, kg. This comparison is used where there is a reliable estimate of the farm use of milk.
# Quick comparison ratio = Total recorded milk yield, kg/ Total milk delivered, kg. This comparison is used where farm use of milk is not estimated.
# Content comparison = Recorded average fat / Bulk tank average fat
# Comparison ratio for fat = Total recorded fat yield, kg/ Total fat produced, kg
# Total recorded milk yield, kg = Ʃ (Individual milk yield, kg)
# Total milk delivered, kg = Total milk delivered, litres * milk density kg/litre
# Total milk produced, kg = (Total milk delivered, litres + Milk used or discarded on the farm, litres) * milk density kg/litre
# Total fat produced, kg = Total milk produced, kg x (Bulk tank fat percent/100)
# Recorded average fat = Ʃ [Individual milk yield kg x (Individual fat percent/100)]/Ʃ (Individual milk yield, kg)

The recommended acceptable range for comparison ratios is 0.95 - 1.05, and for quick comparison ratios 0.90 - 1.00, with due regard to herd size.

=== One day bulk tank data comparison ===
Milk yields and fat yields or contents are compared on the recording day. Comparing the contents is routinely possible where every delivery is sampled or by taking a bulk tank sample (see point [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Bulk_tank_data_comparison 1.10] above for how the comparison is done.)

=== Bulk tank data comparison over a longer period ===
Milk yields and fat yields or contents are compared over a longer period of time, e.g. 4 months or 12 months. This option requires a routine to obtain the applicable data from the dairies or milk buyers. Farm use of milk may be taken into account where applicable.

=== Bulk tank sample ===
Bulk tank samples can be used to verify the milk contents analysis obtained in milk recording. A sample is taken from a well-mixed bulk tank on the recording day. It must represent the milk of the whole 24-hour period. Bulk tank fat and protein contents are then compared to the weighted averages of the fat and protein percent obtained from milk recording. Normally, the difference between the values should not be more than 5%.

=== Supervised or repeated recording ===
Supervised recording is a tool designed to verify that individual cow records are reliable. It is based on repeating the herd recording as soon as possible after the original recording, and the obtained results are compared with the original recording. It is obligatory for ICAR Certificate of Quality (CoQ) holders to practice regular supervision, irrespective of recording methods used.

It is recommended that the supervised recording will follow immediately after the original recording, but for a good reason it can be postponed for up to 7 days.

The farmer and any other staff doing the original recording must not know that a supervised recording will follow. The technician who performs the supervised recording should not be the same person who did the original recording.

Usually supervised recording is done by recording the whole herd again, using the same sampling scheme and recording method (or a reference method) as in the previous recording. When herd size exceeds 200 cows, it is also allowed to do a supervised recording to selected, or randomised groups of animals in the herd.

Choosing the herds for supervised recording may be random or based on preselection. Traits for this preselection may include high yield, great increase in yield, presence of bull dams in the herd, and general suspicions about the correctness of herd results.

The traits compared in supervised recording must include milk and fat. Comparing protein is also recommended.

=== Supervision - example of comparison calculations ===

# Milk, fat and protein yields per cow are calculated for both the original and the supervised milking.
# Individual cow records where results between supervised recording and the original recording differ outside the norms might be excused where a good explanation can be given for exclusion (illness, heat, missed milking)
# Deviations (%) are calculated for each cow and yield constituent according to the formula: deviation = (supervised yield/unsupervised yield)*100-100
# Herd averages of the absolute values for each yield constituent are calculated.
# If the supervised recording occurs within 2 days of the original recording, the acceptable difference in herd averages are 7% for milk and protein and 9% for fat.
# If the supervised recording occurs between 3 and 7 days after the original recording, the acceptable difference of the aforementioned herd averages are 9% for milk and protein and 12% for fat.

The limits mentioned in these examples are typically applied by some of the member organisations, and are not meant to be understood as exact norms. Such norms should be laid down by each member organisation.

=== Evaluation of recording data ===
It is recommended that data quality is evaluated for each herd recording day. When such an evaluation is applied, the following features of the data have to be included:

# Person responsible for the recording.
# ICAR approval and calibration status of the recording equipment if owned by the farmer.
# Number of herd recordings per time period and/or recording interval.
# Number of herd samplings per time period and/or sampling interval.

The following features are also recommended to be included if possible:

# Deviation of milk and fat yields from dairy deliveries.
# Deviation of milk and fat yields from previous or predicted yields.
# Standard deviation of individual cow records.
# Number of recorded and/or sampled milkings within the recording day.
# Number of cows missed or not recorded in the recording.
</div>
</div>
= Procedures =
== Procedure 1: Computing 24-hour Yields ==
<div class="mw-collapsible mw-collapsed">
<div>

=== Methods to calculate 24-hour yield for milk yield and fat percentage from a single milking ===

==== Method of Delorenzo & Wiggans (1986)<ref>Delorenzo, M.A. and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. J. Dairy Sci. 69: 2386-2394.</ref> ====
Daily milk (DMY) and fat yield (DFY) estimates are based on measured yield and milking frequency. An adjustment factor accounts for differences in the average milking interval (expressed in decimal hours) between the preceding milking and the measured milking, and the time of day of the measured milking (started in a.m. or p.m.). For 2X milking, an additional adjustment is applied to milk yield for the interaction between milking interval and stage of lactation, with mid lactation (158 DIM) set to zero. Milking interval does not affect protein and solids non fat (SNF) percentages and so the percentages for the sampled milking are used for test-day estimates. Protein yield is calculated from the measured percentage and the adjusted milk yield.

The prediction of DMY and DFY from single milking on morning or evening in herds milked twice a day requires factors, that are the reciprocal of the proportion of total yield expected from single milkings in relation to the milking interval.

We propose to derive these coefficients (intercept, slope, etc.) for each country separately.

===== Adjustment of milking interval =====
The milking interval is the interval between milking time for the observed milking and the milking time preceding the observed milking. The milking interval is divided into 15-minutes classes. Factors for milk and fat yields may be calculated to each class using Equation 1:

''Equation 1. Factors for milk and fat yields.''
[[File:Equation 1.png|none|thumb|397x397px]]

===== Adjustment of lactation stage =====
Because the lactation stage of the cow has an influence on the effect of different milking intervals on milk production a second adjustment is made for every interval class through a covariate of days in milk as addition:

Covariate x (days in milk - 158)

===== Estimating sample day yields =====
Formulas for prediction sample day yields and percentages in herds with two milkings are:

''Equation 2. Equation for predicting 24-hour milk yield.''
[[File:Equation2.png|none|thumb|428x428px]]

''Equation 3. Equation for predicting 24-hour fat percentage.''
[[File:Equation3.png|none|thumb|431x431px]]

''Equation 4. Equation for predicting 24-hour fat yield.''
[[File:Equation4.png|none|thumb]]

''Equation 5. Equation for predicting 24-hour protein yield.''
[[File:Equation5.png|none|thumb|316x316px]]

===== Calculation examples =====

====== Practical Application ======
Two sets of factors are available for estimating DMY from a single milking, each for morning or evening milking sampling. The factors are calculated from the formula as described above and given in Table 1.
<center>
{| class="wikitable"
| colspan="5" align="left" |'''''Table 1. Factor of milk yield and covariate for herds milked twice a day.'''''
|- style="background-color:#efefef;"
| rowspan="2" align="center" |'''Length of milking interval in hours (minutes in decimal)'''
| colspan="2" align="center" |'''Morning milking'''
| colspan="2" align="center" |'''Evening milking'''
|- style="background-color:#efefef;"
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
|-
| align="center" |< 9.00
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.594
| align="center" |0.00378
|-
| align="center" |9.00-9.24
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.534
| align="center" |0.00485
|-
| align="center" |9.25-9.49
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.477
| align="center" |0.00486
|-
| align="center" |9.50-9.74
| align="center" |2.411
| align="center" |0.00716
| align="center" |2.423
| align="center" |0.00511
|-
| align="center" |9.75-9.99
| align="center" |2.359
| align="center" |0.00726
| align="center" |2.370
| align="center" |0.00473
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |10.00-10.24
| align="center" |2.310
| align="center" |0.00458
| align="center" |2.321
| align="center" |0.00337
|-
| align="center" |10.25-10.49
| align="center" |2.262
| align="center" |0.00399
| align="center" |2.273
| align="center" |0.00214
|-
| align="center" |10.50-10.74
| align="center" |2.217
| align="center" |0.00294
| align="center" |2.227
| align="center" |0.00000
|-
| align="center" |10.75-10.99
| align="center" |2.173
| align="center" |0.00223
| align="center" |2.183
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |11.00-11.24
| align="center" |2.131
| align="center" |0.00000
| align="center" |2.140
| align="center" |0.00000
|-
| align="center" |11.25-11.49
| align="center" |2.091
| align="center" |0.00000
| align="center" |2.099
| align="center" |0.00000
|-
| align="center" |11.50-11.74
| align="center" |2.052
| align="center" |0.00000
| align="center" |2.060
| align="center" |0.00000
|-
| align="center" |11.75-11.99
| align="center" |2.014
| align="center" |0.00000
| align="center" |2.022
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |12.00
| align="center" |2.000
| align="center" |0.00000
| align="center" |2.000
| align="center" |0.00000
|-
| align="center" |12.01-12.24
| align="center" |1.978
| align="center" |0.00000
| align="center" |1.986
| align="center" |0.00000
|-
| align="center" |12.25-12.49
| align="center" |1.943
| align="center" |0.00000
| align="center" |1.951
| align="center" |0.00000
|-
| align="center" |12.50-12.74
| align="center" |1.910
| align="center" |0.00000
| align="center" |1.917
| align="center" |0.00000
|-
| align="center" |12.75-12.99
| align="center" |1.877
| align="center" |0.00000
| align="center" |1.884
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |13.00-13.24
| align="center" |1.846
| align="center" |0.00000
| align="center" |1.852
| align="center" |-0.00190
|-
| align="center" |13.25-13.49
| align="center" |1.815
| align="center" |0.00000
| align="center" |1.822
| align="center" |-0.00231
|-
| align="center" |13.50-13.74
| align="center" |1.786
| align="center" |-0.00167
| align="center" |1.792
| align="center" |-0.00308
|-
| align="center" |13.75-13.99
| align="center" |1.757
| align="center" |-0.00258
| align="center" |1.763
| align="center" |-0.00339
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |14.00-14.24
| align="center" |1.730
| align="center" |-0.00347
| align="center" |1.736
| align="center" |-0.00509
|-
| align="center" |14.25-14.49
| align="center" |1.703
| align="center" |-0.00363
| align="center" |1.709
| align="center" |-0.00471
|-
| align="center" |14.50-14.74
| align="center" |1.677
| align="center" |-0.00332
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |14.75-14.99
| align="center" |1.652
| align="center" |-0.00316
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |≥ 15.00
| align="center" |1.628
| align="center" |-0.00235
| align="center" |1.683
| align="center" |-0.00454
|}
</center>

For estimating daily fat percentage there is only one table independent of morning or evening sampling – refer to Table 2.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" |'''''Table 2. Factor of fat percentage for herds milked twice a day.'''''
|- style="background-color:#efefef;"
|'''Length of milking'''

'''interval in hours'''
|'''Fat (percentage'''

'''factor)'''
|-
|< 9.00
|0.919
|-
|9.00-9.24
|0.927
|-
|9.25-9.49
|0.934
|-
|9.50-9.74
|0.941
|-
|9.75-9.99
|0.948
|-
|
|
|-
|10.00-10.24
|0.955
|-
|10.25-10.49
|0.961
|-
|10.50-10.74
|0.968
|-
|10.75-10.99
|0.974
|-
|
|
|-
|11.00-11.24
|0.980
|-
|11.25-11.49
|0.986
|-
|11.50-11.74
|0.992
|-
|11.75-11.99
|0.997
|-
|
|
|-
|12.00
|1.000
|-
|12.01-12.24
|1.003
|-
|12.25-12.49
|1.008
|-
|12.50-12.74
|1.013
|-
|12.75-12.99
|1.018
|-
|
|
|-
|13.00-13.24
|1.023
|-
|13.25-13.49
|1.028
|-
|13.50-13.74
|1.033
|-
|13.75-13.99
|1.037
|-
|
|
|-
|14.00-14.24
|1.042
|-
|14.25-14.49
|1.046
|-
|14.50-14.74
|1.050
|-
|14.75-14.99
|1.054
|-
|≥ 15.00
|1.058
|}
</center>

Milking-interval factors are calculated using Equation 1, where the intercept and slope are as in Table 3.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 3. Slope and intercept for milk yield and fat yield.'''''
|- style="background-color:#efefef;"
| rowspan="2" |'''Trait'''
| colspan="2" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started in a.m.'''
|'''For measured milking started in p.m.'''
|-
|Milk yield
|0.0654
|0.0634
|0.0363
|-
|Fat yield
|0.1965
|0.1939
|0.0254
|}
</center>
The milking interval has no significant influence on protein percentage. Therefore, the protein percentage of the sampled milking is used as the daily protein percentage.

====== Calculation of daily yields from morning milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Data for a cow from morning milking.'''''
|-
|Begin of recording:
|6:15
|(Morning milking)
|-
|Start of preceding milking:
|17:25
|
|-
|Length of milking interval:
|12 hours 50 minutes
|(Expressed as decimal 12.83)
|-
|Milk results at morning:
|12,0
|Milk-kg
|-
|
|4,12
|Fat-percentage
|-
|
|3,45
|Protein-percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 5. Factors for morning milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.877
|-
|The covariate is
|0
|-
|The factor for fat percentage from Table 2 is
|1.018
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 6. Example calculations for morning milking.'''''
|-
|The sample-day milk yield:
|1.877 x 12,0 kg + 0 x (120 - 158) = 22,5 kg
|-
|The sample-day fat percentage:
|1.018 x 4,12 = 4,19
|-
|The sample-day fat yield:
|22,5 kg x 0,0419 = 0,94 kg
|-
|The sample-day protein yield:
|22,5 kg x 0,0345 = 0,78 kg
|}
</center>

====== Calculation of daily yields from evening milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 7. Data for a cow from evening milking.'''''
|-
|Begin of recording:
|16:48
|Evening milking
|-
|Start of preceding milking:
|6:35
|
|-
|Length of milking interval:
|13 hours 47 minutes
|Expressed as decimal 13.78
|-
|Milk results at evening:
|14,0
|Milk kg
|-
|
|4,00
|Fat percentage
|-
|
|3,40
|Protein percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 8. Factors for evening milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.763
|-
|The covariate is
|<nowiki>-0,00339</nowiki>
|-
|The factor for fat percentage from Table 2 is
|1.037
|}
{| class="wikitable"
| colspan="2" |'''''Table 9. Example calculations for evening milking.'''''
|-
|The sample-day milk yield:
|1.763 x 14,0 kg - 0,00339 x (120 - 158) = 24,8 kg
|-
|The sample-day fat percentage:
|1.037 x 4,00 = 4,15
|-
|The sample-day fat yield:
|24,8 kg x 0,0415 = 1,03 kg
|-
|The sample-day protein yield:
|24,8 kg x 0,0340 = 0,84 kg
|}
</center>

====== Alternate recording of components and milk yield at both milkings ======
For this plan only the sample-day fat yield has to be calculated with regard to milking interval. The milk yield is the sum of evening and morning milk results.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 10. Example data for a cow from both milkings.'''''
|-
|Begin of recording evening:
|17:25
|
|-
|Milk results at evening:
|10:00
|Milk kg (only milking-yield)
|-
|Begin of recording morning:
|6:15
|
|-
|Milk results at morning:
|12:00
|Milk kg
|-
|
|4:20
|Fat percentage
|-
|
|3:50
|Protein percentage
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 11. Factor for fat percentage.'''''
|-
|Length of milking interval:
|12 hours 50 minutes (expressed

as decimal 12.83)
|-
|The factor for fat percentage from Table 2 is
|1.018.
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 12. Example calculation of daily yields.'''''
|-
|The sample-day milk yield:
|10,0 kg + 12,0 kg = 22,0 kg
|-
|The sample-day fat percentage:
|1.018 x 4,20 = 4,28
|-
|The sample-day fat yield:
|22,0 kg x 0,0428 = 0,94 kg
|-
|The sample-day protein yield:
|22,0 kg x 0,0350 = 0,77 kg
|}
</center>

====== Calculation for 3X Milking ======
For 3X herds, a single milking or two consecutive milkings may be weighed. The sample may be collected at one or both of these milkings. Stage of lactation × milking interval adjustments are not used for greater than 2× milking. These AM/PM factors for estimating daily yields in 3X herds should not be confused with factors that adjust 3X records to a 2X basis. Milking-interval factors are calculated using the same formula with the intercept and slope as in Table 13.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" align = "left" |'''''Table 13. Slope and intercept factors for 3X milking.'''''
|- style="background-color:#efefef;"
| rowspan="2" | '''Trait'''
| colspan="3" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started between 2 a.m. and 9:59 a.m.'''
|'''For measured milking started between 10 a.m. and 5:59 p.m.'''
|'''For measured milking started between 6:00 p.m. and 1:59 a.m.'''
|-
|Milk yield
|0.077
|0.068
|0.066
|0.0329
|-
|Fat yield
|0.186
|0.186
|0.182
|0.0186
|}
</center>
When two milkings are included for sampling, the intercepts and intervals for both milkings are included in determining a factor for calculated estimated milk yield that is applied to the total yield from both milkings as in Equation 6.

''Equation 6. Milking interval factor for 3X milking.''
[[File:Equation6.png|none|thumb|536x536px]]
Milk and fat percent factors are calculated separately based on the number of milkings weighed or sampled.

====== Calculation for 4X - 6X Milking ======
The intercept terms for calculating 3X factors (0.077, 0.068, and 0.066) are multiplied by the factor [3 / (milkings per day)] for use in calculating factors for milking frequencies greater than 3X.

==== Method of Liu et al. (2019) ====
A multiple regression method (MRM) is used for estimating 24-hour daily milk yield (DMY), daily fat yield (DFY) and daily protein yield (DPY) based on partial yields from either morning (AM) or evening (PM) milking. Fat percentage (DFP) or protein percentage (DPP) on a 24-hour daily basis are then derived using the estimated 24-hour daily yields. The MRM can be used as a reference method for estimating daily yields and component percentages.

The method of Liu et al. (2019) is an updated version of the method of Liu et al. (2000). The model is only used for farms with 2 time milkings during 24 hours.

The following formula is used to estimate DMY, DFY, DPY based on partial yields (PMY, PFY,PPY) from either morning (AM) or evening (PM) milking:

''Equation 7. Model for predicting 24-hour yield.''

''yijk = a + bijk * xijk''

where:

yijk is the estimated 24-hour daily yield (DMY, DFY or DPY);

xijk is AM or PM partial daily yield on a test day (PMY, PFY, or PPY).

Subscript '''''i''''' represents class of parity effect with 2 levels: first and higher parities.

Subscript '''''j''''' represents class of length of preceding milking interval with 8 levels for AM milking: < 720 minutes, < 740 minutes, < 760 minutes, < 780 minutes, < 800 minutes, < 820 minutes, < 840 minutes, >= 840 minutes and 8 levels for PM milking: < 600 minutes, < 620 minutes, < 640 minutes, < 660 minutes, < 680 minutes, < 700 minutes, < 720 minutes, >= 720 minutes.

Subscript '''''k''''' represents class of lactation stage with 7 classes: < 60 days, < 120 days, < 180 days, < 240 days, < 300 days, < 360 days, >= 360 days.

'''''a''''' is the estimated intercept for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

'''''b'''''ijk is the estimated slope for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

The factors for '''''a''''' and '''''b'''''ijk can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Appendix_1_-_Adjustment_factors_to_calculate_24-hour_yields_using_the_Liu_method Appendix 1].

For a given yield trait a total number of 112 formulae are to be estimated for calculating 24-hour daily yield based on partial yield from either AM or PM milking. Component percentage for fat (DFP) and protein (DPP), on a 24-hour basis is calculated by dividing estimated fat or protein yield by estimated daily milk yield:[[File:Imagefinal.png|center|thumb|339x339px]]

===== Calculation example with method of Liu et al. (2019) =====
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" align = "left" |'''''Table 14. Data from an evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="6" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="6" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="6" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow'''

'''ID'''
|'''Calving date'''
|'''Lactation number'''
| colspan="2" |'''Milk yield (kg)'''
|'''Fat content (%)'''
|'''Protein content (%)'''
|'''Fat yield (kg)'''
|'''Protein yield (kg)'''
|'''Index1'''
|-
|A
|01.01.2020
|1
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1132
|-
|B
|01.01.2020
|2
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1232
|-
|C
|27.03.2020
|1
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1131
|-
|D
|27.03.2020
|2
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1231
|-
|
|
|
|
|
|
|
|
|
|
|}
'''1''' Index is marked in the Appendix table.
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 15. Calculation of 24-hour daily yield and components for evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="3" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="3" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="3" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow ID'''
|'''DMY (kg)'''
|'''DFY (kg)'''
| colspan="2" |'''DPY (kg)'''
|'''DFP (%)'''
|'''DPP (%)'''
|-
|A
|3,47396+25,0

<nowiki>*</nowiki> 1,98268 = 53,0401 ≈ '''53,0'''
|0,2135+0,995

<nowiki>*</nowiki> 1,68050 = 1,8855975
| colspan="2" |0,10471+0,8325* 1,99092 = 1,7621509
|1,8855975 / 53,04096*100

≈ '''3,55'''
|1,7621509 / 53,04096*100

≈ '''3,32'''
|-
|B
|4,15080+25,0* 1,98520 = 53,7808 ≈ '''53,8'''
|0,3635+0,995

<nowiki>*</nowiki> 1,47515 = 1,8312743
| colspan="2" |0,13952+0,8325* 1,97074 = 1,7801611
|1,8312743 / 53,7808*100

≈ '''3,41'''
|1,7801611 / 53,7808*100

≈ '''3,31'''
|-
|C
|2,80244+33,1

<nowiki>*</nowiki> 2,02183 = 69,72501 ≈ '''69,7'''
|0,17663+1,3339 * 1,72438 = 2,4767805
| colspan="2" |0,11078+1,1122 * 1,96422 = 2,2953855
|2,4767805 / 69,725013*100

≈ '''3,55'''
|2,2953855 / 69,725013*100

≈ '''3,29'''
|-
|D
|3,85525+33,1 * 2,00429 = 70,19725 ≈ '''70,2'''
|0,27991+1,3339 * 1,62403 = 2,4462036
| colspan="2" |0,12863+1,1122* 1,98973 = 2,3416077
|2,4462036 / 70,7197249*100 ≈ '''3,48'''
|2,3416077 / 70,7197249*100 ≈ '''''3,34'''''
|-
|
|
|
|
|
|
|
|}
</center>
'''Note''' that intercepts and slopes of the applied regression formulae are underscored.

===== Fat correction for equal measure sampling =====
With Equal measure sampling, it is advisable to use Equation 8 (or the like) to correct fat contents:

Equation 8. Fat correction for equal measure sampling.

Fat, % = Analysed fat, % + 0.69 – 1.3 x (morning milk/ 24-hour milk)

The relation of morning milk to 24-hour milk is to be calculated to at least four decimals.

==== 1.1 Method of Kyntäjä & Nokka (2021)<ref name=":3" />: 24-hour correction factors for fat percentage ====
This method can be applied to calculate 24-hour correction factors for fat percentage, in case the milk recording is based on two milkings, with at least one known milk yield and one sample. A 24-hour recording day is assumed.

The conventional way to calculate correction factors is based on a data set where all milkings have been recorded and analysed separately. This approach requires a lot of effort and extra analysis, and is not cheap to organise. Organisations that have access to a large number of records may be able to use those data to calculate correction factors even if they have no extra analysis.

Requirements for the data set:

# The data set has to be large enough. Every single factor needs to be based on at least 10,000 or, even better, 100,000 observations.
# Each individual data set must contain at least one preceding milking interval, milk weight, and analysed sample. If it contains more milk weights, intervals etc. that is even better. It is also good to include breed, lactation number, days in milk and other data that may have an effect on the factors.

===== Calculation example of the method of Kyntäjä & Nokka (2021)<ref>Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. ICAR Technical Series no. 25: 171-175.</ref> =====

====== The accumulated data set ======
Since 2003, Finland had accumulated a data set of 7.5 million recordings with data on the time of the sampled and preceding milking as reported by the farmer, the lab analysis results, and the 24-hour milk yield. Grouped according to the preceding interval, the analysed fat content gives a nice sigmoid curve with the highest fat content found after a 540 to 630 minutes’ interval (9 to 10.5 hours) and the lowest at 810 to 930 minutes (13.5 to 15.5 hours).
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 16. Average analysed milk fat percentage by preceding interval class, 2003 – 2020.'''''
|- style="background-color:#efefef;"
|'''Interval before'''

'''Sampling (minutes)'''
|'''Number of samples'''
|'''Median interval in the class'''
|'''Average fat content analysed (%)'''
|-
|<510
|93,577
|495
|4.20
|-
|510-539
|19,523
|525
|4.70
|-
|540-569
|111,268
|555
|4.79
|-
|570-599
|253,807
|585
|4.83
|-
|600-629
|1,461,587
|615
|4.75
|-
|630-659
|919,968
|645
|4.66
|-
|660-689
|1,168,683
|675
|4.56
|-
|690-719
|223,877
|705
|4.42
|-
|720-749
|517,447
|735
|4.28
|-
|750-779
|212,428
|765
|4.16
|-
|780-809
|924,014
|795
|4.12
|-
|810-839
|698,463
|825
|4.09
|-
|840-869
|1,104,778
|855
|4.07
|-
|870-899
|154,561
|885
|4.05
|-
|900-929
|77,024
|915
|4.07
|-
|>929
|26,977
|945
|4.13
|}
</center>

The results were also divided into subgroups according to lactation number, phase of lactation, and breed. The effect of the preceding milk interval on milk fat seems to be bigger with older cows and in the beginning of lactation. It was also bigger with Ayrshire cows as compared with Holsteins. At this point, however, the decision was made not to take these factors into account when calculating new correction factors.

====== Calculation of new factors ======
The results above were turned into a simple set of correction factors, dependent solely on the preceding interval. In order to do this, two assumptions were made:

# A 24-hour recording day was assumed. This way, we can deduce the second milking interval from the one we know and mirror the fat percent for that milking.
# Milk secretion rate was assumed to be constant around the 24-hour period. This allows us to deduce the share of the 24-hour yield produced at each milking.

These assumptions allow us to create the new correction factors by mirroring the milk yield and milk fat content in the milking whose actual data we have not got. This way, we get the following formula:

Equation 9. Correction factor.
[[File:Equation9.png|none|thumb|545x545px]]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left" |'''''Table 17. Calculation of the mirrored milking and the correction factors'''''
|- style="background-color:#efefef;"
|'''Interval before sampling (minutes)'''
|'''Average fat in the sampled milking (%)'''
|'''Share of 24-hour milk in the sampled milking'''
|'''Mirrored interval (minutes)'''
|'''Average fat in the mirrored milking (%)'''
|'''Calculated 24-hour average fat(%)'''
|'''Correction factor'''
|-
|<510
|4.21
|0.34
|>929
|4.14
|4.16
|0.989
|-
|510-539
|4.77
|0.36
|900-929
|4.08
|4.33
|0.907
|-
|540-569
|4.82
|0.39
|870-899
|4.05
|4.35
|0.903
|-
|570-599
|4.84
|0.41
|840-869
|4.07
|4.38
|0.906
|-
|600-629
|4.76
|0.43
|810-839
|4.09
|4.37
|0.919
|-
|630-659
|4.66
|0.45
|780-809
|4.12
|4.36
|0.936
|-
|660-689
|4.56
|0.47
|750-779
|4.16
|4.35
|0.953
|-
|690-719
|4.43
|0.49
|720-749
|4.29
|4.36
|0.984
|-
|720-749
|4.29
|0.51
|690-719
|4.43
|4.36
|1.016
|-
|750-779
|4.16
|0.53
|660-689
|4.56
|4.35
|1.046
|-
|780-809
|4.12
|0.55
|630-659
|4.66
|4.36
|1.059
|-
|810-839
|4.09
|0.57
|600-629
|4.76
|4.37
|1.070
|-
|840-869
|4.07
|0.59
|570-599
|4.84
|4.38
|1.076
|-
|870-899
|4.05
|0.61
|540-569
|4.82
|4.35
|1.073
|-
|900-929
|4.08
|0.64
|510-539
|4.77
|4.33
|1.062
|-
|>929
|4.14
|0.66
|<510
|4.21
|4.16
|1.006
|}
</center>

=== Methods to calculate 24-hour yields in Automatic Milking Systems ===

==== General remarks about calculation of 24-hour milk yield ====
It is characteristic for AMS systems that individual cows set their own milking rhythm, thus making it largely irrelevant to use the traditional model of measuring milk yields and sampling at all milkings in the herd during the recording day. In order to determine how much an individual cow’s real 24-hour milk, fat and protein yield is, more complex calculations are required, especially with milk fat that varies considerably from milking to milking. For protein content and cell counts, no correction is needed for a one-milking sample.

The basic idea with calculating a 24-hour milk yield from AMS data is that milk yields per milking are converted into milk yield per time unit (minute or hour) during the preceding interval. This milk yield per time unit is then converted into milk yield in 24 hours. In order to do this, the data set must also contain time stamps for each milking.

How many milkings or how long a measurement period is used for creating 24-hour yields depends on the milk recording organisation. The fewer milkings are used the more random variance there will be in the individual cow milk yields. The absolute minimum is two milkings with preceding intervals, while a measuring period of 96 hours is recommended.

The sampled milking must always be inside the milk yield measurement period. For the calculation of fat and protein yields, it is recommended to use only those milk yields that are from the same period or day. With Z sampling, the 24-hour fat and protein yields may be calculated based on a shorter measurement period than what is used for calculating the 24-hour milk yields.

==== Calculation of milk yield using data of several days (Lazenby ''et al''., 2002<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Automatic Milking Systems (AMS). The average of most recent milk weights can be calculated using a number of preceding milkings or a number of preceding days. If number of milkings is used, the optimal estimate of the milking rate is obtained using an average of current milking together with the 12 most recent milkings back in time. The optimal estimate is the maximum value of the difference curve at which the correlation with the ‘true’ 24-hour milk yield is greatest and the variance across milkings is minimized. If number of days is used, the optimal estimate of the milking rate is obtained using an average of all milkings occurred in the last 96 hours (4 most recent days). In Table 18 the percent of maximum difference for various number of milkings and days is reported. The optimal estimate is independent from stage of lactation and parity.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 18. Percent maximum for different number of days and milkings.'''''
|- style="background-color:#efefef;"
|'''Days'''
|'''Percent Max.'''
|'''Current milking'''

'''+ most recent milkings'''
|'''Percent max.'''
|-
|1
|49.38
|10
|97.85
|-
|2
|77.26
|11
|99.08
|-
|3
|92.34
|12
|99.70
|-
|4
|98.91
|13
|99.81
|-
|5
|98.50
|14
|99.40
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table19.png|center|thumb|911x911px]]
Therefore, 24-hour yield estimation using most recent milkings (1+12) is computed using Equation 10.

''Equation 10. 24-hour yield estimation using 12 previous milkings from AMS.''
[[File:Equation10.png|none|thumb|527x527px]]
and, 24-hour yield estimation using all milkings occurred in the last 96 hours (most recent 4 days), all milking in the last 4 days are included is computed using Equation 11.

''Equation 11. 24 hours yield estimation using milkings from the last 96 hours from AMS''
[[File:Equation11.png|none|thumb|534x534px]]

===== Advantages and disadvantages of this method =====
In terms of Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between milk weights and contents may arise if contents are recorded on one day only. Moreover, some cows may begin or finish their lactation during the period of recording. In this case the computation of milk yield must be adapted. The number of data that need to be validated is higher (for instance, contents have short interval between two milkings).

==== Calculation of milk yield using data on 1 day (Bouloc ''et al''., 2002<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
When the number of milkings is reduced to milkings obtained during one day only, the accuracy of the estimation of the true performance is the same as classical milk recording methods with the same interval between two test days. For instance, Milk Yield estimated from all the milkings recorded during 24 hours, and with an interval between two test days of four weeks has the same accuracy as A4.

==== Calculation of fat and protein yield (Galesloot & Peeters, 2000<ref name=":1" />) ====
Calculation of fat and protein percent must be based on milk weights at time of sampling. The 24-hour protein percentage can be predicted by the protein percentage of the sample without adjustment. However, the 24-hour fat percentage is more difficult to predict, as levels of fat percent are inversely proportional to the amount of milk yield. It is important then to have a close connection between time of samples and actual milk yields.

The Peeters and Galesloot method is a multiple linear regression model for estimating 24-hour fat percent and yields from one-sampled milking during the AMS sampling period. Six different statistical models were tested. This method takes into account fat percent, protein percent, milk weight and milking interval of the sampled milking, milking interval and milk weight of the previous milking (simple model). Another model, based on six different classification of variables (Ca - Cf) such as, time of sampled milking, interval preceding the sampled milking, ratio of fat to protein percent, parity, lactation stage, can be applied (complex model).

===== Simple model =====
24-hour Fat% = b0 + b1* Fat%(n) + b2* Prot%(n) + b3* Int(n) + b4* Int(n-1) + b5* Milk(n) + b6* Milk (n-1) + e

b0= Intercept, b1 to b6 = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, e = Residual effect.

===== Complex model =====
24-hour Fat%i = b0i + b1i* Fat%(n) + b2i* Prot%(n) + b3i* Int(n) + b4i* Int(n-1) + b5i* Milk(n) + b6i* Milk(n-1) + ei

b0i = Intercept, b1i to b6i = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, ei = Residual effect

i = subclass of classification for class variables Cx for x = a, b, c, d, e, f

Ca = Day Time of sampled milking (h) 0-5.59, 6.00-11.59, 12.00-17.59, 18.00-23.59

Cb = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440

Cc = Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

Cd = Parity 1, 2, ≥ 3

Ce = Lactation stage 1-99, 100-199, ≥200

Cf = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440 and Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

The best prediction of 24-hour fat percent and 24-hour fat yields from this method, includes fat percent, protein percent, milk weight and milking interval of the sampled milking, milk weight and milking interval of the preceding milking and the interaction between milking interval, the ratio of fat to protein percent of the sampled milking (complex model corresponding to Cf classification).

The Peeters and Galesloot method has been updated by Roelofs et al. (2006)<ref>Peeters, R. and P. J. B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. J Dairy Sci. 85:682-688.</ref>. The Roelofs method is described in [[Section 02 – Cattle Milk Recording#Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme|Appendix 2]] of this Section.

N.B. This method has been developed by CRV. CRV has available a set of parameters, estimated with this method. For more information about costs and advice on application of this method, please contact CRV. ICAR has no benefit from the application of this method or any other method described in these guidelines.

==== Calculation example of 24-hour fat and protein yields with sampling scheme M ====
With this method, all milkings in a 24-hour recording period must be sampled. The obtained separate analysis results are then used to compute a 24-hour yield of milk solids, and a weighted average of their content.

Individual milkings (last 96 hours) and recording day contents:
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left" |'''''Table 20. Calculation of 24-hour fat and protein contents with sampling scheme M.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY/MM/DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat%'''
|'''Protein%'''
|-
|1
|2021/09/09
|20:45
|525
|13.7
|26.1
|
|
|-
|2
|2021/09/10
|5:30
|617
|16.0
|25.9
|
|
|-
|3
|2021/09/10
|15:47
|720
|18.7
|26.0
|
|
|-
|4
|2021/09/11
|3:25
|645
|16.8
|26.0
|
|
|-
|5
|2021/09/11
|14:10
|899
|18.3
|20.3
|
|
|-
|6
|2021/09/11
|23:27
|557
|14.6
|26.2
|
|
|-
|7
|2021/09/12
|10:51
|684
|17.4
|25.4
|4.53
|3.17
|-
|8
|2021/09/12
|19:44
|533
|14.1
|26.5
|4.92
|3.18
|-
|9
|2021/09/13
|1:35
|351
|9.9
|28.2
|5.92
|3.07
|}
</center>

For example, calculation of fat% on recording day:

24-hour Fat% = (9.9 kg milk x 5.92% fat + 14.1 kg milk x 4.92 % fat + 17.4 kg milk x 4.53 % fat) / (9.9 + 14.1 + 17.4) kg milk = 5.00 %

To calculate the 24-hour fat yield, the calculated 24-hour milk yield is multiplied by the fat content thus obtained (5.00 %).

The same method is used for protein, somatic cell count, urea, lactose and other milk constituents.

Estimation of milk contents: It is recommended to set the robot not to take samples if the preceding milking of the individual cow is not more than 4 hours earlier. If such milkings occur the milk sampled from them is not suitable for 24-hour fat calculation.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left"|'''''Table 21. Calculation of 24-hour fat and protein contents with sampling scheme M where one milking interval was shorter than 4 hours.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY-MM-DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat %'''
|'''Protein%'''
|-
|1
|2021/11/12
|20:05
|590
|15.4
|26.4
|
|
|-
|2
|2021/11/13
|6:31
|626
|16.3
|26.0
|
|
|-
|3
|2021/11/13
|17:12
|641
|17.1
|26.7
|
|
|-
|4
|2021/11/14
|4:40
|688
|17.5
|25.4
|
|
|-
|5
|2021/11/14
|15:11
|631
|16.4
|26.0
|
|
|-
|6
|2021/11/15
|2:25
|674
|16.5
|24.5
|
|
|-
|7
|2021/11/15
|9:47
|452
|10.8
|23.9
|
|
|-
|8
|2021/11/15
|18:30
|523
|13.6
|26.0
|4.71
|3.36
|-
|9
|2021/11/15
|21:15
|165
|3.1
|18.8
|5.161
|3.481
|-
|10
|2021/11/16
|7:49
|634
|16.5
|26.0
|4.47
|3.21
|}
1 Time between two consecutive milkings shorter than 4 hours, data not taken into account for calculation of milk contents.
</center>

Calculation of the fat content of milk during the recording day:

24-hour Fat% = (16.5 kg milk x 4.47 % fat + 13.6 kg milk x 4.71 % fat) / (16.5 kg + 13.6 kg) = 4.57 %

The same method is used for protein, somatic cells, urea, lactose and other milk constituents.

=== Methods to calculate 24-hour yields from electronic milk meters ===

==== Using data on more than one day (Hand ''et al''., 2006<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. J. Dairy Sci. 89:1723–1726.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Electronic Milk Meters. The average of most recent milk weights can be calculated using a number of preceding days. Table 22 reports the concordance correlations for a range of multiple-day averages. As soon as at least the 3 preceding days are used in the calculation, the concordance correlation reaches a high value of at least 0.981. There are no significant differences between 3, 4, 5, 6 and 7-day averages. The correlations are independent from stage of lactation and parity. Thus, 24-hour yields can be the average of from 3 to 7 daily milkings previous to the test day when fat and protein samples were taken.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 22. Concordance correlations for different multiple-day averages.'''''
|- style="background-color:#efefef;"
|'''Multiple-day average'''
|'''Concordance correlation'''
|-
|1
|0.957
|-
|2
|0.975
|-
|3
|0.981
|-
|4
|0.981
|-
|5
|0.982
|-
|6
|0.981
|-
|7
|0.981
|-
|10
|0.979
|-
|14
|0.977
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table20.png|center|thumb|923x923px]]

Therefore, 24-hour yield estimation averaging over 5 days is given by Equation 12.

''Equation 12. 24-hour yield estimation averaging over 5 days.''
[[File:Equation12.png|center|thumb|601x601px]]

===== Advantages and disadvantages of this method =====
Concerning Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between Milk weights and contents have been shown. The estimation bias increases proportionally to the number of days use to compute the 24-hour average. Thus, this method is recommended only if milk weight is the only variable of interest. If milk contents are of interest then the milk weight should be calculated using the milkings from the same day of sampling.

==== Estimation of 24-hour fat and protein yield ====
Fat and protein yields should be determined from the 24-hour yield on the day of sampling, and not the averaged value.

=== Calculation of daily fat percentage from single samples by Gerke et al., 2025 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Gerke.xlsx here]

Constant access to the automatic milking system (AMS) leads to varying milking frequency of cows and subsequently varying milking interval lengths (MI) and milk yield (MY) of single milkings. This influences milk production and can result in variable milk composition in individual milkings during the day. Therefore, the fat percentage from one sampled milking must be adjusted before it can be used as a daily value. The method described specifies the data required and the calculation procedure for deriving a corrected 24 h milk fat percentage from a single sample on test day (TD) in AMS herds.

==== Model specification ====
The multiple linear regression includes transformation, interaction, and polynomial parameters to model non-linearity and thereby improve prediction accuracy. Beside F% of a single milking (''m'') on TD, the model focused on lactation characteristics and milk recording data of up to 4 preceding milkings. With milking intervals ranging between 4 and 20 hours, the method can be applied to milk recording samples from cows with 2 or 3 milkings whose milking intervals lengths (MI) before sampling accumulate to less than 24 h.

The functional form of the model described below specifies the data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample:[[File:Image A.png|center|thumb|636x636px|'''Data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample''']]
</div>where:

DF% = estimated 24 h fat percentage on TD

''m'' = sampled milking on TD

''m-x'' = x milkings before the milking where the sample was taken (x: 1-3)

F% = fat percentage of the sampled milking ''m''

MY(''m'') = milk yield (kg) of ''m''

MI(''m'') = length of time interval (min) preceding the sampled milking ''m''

MY(''m''-x) = milk yields of the 1-3 preceding milkings of ''m''

MI(''m''-x) = milking interval length corresponding to MY(''m''-x)

DIM = days in milk on TD ranging between 5 and 330 d

Parity = parity class (e.g primiparous = 1 and multiparous = 0)

Daytime = time-of-day group of ''m'' (e.g. morning/noon/evening)

e = residual error

The method and its implementation are described in detail by Gerke et al. (2025).

==== Calculation and examples ====
The mathematical notation, with the corresponding regression coefficients in Table 1 for calculating the daily fat percentage (DF%):[[File:Calculating the daily fat percentage (DF%).jpg|center|Calculating the daily fat percentage (DF%)|thumb|511x511px]][[File:Calculating the daily fat percentage (DF%) 2.jpg|center|frame|'''Table 1. Coefficients for regression formula.''']]
</div>
[[File:Example data required for estimating 24 h fat percentage (DF%).jpg|alt=Example data required for estimating 24 h fat percentage (DF%)|center|frame|'''Table 2.''' '''Example data required for estimating 24 h fat percentage (DF%)''']]
Based on the data assembled on TD (Table 2), the corrected 24 h fat percentage (DF%) can be calculated using the mathematical formula und its corresponding coefficients listed in Table 1 as shown in the following examples:
[[File:Corrected 24 h fat percentage.jpg|alt=Corrected 24 h fat percentage|center|thumb|661x661px|'''Corrected 24 h fat percentage''']]

=== Reference ===
Gerke, J. S., Kammer, M., Werner, A., Köstler, R., Piepenburg, J., Mayerhofer, M., … Duda, J. (2025). Estimating daily fat percentage from single samples in herds with automatic milking system using a regression model. ''Livestock Science'', ''293'', 105649. doi: 10.1016/j.livsci.2025.105649

=== Calculation of daily fat percentage from single samples by Jenko et al., 2008, 2010 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Jenko.xlsx here]

This method estimates daily milk yield (DMY), daily fat yield (DFY), and daily protein yield (DPY) in the alternate one-milking recording (T) scheme. Daily fat percentage (DFP) and daily protein percentage (DPP) are then derived from the daily yield (DY) estimates. Utilizing this method allows us to remove the risk of underestimating high and overestimating low DY and contents.

The following formula is used to estimate the DY from the partial yield (PY) and the estimated PY/DY ratio (y):

DY=PYi/yi

where the subscript i is either morning (a.m.) or evening (p.m.).

The value of y is calculated based on the milking interval in minutes (MI), estimated intercept (µ) and regression coefficients (b1 and b2) for yield traits in a.m. or p.m. milking using the following equations for DMY and DPY:

'''Equation 1. Model for milk yield and protein yield.'''

yi = µ + b1 × MI

and for DFY

'''Equation 2. Model for fat yield.'''

yi = µ + b1 × MI + b2 × MI2

The intercept and regression coefficients can be either estimated from the data with records from both a.m. and p.m. milking or the estimates from Table 1 can be applied.

'''Table 1. Intercept and regression coefficients for calculation of daily yield.'''
{| class="wikitable"
|'''Daily yield'''
|'''Milking'''
|'''µ'''
|'''b1'''
|'''b2'''
|-
|DMY
|a.m.
|0,1081000000
|0,0005503000
|
|-
|
|p.m.
|0,0884200000
|0,0005683000
|
|-
|DPY
|a.m.
|0,1124000000
|0,0005419000
|
|-
|
|p.m.
|0,0966400000
|0,0005593000
|
|-
|DFY .
|a.m.
|0,5903000000
|<nowiki>-0,0005093000</nowiki>
|0,0000005377
|-
|
|p.m.
|0,1574000000
|0,0006705000
|<nowiki>-0,0000002744</nowiki>
|}
Finally, daily fat percentage (DFP) and daily protein percentage (DPP) are calculated from the estimated DY:

DFP=DFY/DMY × 100

DPP=DPY/DMY × 100

==== Calulation example with method of Jenko et al. (2008, 2010) ====
Example of the calculations of daily yields from morning milking and evening milking is presented in tables 3 and 4. Data from the Delorenzo and Wiggans method is used in the calculations (Table 2).

'''Table 2. Data for morning and evening milking.'''
{| class="wikitable"
|'''Milking'''
|'''a.m.'''
|'''p.m.'''
|-
|Beginning of recording
|06:15
|20:22
|-
|Start of preceding milking
|17:25
|06:35
|-
|Milking interval (min)
|770
|827
|-
|'''Milking results'''
|
|
|-
|Milk (kg)
|12,00
|14,00
|-
|Protein (%)
|3,45
|3,40
|-
|Fat (%)
|4,12
|4,00
|}

'''Table 3. Calculation of partial yield (PY) and calculation of y value.'''
{| class="wikitable"
|Trait
|Milking
|PY (%)
|PY (kg)
|y
|-
|Milk
|a.m.
|
|12,00
|0,1081000000 + 0,0005503000 x 770 = 0,531831
|-
|
|p.m.
|
|14,00
|0,0884200000 + 0,0005683000 x 827 = 0,558404
|-
|Protein
|a.m.
|3,45
|12,00 / 3,45 = 0,41
|0,1124000000 + 0,0005419000 x 770 = 0,529663
|-
|
|p.m.
|3,40
|14,00 / 3,40 = 0,48
|0,0966400000 + 0,0005593000 x 827 = 0,559181
|-
|Fat
|a.m.
|

4,12
|12,00 / 4,12 = 0,49
|0,5903000000 -0,0005093000 x 770 + 0,0000005377 x 7702 = 0,516941
|-
|
|p.m.
|

4,00
|12,00 / 4,00 = 0,56
|0,1574000000 +0,0006705000 x 827 - 0,0000002744 x 8272 = 0,524233
|}

'''Table 4. Calculation of daily yield (DY, kg) and daily components (DY, %).'''
{| class="wikitable"
|Trait
|DY
|Milking
|DY (kg)
|DY (%)
|-
|Milk
|DMY
|a.m.
|12,00 / 0,531831 = 22,56356
|
|-
|
|
|p.m.
|14,00 / 0,531831 = 25,07145
|
|-
|Protein
|DPY
|a.m.
|0,41 / 0,529663 = 0,781629
|(0,781629 / 22,56356) x 100 = 3,46
|-
|
|
|p.m.
|0,48 / 0,559181 = 0,851245
|(0,851245 / 25,07145) x 100 = 3,40
|-
|Fat
|DFY
|a.m.
|0,49 / 0,516941 = 0,956395
|(0,956395 / 22,56356) x 100 = 4,24
|-
|
|
|p.m.
|0,56 / 0,524233 = 1,068227
|(1,068227 / 25,07145) x 100 = 4,26
|}

==== References ====

* Jenko, J., Perpar, T., Logar, B., Sadar, M., Ivanovič, B., Jeretina, J., Verbič, J., Podgoršek, P. 2008. Comparison of different models for estimating daily yields from a.m./p.m. milkings in Slovenian dairy scheme. Presented at the 36th ICAR Session, Niagara Falls, New York, United States, June 16-20, 2008.
* Jenko, J., Perpar, T., Gorjanc G., Babnik, D. 2010. Evaluation of different approaches for the estimation of daily yield from single milk testing scheme in cattle, J. Dairy Res., 77 (2010), pp. 137-143; DOI: 10.1017/S0022029909990586

</div>
</div>

== Procedure 2 – Computing of Accumulated Lactation Yield ==
<div class="mw-collapsible mw-collapsed">
<div>
=== The Test Interval Method (TIM) (Sargent, 1968<ref>Sargent, F. D., V. H. Lyton, and 0. G. Wall, J r . 1968. Test interval method of calculating Dairy Herd Improvement Association records. J. Dairy Sci. 51:170.</ref>) ===
Test Interval Method is the reference method for calculating accumulated yields. Another adaptation of the method is the Centering Date Method where the yields from the preceding recording are used until the mid point of the recording interval and then substituted by the yields from the following recording.

The following equations are used to compute the lactation record for milk yield (MY), for fat (and protein) yield (FY), and for fat (and protein) percent (FP).
[[File:Equation1111.png|none|thumb|653x653px]]
Where:
M1, M2, Mn are the weights in kilograms, given to one decimal place, of the milk yielded in the 24 hours of the recording day.

F1, F2, Fn are the fat yields estimated by multiplying the milk yield and the fat percent (given to at least two decimal places) collected on the recording day.

I1, I2, In-1 are the intervals, in days, between recording dates.

I0 is the interval, in days, between the lactation period start date and the first recording date.

In is the interval, in days, between the last recording date and the end of the lactation period.

The equation applied for fat yield and percentage must be applied for any other milk components such as protein and lactose.

Details of how to apply the formulae are shown in Table 3 using the example data in Table 1, below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" align = "left" |'''''Table 1. Raw data used in example (TIM).'''''
|- style="background-color:#efefef;"
| colspan="6" align = "left"|'''Data:'''

'''Calving March 25'''
|- style="background-color:#efefef;"
|
|'''Date of'''

'''recording'''
|'''Number'''

'''of days'''
|'''Quantity of milk'''

'''weighed in kg'''
|'''Fat'''

'''percentage'''
|'''Fat'''

'''in grams'''
|-
|April
|8
|14
|28.2
|3.65
|1 029
|-
|May
|6
|28
|24.8
|3.45
|856
|-
|June
|5
|30
|26.6
|3.40
|904
|-
|July
|7
|32
|23.2
|3.55
|824
|-
|August
|2
|26
|20.2
|3.85
|778
|-
|August
|30
|28
|17.8
|4.05
|721
|-
|September
|25
|26
|13.2
|4.45
|587
|-
|October
|27
|32
|9.6
|4.65
|446
|-
|November
|22
|26
|5.8
|4.95
|287
|-
|December
|20
|28
|4.4
|5.25
|231
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left"|'''''Table 2. Lactation period summary (TIM).'''''
|-
|Beginning of lactation:
|March 26
|-
|End of lactation:
|January 3
|-
|Duration of lactation period:
|284 days
|-
|Number of testings (weighings):
|10
|}
</center>
<center>
{| class="wikitable"
| colspan="8" |'''''Table 3. Computations using Test Interval Method.'''''
|- style="background-color:#efefef;"
| colspan="3" rowspan="2" |'''Interval'''

'''both days included'''
|
| colspan="2" |'''Daily production'''
| colspan="2" |'''Sum'''
|- style="background-color:#efefef;"
|'''Days'''
|'''Kg milk'''
|'''Grams of fat'''
|'''Kg milk'''
|'''Kg fat'''
|-
|Mar 26
|<nowiki>-</nowiki>
|Apr 8
|14
|28.2
|1 029
|395
|14.410
|-
|Apr 9
|<nowiki>-</nowiki>
|May 6
|28
|(28.2+24.8)/2
|(1 029+856) /2
|742
|26.389
|-
|May 7
|<nowiki>-</nowiki>
|June 5
|30
|(24.8+26.6) /2
|(856+904) /2
|771
|26.400
|-
|June 6
|<nowiki>-</nowiki>
|July 7
|32
|(26.6+23.2) /2
|(904+824) /2
|797
|27.648
|-
|July 8
|<nowiki>-</nowiki>
|Aug. 2
|26
|(23.2+20.2) /2
|(824+778) /2
|564
|20.817
|-
|Aug. 3
|<nowiki>-</nowiki>
|Aug 30
|28
|(20.2+17.8) /2
|(778+721) /2
|532
|20.980
|-
|Aug 31
|<nowiki>-</nowiki>
|Sept. 25
|26
|(17.8+13.2) /2
|(721+587) /2
|403
|17.008
|-
|Sept. 26
|<nowiki>-</nowiki>
|Oct. 27
|32
|(13.2+9.6) /2
|(587+446) /2
|365
|16.541
|-
|Oct. 28
|<nowiki>-</nowiki>
|Nov. 22
|26
|(9.6+5.8) /2
|(446+287) /2
|200
|9.536
|-
|Nov. 23
|<nowiki>-</nowiki>
|Dec. 20
|28
|(5.8+4.4) /2
|(287+231) /2
|143
|7.253
|-
|Dec. 21
|<nowiki>-</nowiki>
|Jan. 3
|14
|4.4
|231
|62
|3.234
|-
|
|
|
|284
|
|
|4973
|190.216
|-
| colspan="8" |
|-
| colspan="8" |Total quantity of milk: 4 973. kg
|-
| colspan="8" |Total quantity of fat: 190 kg
|-
| colspan="8" |Average fat percentage (190.216 / 4973) x 100 = 3.82%
|}
</center>

=== Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. Livest. Prod. Sci. 17:l.</ref>) ===
With the method 'Interpolation using Standard Lactation Curves' missing test day yields and 305 day projections are predicted. The method makes use of separate standard lactation curves representing the expected course of the lactation, for a certain herd production level, age at calving and season of calving and yield trait. By interpolation using standard lactation curves, the fact that after calving milk yield generally increases and subsequently decreases is taken into account. The daily yields are predicted for fixed days of the lactation: day 0, 10, 30, 50 etc.

The cumulative yield is calculated as follows in :
[[File:Equation2222222.png|none|thumb|474x474px]]
where:

yi = the i-th daily yield;

INTi = the interval in days between the daily yields yi and yi+1;

''n'' = total number of daily yields (measured daily yields and predicted daily yields).

The next example illustrates the calculation of a record in progress. The cow was tested at day 35 and day 65 of the lactation. To determine the lactation yield, daily milk yields are determined for day 0, 10, 30 and 50 of the lactation, by means of the standard lactation curves. The daily yields are in Table 4.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Measured and derived daily yields, used to calculate the record in progress in the example (ISLC).'''''
|- style="background-color:#efefef;"
|'''Day of lactation'''
|'''Milk (kg)'''
|'''Note'''
|-
|0
|25.9
|Predicted
|-
|10
|27.8
|Predicted
|-
|30
|31.7
|Predicted
|-
|35
|31.8
|Measured
|-
|50
|32.9
|Interpolated using standard lactation curve
|-
|65
|33.0
|Measured
|}
</center>

Next, the record in progress can be calculated by means of the formula for a cumulative yield as follows:

[(10 - 1) * 25.9 + (10+1) * 27.8] / 2 +

[(20 - 1) * 27.8 + (20+1) * 31.7] / 2 +

[(5 - 1) * 31.7 + (5+1) * 31.8] / 2 +

[(15 - 1) * 31.8 + (15+1) * 32.9] / 2 +

[(15 - 1) * 32.9 + (15+1) * 33.0] / 2 = 2005.3 kg.

This corresponds to the surface below the line through the predicted and measured daily yields (see Figure 1).
[[File:Figure1.png|center|thumb|621x621px|''Figure 1. Example of calculation of record in progress.'']]

=== Best prediction (BP) (VanRaden, 1997<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. J. Dairy Sci. 80:3015-3022.</ref>) ===
Recorded milk weights are combined into a lactation record using standard selection index methods. Let vector y contain M1, M2, to Mn and let E('''y''') contain corresponding the expected values for each recorded day. The E(y) are obtained from standard lactation curves for the population or for the herd and should account for the cow's age and other environmental factors such as season, milking frequency, etc. The yields in '''y''' covary as a function of the recording interval between them (I). Diagonal elements in Var(y) are the population or herd variance for that recording day and off diagonals are obtained from autoregressive or similar functions such as Corr(M1, M2)=0.995I for first lactations or 0.992I for later lactations. Covariances of one observation with the lactation yield, for example Cov(M1, MY), are the sum of 305 individual covariances. E(MY) is the sum of 305 daily expected values. Lactation milk yield is then predicted as Equation 3:
[[File:Equation333333.png|none|thumb|640x640px]]
With best prediction, predicted milk yields have less variance than true milk yields. With TIM, estimated yields have more variance than true yields. The reason is that predicted yields are regressed toward the mean unless all 305 daily yields are observed. With best prediction, the predicted MY for a lactation without any observed yields is E(MY) which is the population or herd mean for a cow of that age and season. With TIM, the estimated MY is undefined if no daily yields are recorded.

Milk, fat, and protein yields can be processed separately using single-trait best prediction or jointly using multi-trait best prediction. Replacement of M1, M2, to Mn with F1, F2, to Fn or P1, P2, to Pn gives the single-trait predictions for fat or for protein. Multi-trait predictions require larger vectors and matrices but similar algebra. Products of trait correlations and autoregressive correlations, for example, may provide the needed covariances.

=== Multiple-Trait Procedure (MTP) (Schaeffer & Jamrozik, 1996<ref>Schaeffer, L.R., and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. J. Dairy Sci. 79:2044-2055.</ref>) ===
The Multiple-Trait Procedure predicts 305-d lactation yields for milk, fat, protein and SCS, incorporating information about standard lactation curves and covariances between milk, fat, and protein yields and SCS. Test day yields are weighted by their relative variances, and standard lactation curves of cows of similar breed, region, lactation number, age, and season of calving are used in the estimation of lactation curve parameters for each cow. The multiple-trait procedure can handle long intervals between test days, test days with milk only recorded, and can make 305-d predictions on the basis of just one test day record per cow. The procedure also lends itself to the calculation of peak yield, day of peak yield, yield persistency, and expected test-day yields, which could be useful management tools for a producer on a milk recording program.

The MTP method is based upon Wilmink's model in conjunction with an approach incorporating standard curve parameters for cows with the same production characteristics. Wilmink's function for one trait is given by Equation 4.

Equation 4. Wilmink function for one trait (MTP).

y = A + B''t'' ± C''exp'' (-0.05''t'') + ''e''

where y is yield on day t of lactation, A, B, and C are related to the shape of the lactation curve.

The parameters A, B, and C need to be estimated for each yield trait. The yield traits have high phenotypic correlations, and MTP would incorporate these correlations. Use of MTP would allow for the prediction of yields even if data were not available on each test day for a cow.

The vector of parameters to be estimated for one cow are designated:
[[File:Vectro.png|center|thumb]]
where M, F, and P represent milk, fat, and protein, respectively, and S represents somatic cell score. The vector c is to be estimated from the available test-day records. Let c0 represent the corresponding parameters estimated across all cows with the same production characteristics as the cow in question.

Let
[[File:Vector2.png|center|thumb]]

be the vector of yield traits and somatic cell scores on test ''k'' at day ''t'' of the lactation.

The incidence matrix, ''Xk'', is constructed as follows:
[[File:Vector3.png|center|thumb|558x558px]]

The MTP equations are:
[[File:Equation55555.png|none|thumb|560x560px]]
and ''n'' is the number of tests for that cow. ''Rk'' is a matrix of order 4 that contains the variances and covariances among the yields on ''kth'' test at day ''t'' of lactation. The elements of this matrix were derived from regression formulas based on fitting phenotypic variances and covariances of yields to models with ''t'' and ''t2'' as covariables. Thus, element ''ij'' of ''Rk'' would be determined by

rij(t) = ß0ij + ß1ij (t) + ß2ij (t2)

G is a 12 x 12 matrix containing variances and covariances among the parameters in '''ĉ''' and represents the cow to cow variation in these parameters, which includes genetic and permanent environmental effects, but ignores genetic covariances between cows. The parameters for '''''G''''' and '''''Rk''''' vary depending on the breed, but must be known. Initially, these matrices were allowed to vary by region of Canada in addition to breed, but this meant that there could exist two cows with identical production records on the same days in milk, but because one cow was in one region and the other cow was in another region, then the accuracy of their predictions would be different. This was considered to be too confusing for dairy producers, so that regional differences in variance-covariance matrices were ignored and one set of parameters would be used for all regions for a particular breed. Estimation of G is described later.

If a cow has a test, but only milk yield is reported, then

y’k(Mk 0 0 0)

and
[[File:And.png|center|thumb|540x540px]]

The inverse of '''''Rk''''' is the regular inverse of the nonzero submatrix within '''''Rk''''', ignoring the zero rows and columns. Thus, missing yields can be accommodated in MTP.

Accuracy of predicted 305-d lactation totals depends on the number of test-day records during the lactation and DIM associated with each test. Thus, any prediction procedure will require reliability figures to be reported with all predictions, especially if fewer tests at very irregular intervals are going to be frequent in milk recording. At the moment, an approximate procedure is applied that uses the inverse elements of '''(X’R-1X + G-1) -1.'''

==== 1.1 Example calculations ====
Four test day records on a 25 month old, Holstein cow calving in June from Ontario are given in the Table 5 below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 5. Example test day data for a cow (MTP).'''''
|- style="background-color:#efefef;"
|'''Test no.'''
|'''DIM=''t'''''
|'''Exp(-0.05''t'')'''
|'''Milk (kg)'''
|'''Fat (kg)'''
|'''Protein (kg)'''
|'''SCS'''
|-
|1
|15
|0.47237
|28.8
|
|
|3.130
|-
|2
|54
|0.06721
|29.2
|1.12
|0.87
|2.463
|-
|3
|188
|0.000083
|23.7
|0.97
|0.78
|2.157
|-
|4
|250
|0.0000037
|20.8
|
|
|2.619
|}
</center>

Notice that two tests do not have fat and protein yields, and that intervals between tests are irregular and large. The vector of standard curve parameters based on all available comparable cow, is
[[File:Vector4.png|center|thumb]]
The R^(-1)_k matrices for each test day need to be constructed. These matrices are derived from regression equations. The equations for Holsteins were:
<center>
{| class="wikitable" style="text-align: center;"
|''rMM(t) =''
|71.0752 - 0.281201''t'' + 0.0004977''t2''
|-
|''rMF(t) =''
|2.4365 - 0.013274''t'' + 0.0000302''t2''
|-
|''rMP(t) =''
|2.0504 - 0.008286''t'' + 0.0000163''t2''
|-
|''rMS(t) =''
|<nowiki>-1.7993 + 0.013209</nowiki>''t'' - 0.000056''t2''
|-
|''rFF(t) =''
|0.1312 - 0.000725''t'' + 0.000001586''t2''
|-
|''rFP(t) =''
|0.0739 - 0.000386''t'' + 0.000000926''t2''
|-
|''rFS(t) =''
|<nowiki>- 0.0386 + 0.000292</nowiki>''t'' - 0.000001796''t2''
|-
|''rPP(t) =''
|0.066 - 0.000267''t'' + 0.0000005636''t2''
|-
|''rPS(t) =''
|<nowiki>- 0.0404 + 0.000369</nowiki>''t'' - 0.000001743''t2''
|-
|''rSS(t) =''
|3.0404 - 0.000083''t'' - 0.000006105''t2''
|}
</center>

The inverses of the residual variance-covariance matrices for yields for the four test days are as follows:
<center>
{| class="wikitable" style="text-align: center;"
|
|0.0151259
|0
|0
|0.0080354
|-
|'''R^(-1)_1''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0080354
|0
|0
|0.3334553
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.1685584
|0.345947
|<nowiki>-4.851935</nowiki>
|0.0254775
|-
|'''R^(-1)_2''' = =
|<nowiki>-0.345947</nowiki>
|26.830915
|<nowiki>-17.40281</nowiki>
|<nowiki>-0.041445</nowiki>
|-
|
|<nowiki>-4.851935</nowiki>
|<nowiki>-17.40281</nowiki>
|187.18579
|<nowiki>-0.584885</nowiki>
|-
|
|0.0254775
|<nowiki>-0.041445</nowiki>
|<nowiki>-0.584885</nowiki>
|0.3365425
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.2620161
|0.1479068
|<nowiki>-7.943903</nowiki>
|0.0316069
|-
|'''R^(-1)_3''' = =
|0.1479068
|54.446977
|<nowiki>-56.01333</nowiki>
|0.3306741
|-
|
|<nowiki>-7.943903</nowiki>
|<nowiki>-56.01333</nowiki>
|317.9609
|<nowiki>-0.92601</nowiki>
|-
|
|0.0316069
|0.3306741
|<nowiki>-0.92601</nowiki>
|0.3654369
|}
{| class="wikitable" style="text-align: center;"
|

|0.0329465
|0
|0
|0.0251039
|-
|'''R^(-1)_4''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0251039
|0
|0
|0.3981981
|}

Inverse matrix G^(-1) of order 12 is the same for all cows of the same breed:

[[File:Left 6x6.jpg|center|thumb|600x600px|Inverse matrix G^(-1) of order 12]]

</center>
Note that many covariances between different parameters of the lactation curves have been set to zero. When all covariances were included, the prediction errors for individual cows were very large, possibly because the covariances were highly correlated to each other within and between traits. Including only covariances between the same parameter among traits gave much smaller prediction errors.

The elements of the MTP equations of order 12 for this cow are shown in partitioned format also:

'''X’R-1X ='''
<center>[[File:Elements of the MTP equations of order 12.jpg|center|thumb|600x600px|Elements of the MTP equations of order 12]]
</center>
[[File:Equation7.png|center|thumb|632x632px]]

The solution vector for this cow is
[[File:Equation6666.png|center|thumb]]

To predict 305-day yields, Y305
[[File:Equation7777.png|none|thumb|551x551px]]
Equation 6 is used separately for each trait (milk, fat, protein, and SCS). The results for this cow were 7456 kg milk, 301 kg fat, and 239 kg protein. The result for SCS is divided by 305 to give an average daily SCS of 2.477.
</div>
</div>

= Appendices =
== Appendix 1 - Adjustment factors to calculate 24-hour yields using the Liu method ==
<div class="mw-collapsible mw-collapsed">
<div>
In Table 6 the adjustment factors to calculate 24-hour yields, using the Liu method, can be found. The description of the Liu method can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2.]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" |'''''Table 1. Adjustment factors to calculate 24-hour yields using the Liu method. Milking time (MT) is either 1 (PM) or 2 (AM), i = parity class, j= milking interval class and k = stage of lactation class.'''''
|- style="background-color:#efefef;"
|'''MT'''
|'''i'''
|'''j'''
|'''k'''
| colspan="2" |'''Milk yield (DMY)'''
| colspan="2" |'''Fat yield (DFY)'''
| colspan="2" |'''Protein yield (DPY)'''
|-
| colspan="4" |
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|-
|1
|1
|1
|1
|5.29333
|1.83283
|0.30911
|1.43518
|0.18984
|1.77461
|-
|1
|1
|1
|2
|4.17676
|1.97447
|0.2803
|1.56914
|0.12246
|2.00568
|-
|1
|1
|1
|3
|4.26476
|1.95945
|0.18826
|1.82468
|0.12624
|2.0137
|-
|1
|1
|1
|4
|3.41282
|2.01814
|0.25025
|1.64707
|0.12519
|1.99629
|-
|1
|1
|1
|5
|1.79548
|2.22665
|0.06578
|2.09515
|0.05249
|2.24065
|-
|1
|1
|1
|6
|3.7751
|1.95508
|0.12854
|1.93892
|0.11936
|2.00979
|-
|1
|1
|1
|7
|1.544
|2.1478
|0.06425
|2.06779
|0.0569
|2.13851
|-
|1
|1
|2
|1
|5.8584
|1.79409
|0.33193
|1.42953
|0.20756
|1.7288
|-
|1
|1
|2
|2
|5.45524
|1.84258
|0.32877
|1.43235
|0.21332
|1.74001
|-
|1
|1
|2
|3
|4.64052
|1.86706
|0.27155
|1.57017
|0.16439
|1.84539
|-
|1
|1
|2
|4
|2.86835
|2.06209
|0.18647
|1.79403
|0.10803
|2.0193
|-
|1
|1
|2
|5
|2.11336
|2.12055
|0.10435
|1.97206
|0.07193
|2.10651
|-
|1
|1
|2
|6
|2.00673
|2.0636
|0.1386
|1.83336
|0.06892
|2.06532
|-
|1
|1
|2
|7
|1.71752
|2.11269
|0.06501
|2.0379
|0.05569
|2.12881
|-
|1
|1
|3
|1
|2.80244
|2.02183
|0.17663
|1.72438
|0.11078
|1.96422
|-
|1
|1
|3
|2
|3.47396
|1.98268
|0.2135
|1.6805
|0.10471
|1.99092
|-
|1
|1
|3
|3
|2.81702
|2.04348
|0.20754
|1.71868
|0.1127
|1.98403
|-
|1
|1
|3
|4
|3.1989
|1.998
|0.21578
|1.6991
|0.10802
|1.99517
|-
|1
|1
|3
|5
|2.47055
|2.04826
|0.15418
|1.83151
|0.07492
|2.07547
|-
|1
|1
|3
|6
|1.923
|2.07728
|0.11783
|1.89678
|0.06457
|2.08391
|-
|1
|1
|3
|7
|1.85264
|2.0873
|0.13047
|1.86711
|0.071
|2.06917
|-
|1
|1
|4
|1
|2.75042
|1.96631
|0.24794
|1.61741
|0.09248
|1.95376
|-
|1
|1
|4
|2
|2.97505
|1.96711
|0.20029
|1.71842
|0.09381
|1.97081
|-
|1
|1
|4
|3
|2.33365
|2.02986
|0.17021
|1.79996
|0.07631
|2.03167
|-
|1
|1
|4
|4
|3.41505
|1.94107
|0.1845
|1.76799
|0.10989
|1.95456
|-
|1
|1
|4
|5
|2.67488
|1.97797
|0.13433
|1.85893
|0.09432
|1.97755
|-
|1
|1
|4
|6
|1.89907
|2.04841
|0.08715
|1.96251
|0.07132
|2.04225
|-
|1
|1
|4
|7
|1.80326
|2.03554
|0.1251
|1.86477
|0.06072
|2.04747
|-
|1
|1
|5
|1
|2.76763
|1.92863
|0.15754
|1.72474
|0.10187
|1.88749
|-
|1
|1
|5
|2
|3.36896
|1.92048
|0.2236
|1.64149
|0.12369
|1.8823
|-
|1
|1
|5
|3
|2.22763
|2.00452
|0.17614
|1.7474
|0.08019
|1.9782
|-
|1
|1
|5
|4
|2.44625
|1.97049
|0.17217
|1.74753
|0.0889
|1.94647
|-
|1
|1
|5
|5
|2.379
|1.97307
|0.15965
|1.76134
|0.0896
|1.94575
|-
|1
|1
|5
|6
|1.62948
|2.02491
|0.11021
|1.85546
|0.0852
|1.94593
|-
|1
|1
|5
|7
|1.45651
|2.0254
|0.07479
|1.92789
|0.05846
|2.00196
|-
|1
|1
|6
|1
|2.01088
|1.9497
|0.16548
|1.68143
|0.101
|1.85846
|-
|1
|1
|6
|2
|2.96605
|1.93064
|0.25841
|1.52566
|0.12097
|1.86061
|-
|1
|1
|6
|3
|2.2281
|1.96085
|0.19036
|1.69013
|0.08032
|1.9375
|-
|1
|1
|6
|4
|2.39473
|1.952
|0.17854
|1.72423
|0.06863
|1.97582
|-
|1
|1
|6
|5
|2.37955
|1.94127
|0.19579
|1.66419
|0.08447
|1.93156
|-
|1
|1
|6
|6
|0.36203
|2.12393
|0.14291
|1.75822
|0.03845
|2.04562
|-
|1
|1
|6
|7
|1.5702
|1.96794
|0.1336
|1.76796
|0.06449
|1.94829
|-
|1
|1
|7
|1
|3.93654
|1.82772
|0.2359
|1.61894
|0.15032
|1.76054
|-
|1
|1
|7
|2
|4.39662
|1.81581
|0.24969
|1.5881
|0.16909
|1.74794
|-
|1
|1
|7
|3
|3.78325
|1.82778
|0.19228
|1.71802
|0.12368
|1.8268
|-
|1
|1
|7
|4
|3.39116
|1.86302
|0.1969
|1.71838
|0.12282
|1.848
|-
|1
|1
|7
|5
|3.20111
|1.83255
|0.09893
|1.86309
|0.1044
|1.84257
|-
|1
|1
|7
|6
|3.75639
|1.78665
|0.25205
|1.56174
|0.14105
|1.76802
|-
|1
|1
|7
|7
|1.42153
|1.95649
|0.09226
|1.85882
|0.04636
|1.96245
|-
|1
|1
|8
|1
|2.3454
|1.90436
|0.14321
|1.77423
|0.10703
|1.82306
|-
|1
|1
|8
|2
|3.97557
|1.82746
|0.26651
|1.58374
|0.15298
|1.76385
|-
|1
|1
|8
|3
|4.26939
|1.80503
|0.22918
|1.64925
|0.12924
|1.81061
|-
|1
|1
|8
|4
|2.90779
|1.89861
|0.18578
|1.73968
|0.13948
|1.79679
|-
|1
|1
|8
|5
|2.8265
|1.87632
|0.19374
|1.67929
|0.12377
|1.80944
|-
|1
|1
|8
|6
|2.26312
|1.87397
|0.09917
|1.82528
|0.08819
|1.84453
|-
|1
|1
|8
|7
|0.31382
|2.04402
|0.05049
|1.95773
|0.02612
|1.99012
|-
|1
|2
|1
|1
|4.63752
|1.99615
|0.31102
|1.58962
|0.16637
|1.96686
|-
|1
|2
|1
|2
|5.56226
|1.91521
|0.26761
|1.64342
|0.16973
|1.94145
|-
|1
|2
|1
|3
|4.51983
|1.96962
|0.26221
|1.65088
|0.12245
|2.03857
|-
|1
|2
|1
|4
|4.51563
|1.93033
|0.18468
|1.80715
|0.15252
|1.94807
|-
|1
|2
|1
|5
|2.60334
|2.07338
|0.16011
|1.81257
|0.09892
|2.05493
|-
|1
|2
|1
|6
|2.86068
|1.98457
|0.15381
|1.79197
|0.08619
|2.04046
|-
|1
|2
|1
|7
|1.6596
|2.11753
|0.13089
|1.83687
|0.09908
|1.96479
|-
|1
|2
|2
|1
|3.94656
|2.03607
|0.23716
|1.6988
|0.19559
|1.88765
|-
|1
|2
|2
|2
|4.20525
|1.98621
|0.3553
|1.46663
|0.1657
|1.92175
|-
|1
|2
|2
|3
|3.31729
|2.04589
|0.29682
|1.57761
|0.12491
|2.00945
|-
|1
|2
|2
|4
|1.95977
|2.13926
|0.16059
|1.79846
|0.06713
|2.12835
|-
|1
|2
|2
|5
|1.49014
|2.14889
|0.10057
|1.90772
|0.05279
|2.14047
|-
|1
|2
|2
|6
|0.82235
|2.22517
|0.07573
|1.94963
|0.04014
|2.17549
|-
|1
|2
|2
|7
|1.53608
|2.08972
|0.11472
|1.81148
|0.0676
|2.03957
|-
|1
|2
|3
|1
|3.85525
|2.00429
|0.27991
|1.62403
|0.12863
|1.98973
|-
|1
|2
|3
|2
|4.1508
|1.9852
|0.3635
|1.47515
|0.13952
|1.97074
|-
|1
|2
|3
|3
|3.31493
|2.02332
|0.31131
|1.55183
|0.11703
|2.00696
|-
|1
|2
|3
|4
|2.47354
|2.0652
|0.20828
|1.71637
|0.09402
|2.04147
|-
|1
|2
|3
|5
|1.68517
|2.08809
|0.14418
|1.80246
|0.06917
|2.05808
|-
|1
|2
|3
|6
|1.316
|2.12714
|0.11206
|1.87179
|0.04723
|2.12486
|-
|1
|2
|3
|7
|0.4841
|2.20538
|0.04633
|2.02915
|0.02369
|2.18113
|-
|1
|2
|4
|1
|2.82623
|2.01819
|0.25826
|1.69268
|0.11251
|1.97665
|-
|1
|2
|4
|2
|3.24039
|1.9811
|0.36283
|1.50648
|0.11719
|1.96246
|-
|1
|2
|4
|3
|2.4545
|2.03386
|0.19627
|1.75339
|0.09698
|2.00807
|-
|1
|2
|4
|4
|2.46446
|2.01626
|0.17827
|1.76414
|0.08026
|2.02912
|-
|1
|2
|4
|5
|2.11339
|2.00724
|0.14884
|1.77964
|0.07749
|2.00585
|-
|1
|2
|4
|6
|1.51141
|2.04563
|0.11559
|1.82474
|0.06194
|2.02586
|-
|1
|2
|4
|7
|0.95936
|2.09963
|0.07044
|1.95281
|0.03645
|2.0993
|-
|1
|2
|5
|1
|3.36561
|1.97323
|0.2649
|1.65361
|0.13019
|1.92402
|-
|1
|2
|5
|2
|3.66222
|1.95479
|0.35065
|1.51028
|0.14652
|1.89882
|-
|1
|2
|5
|3
|3.20442
|1.96165
|0.28676
|1.58823
|0.12031
|1.93028
|-
|1
|2
|5
|4
|1.78673
|2.0426
|0.17183
|1.75198
|0.0678
|2.02025
|-
|1
|2
|5
|5
|1.61868
|2.01988
|0.11914
|1.80878
|0.06624
|1.99283
|-
|1
|2
|5
|6
|1.30123
|2.02218
|0.10515
|1.80653
|0.05345
|2.00292
|-
|1
|2
|5
|7
|0.65695
|2.08269
|0.06835
|1.89102
|0.0332
|2.0525
|-
|1
|2
|6
|1
|2.3773
|1.9669
|0.24867
|1.6336
|0.08319
|1.94741
|-
|1
|2
|6
|2
|2.82556
|1.95506
|0.31731
|1.51798
|0.12008
|1.89324
|-
|1
|2
|6
|3
|2.7235
|1.94883
|0.30621
|1.5177
|0.09365
|1.93764
|-
|1
|2
|6
|4
|1.77727
|1.98273
|0.17989
|1.69341
|0.07314
|1.95161
|-
|1
|2
|6
|5
|0.81041
|2.05295
|0.13961
|1.74391
|0.04468
|2.01091
|-
|1
|2
|6
|6
|0.72188
|2.0465
|0.09874
|1.79927
|0.03137
|2.03309
|-
|1
|2
|6
|7
|1.21598
|1.97942
|0.07065
|1.87211
|0.04484
|1.98491
|-
|1
|2
|7
|1
|3.55054
|1.89128
|0.27402
|1.61031
|0.10827
|1.89085
|-
|1
|2
|7
|2
|5.0062
|1.81574
|0.3119
|1.54857
|0.18009
|1.76865
|-
|1
|2
|7
|3
|3.95204
|1.84947
|0.30465
|1.53907
|0.16048
|1.789
|-
|1
|2
|7
|4
|2.36233
|1.9168
|0.18751
|1.70412
|0.09531
|1.88355
|-
|1
|2
|7
|5
|1.48851
|1.94443
|0.09973
|1.81041
|0.05904
|1.92497
|-
|1
|2
|7
|6
|1.22525
|1.94454
|0.06617
|1.87082
|0.05516
|1.91259
|-
|1
|2
|7
|7
|1.13847
|1.93756
|0.08109
|1.83388
|0.04706
|1.93165
|-
|1
|2
|8
|1
|4.09874
|1.87708
|0.20312
|1.73434
|0.15506
|1.83083
|-
|1
|2
|8
|2
|4.66403
|1.84302
|0.31808
|1.56093
|0.18049
|1.78288
|-
|1
|2
|8
|3
|3.24375
|1.89351
|0.2827
|1.59546
|0.13583
|1.83427
|-
|1
|2
|8
|4
|2.24175
|1.92084
|0.17795
|1.72611
|0.09636
|1.87438
|-
|1
|2
|8
|5
|1.63783
|1.93625
|0.1225
|1.78642
|0.0659
|1.90934
|-
|1
|2
|8
|6
|2.01753
|1.89095
|0.13742
|1.74752
|0.08289
|1.86553
|-
|1
|2
|8
|7
|0.97568
|1.97215
|0.05926
|1.88807
|0.04057
|1.95672
|-
|2
|1
|1
|1
|3.44076
|1.73133
|0.27759
|1.55037
|0.13323
|1.68913
|-
|2
|1
|1
|2
|4.99596
|1.64527
|0.2322
|1.58033
|0.17533
|1.62422
|-
|2
|1
|1
|3
|3.83372
|1.68144
|0.25087
|1.52033
|0.14525
|1.66706
|-
|2
|1
|1
|4
|3.87034
|1.68102
|0.20979
|1.60153
|0.13627
|1.68885
|-
|2
|1
|1
|5
|1.76134
|1.80424
|0.15241
|1.70485
|0.06231
|1.81524
|-
|2
|1
|1
|6
|0.79304
|1.89072
|0.09906
|1.80312
|0.03277
|1.89435
|-
|2
|1
|1
|7
|1.43535
|1.80614
|0.0593
|1.81589
|0.0407
|1.85002
|-
|2
|1
|2
|1
|3.72284
|1.68499
|0.19226
|1.66567
|0.1237
|1.66453
|-
|2
|1
|2
|2
|4.42667
|1.66508
|0.24314
|1.55652
|0.14361
|1.66251
|-
|2
|1
|2
|3
|2.7019
|1.75871
|0.32717
|1.38452
|0.11056
|1.72312
|-
|2
|1
|2
|4
|2.41538
|1.75937
|0.14575
|1.68355
|0.09038
|1.74138
|-
|2
|1
|2
|5
|1.65412
|1.81649
|0.13926
|1.70623
|0.0597
|1.81378
|-
|2
|1
|2
|6
|2.0843
|1.7735
|0.21052
|1.57508
|0.07244
|1.78566
|-
|2
|1
|2
|7
|1.43238
|1.80651
|0.08031
|1.78712
|0.05269
|1.81727
|-
|2
|1
|3
|1
|2.45314
|1.77068
|0.18152
|1.73443
|0.07657
|1.78025
|-
|2
|1
|3
|2
|3.01217
|1.70966
|0.19388
|1.66175
|0.05624
|1.80606
|-
|2
|1
|3
|3
|2.09997
|1.74945
|0.14493
|1.68277
|0.05446
|1.7922
|-
|2
|1
|3
|4
|2.36683
|1.71741
|0.12244
|1.71407
|0.06775
|1.75721
|-
|2
|1
|3
|5
|1.56776
|1.75755
|0.08776
|1.76946
|0.04244
|1.79675
|-
|2
|1
|3
|6
|1.63824
|1.75452
|0.09422
|1.76794
|0.04181
|1.80604
|-
|2
|1
|3
|7
|0.74114
|1.83421
|0.08039
|1.78306
|0.02347
|1.85596
|-
|2
|1
|4
|1
|1.47047
|1.78588
|0.17271
|1.69379
|0.06511
|1.74985
|-
|2
|1
|4
|2
|2.22168
|1.72985
|0.20701
|1.59429
|0.08178
|1.71455
|-
|2
|1
|4
|3
|2.50108
|1.69618
|0.16828
|1.61962
|0.08598
|1.70516
|-
|2
|1
|4
|4
|1.97141
|1.7202
|0.1446
|1.66357
|0.06856
|1.73201
|-
|2
|1
|4
|5
|1.17054
|1.75879
|0.1172
|1.69234
|0.04624
|1.75806
|-
|2
|1
|4
|6
|1.74755
|1.70968
|0.12562
|1.67603
|0.0629
|1.72333
|-
|2
|1
|4
|7
|0.52482
|1.80155
|0.07345
|1.75615
|0.02671
|1.79288
|-
|2
|1
|5
|1
|1.76464
|1.76219
|0.24301
|1.59094
|0.07156
|1.73136
|-
|2
|1
|5
|2
|1.99594
|1.73438
|0.1984
|1.5954
|0.06489
|1.73449
|-
|2
|1
|5
|3
|1.8804
|1.72362
|0.13019
|1.67977
|0.06783
|1.71916
|-
|2
|1
|5
|4
|1.83337
|1.71477
|0.11197
|1.70244
|0.05764
|1.73194
|-
|2
|1
|5
|5
|1.49752
|1.72615
|0.13128
|1.65461
|0.04656
|1.7433
|-
|2
|1
|5
|6
|1.3042
|1.7305
|0.07173
|1.75315
|0.04482
|1.7399
|-
|2
|1
|5
|7
|2.00868
|1.67669
|0.12298
|1.64761
|0.09175
|1.64669
|-
|2
|1
|6
|1
|0.84993
|1.75972
|0.12918
|1.74026
|0.0328
|1.74802
|-
|2
|1
|6
|2
|1.93666
|1.67406
|0.16606
|1.59943
|0.04535
|1.7106
|-
|2
|1
|6
|3
|2.12115
|1.64964
|0.19988
|1.50821
|0.05229
|1.68986
|-
|2
|1
|6
|4
|0.68831
|1.73901
|0.09674
|1.6838
|0.01696
|1.75787
|-
|2
|1
|6
|5
|1.13081
|1.69479
|0.06413
|1.72559
|0.04936
|1.67757
|-
|2
|1
|6
|6
|0.5893
|1.72537
|0.02598
|1.80138
|0.01591
|1.74082
|-
|2
|1
|6
|7
|0.72519
|1.71955
|0.03157
|1.78405
|0.02889
|1.71972
|-
|2
|1
|7
|1
|1.85937
|1.66064
|0.2416
|1.49676
|0.06807
|1.63599
|-
|2
|1
|7
|2
|1.8527
|1.64892
|0.2374
|1.43845
|0.06336
|1.6431
|-
|2
|1
|7
|3
|1.56905
|1.66084
|0.15434
|1.55598
|0.04336
|1.68109
|-
|2
|1
|7
|4
|0.74968
|1.69857
|0.13496
|1.56636
|0.02871
|1.6933
|-
|2
|1
|7
|5
|1.08222
|1.65925
|0.10847
|1.613
|0.03305
|1.67829
|-
|2
|1
|7
|6
|1.1124
|1.68059
|0.14267
|1.57525
|0.04416
|1.6776
|-
|2
|1
|7
|7
|0.88031
|1.6751
|0.10534
|1.60483
|0.04216
|1.66444
|-
|2
|1
|8
|1
|0.62802
|1.72402
|0.19225
|1.54631
|0.03247
|1.69368
|-
|2
|1
|8
|2
|0.83902
|1.68303
|0.15492
|1.53421
|0.05922
|1.61411
|-
|2
|1
|8
|3
|1.33727
|1.63407
|0.19835
|1.43309
|0.05874
|1.61141
|-
|2
|1
|8
|4
|1.06381
|1.64762
|0.11026
|1.58762
|0.04019
|1.64574
|-
|2
|1
|8
|5
|1.13714
|1.61716
|0.13322
|1.53166
|0.05648
|1.59149
|-
|2
|1
|8
|6
|1.19134
|1.60463
|0.11089
|1.54864
|0.06258
|1.56912
|-
|2
|1
|8
|7
|1.58872
|1.60204
|0.066
|1.64659
|0.04748
|1.63282
|-
|2
|2
|1
|1
|3.46775
|1.78609
|0.28956
|1.68515
|0.15003
|1.72171
|-
|2
|2
|1
|2
|5.69879
|1.67614
|0.3725
|1.5045
|0.19774
|1.64659
|-
|2
|2
|1
|3
|5.18985
|1.66571
|0.40124
|1.40574
|0.17828
|1.65793
|-
|2
|2
|1
|4
|3.43435
|1.74182
|0.20332
|1.66994
|0.11075
|1.76221
|-
|2
|2
|1
|5
|2.48643
|1.76219
|0.13714
|1.7396
|0.09636
|1.75624
|-
|2
|2
|1
|6
|1.41151
|1.82292
|0.15415
|1.6725
|0.06549
|1.80013
|-
|2
|2
|1
|7
|0.9096
|1.8409
|0.08811
|1.7823
|0.03467
|1.85275
|-
|2
|2
|2
|1
|1.85358
|1.83615
|0.28355
|1.64765
|0.06055
|1.83138
|-
|2
|2
|2
|2
|3.81188
|1.74978
|0.25972
|1.62799
|0.11238
|1.7646
|-
|2
|2
|2
|3
|3.16717
|1.76679
|0.29832
|1.53409
|0.09407
|1.78959
|-
|2
|2
|2
|4
|2.33664
|1.78934
|0.22694
|1.60101
|0.07273
|1.80371
|-
|2
|2
|2
|5
|2.01675
|1.79303
|0.10664
|1.79792
|0.06062
|1.8184
|-
|2
|2
|2
|6
|1.80809
|1.80081
|0.13659
|1.70935
|0.07335
|1.79213
|-
|2
|2
|2
|7
|1.01661
|1.8295
|0.0548
|1.84688
|0.03414
|1.84213
|-
|2
|2
|3
|1
|2.01474
|1.8142
|0.21867
|1.74325
|0.05359
|1.83088
|-
|2
|2
|3
|2
|3.53989
|1.71985
|0.28196
|1.60868
|0.10823
|1.73763
|-
|2
|2
|3
|3
|3.38412
|1.69907
|0.27409
|1.56164
|0.11042
|1.71397
|-
|2
|2
|3
|4
|2.2171
|1.74622
|0.16076
|1.70107
|0.07372
|1.75906
|-
|2
|2
|3
|5
|1.11799
|1.80944
|0.11087
|1.75678
|0.03792
|1.81891
|-
|2
|2
|3
|6
|1.40464
|1.76033
|0.10048
|1.72933
|0.05342
|1.75745
|-
|2
|2
|3
|7
|0.11328
|1.8972
|0.04052
|1.87101
|0.00787
|1.88753
|-
|2
|2
|4
|1
|2.59777
|1.74476
|0.28154
|1.66509
|0.10763
|1.71072
|-
|2
|2
|4
|2
|3.53853
|1.69511
|0.38311
|1.46839
|0.13243
|1.66523
|-
|2
|2
|4
|3
|2.80538
|1.70587
|0.26686
|1.55787
|0.1126
|1.68024
|-
|2
|2
|4
|4
|2.18191
|1.72068
|0.18333
|1.65612
|0.085
|1.71029
|-
|2
|2
|4
|5
|1.23383
|1.7716
|0.12824
|1.71179
|0.04845
|1.76628
|-
|2
|2
|4
|6
|0.85652
|1.79279
|0.0763
|1.79314
|0.03563
|1.78528
|-
|2
|2
|4
|7
|0.97995
|1.77178
|0.0797
|1.7577
|0.03846
|1.77043
|-
|2
|2
|5
|1
|2.47016
|1.74985
|0.32061
|1.60073
|0.10455
|1.71058
|-
|2
|2
|5
|2
|3.76194
|1.68979
|0.32787
|1.54675
|0.11781
|1.69109
|-
|2
|2
|5
|3
|2.61421
|1.70766
|0.20307
|1.64866
|0.08315
|1.71378
|-
|2
|2
|5
|4
|1.6809
|1.74028
|0.16795
|1.66491
|0.06202
|1.73305
|-
|2
|2
|5
|5
|1.31241
|1.75722
|0.14383
|1.68302
|0.05338
|1.74562
|-
|2
|2
|5
|6
|1.66563
|1.71781
|0.12721
|1.69231
|0.06147
|1.72101
|-
|2
|2
|5
|7
|0.87471
|1.74991
|0.07882
|1.71706
|0.04173
|1.73246
|-
|2
|2
|6
|1
|1.70055
|1.72832
|0.20839
|1.67759
|0.06001
|1.71779
|-
|2
|2
|6
|2
|3.20558
|1.65143
|0.33676
|1.47797
|0.09642
|1.6546
|-
|2
|2
|6
|3
|1.5827
|1.71538
|0.19719
|1.62038
|0.05324
|1.71254
|-
|2
|2
|6
|4
|1.7692
|1.69473
|0.14854
|1.66225
|0.05758
|1.69946
|-
|2
|2
|6
|5
|1.33003
|1.70542
|0.10726
|1.69398
|0.04565
|1.7096
|-
|2
|2
|6
|6
|1.01266
|1.71155
|0.09376
|1.70285
|0.04005
|1.70822
|-
|2
|2
|6
|7
|0.9856
|1.70091
|0.06454
|1.73063
|0.0394
|1.69796
|-
|2
|2
|7
|1
|2.02441
|1.67788
|0.30435
|1.5407
|0.08673
|1.63673
|-
|2
|2
|7
|2
|1.43949
|1.71143
|0.30098
|1.47963
|0.06527
|1.67295
|-
|2
|2
|7
|3
|1.68946
|1.66442
|0.24777
|1.47116
|0.06594
|1.64834
|-
|2
|2
|7
|4
|1.10967
|1.68591
|0.15663
|1.60109
|0.04949
|1.67069
|-
|2
|2
|7
|5
|0.77866
|1.70882
|0.11248
|1.64389
|0.03402
|1.70215
|-
|2
|2
|7
|6
|0.67502
|1.69719
|0.10289
|1.62419
|0.03507
|1.67744
|-
|2
|2
|7
|7
|0.65216
|1.70336
|0.05545
|1.73388
|0.02233
|1.72102
|-
|2
|2
|8
|1
|1.33877
|1.67358
|0.18369
|1.64385
|0.06055
|1.63818
|-
|2
|2
|8
|2
|0.71697
|1.71038
|0.25461
|1.49037
|0.04798
|1.66397
|-
|2
|2
|8
|3
|2.13197
|1.62429
|0.2393
|1.47673
|0.08136
|1.6065
|-
|2
|2
|8
|4
|1.16932
|1.66188
|0.13759
|1.60108
|0.0463
|1.64856
|-
|2
|2
|8
|5
|1.48369
|1.62387
|0.12547
|1.58988
|0.06919
|1.5925
|-
|2
|2
|8
|6
|1.18879
|1.65442
|0.10031
|1.62813
|0.07392
|1.58846
|-
|2
|2
|8
|7
|0.58052
|1.68546
|0.02696
|1.7382
|0.01982
|1.70519
|}
</center>
</div>
</div>

== Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme ==
<div class="mw-collapsible mw-collapsed">
<div>
=== Abstract ===
Based on comments on imprecision of the estimation method for 24-hour fat % in AM/PM milk recording schemes the regression formula was extended and re-estimated. Non-linearity for the existing effects of protein % of the milk sample, interval before sampling, milk amount of sample, milk amount of previous milking and interval before the previous milking was incorporated by using polynomials. Extensions were made by adding the effects of time of sampling, parity and month of sampling as class variables and lactation stage as polynomial. In total a reduction of the standard deviation of the difference between true and estimated 24-hour fat % of 2.4% was reached (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

'''''Keywords''''': estimation, fat %, AM/PM.

=== Introduction ===
The AM/PM milk recording routine is based on only one morning (a.m.) or evening (p.m.) milk sample which are collected in an alternating way. A condition to take part in this AM/PM milk recording in The Netherlands is that on farm electronic milk measurements (EMM) are available. EMM-data consists of time of milking and milk quantity of every milking. Based on one milk sample and the EMM-data the 24-hour fat % is estimated (Peeters & Galesloot, 2002<ref name=":2">Peeters, R. and P. Galesloot, 2002.Estimating daily fat yield from a single milking on test day for herds with a robotic milking system. J. Dairy Sci. 85, 682-688.</ref>). Also for farms with an automatic milking system (AMS) this estimation is used when only one milk sample is available for analysis on milk composition.

Based on comments from farmers on fluctuations in 24-hour fat % preliminary research was conducted. This showed that the current estimation caused an underestimation of 24-hour fat % based on an a.m.-sample of 0.09% while the estimate based on a p.m.-sample was overestimated by 0.05%. Possible causes for this fluctuation are differences in milk-fat synthesis between day- and night-time as was shown by Gilbert et al. (1972) <ref>Gilbert, G.R., G.L. Hargrove and M. Kroger, 1972. Diurnal variations in milk yield, fat yield, milk fat % and milk protein % by the test interval method. J. Dairy Sci. 56, 409-410.</ref>and Lee & Wardorp (1984)<ref>Lee, A.J. and Wardorp, 1984. Predicting daily milk yield, fat percent, and protein percent from morning or afternoon tests. J. Dairy Sci. 67, 351-360.</ref>. Other factors of imprecision in the current estimation can be caused by lactation stage and parity, two factors that are accounted for in the method of Liu et al. (2000)<ref>Liu, Z., R. Reents, F. Reinhardt and K Kuwan, 2000. Approaches to estimating daily yield from single milk testing schemes and use of a.m.-p.m. records in test-day model genetic evaluation in dairy cattle. J. Dairy Sci. 83, 2672-2682.</ref>.

The objective of this research is to re-estimate the regression formula which is used to estimate the 24-hour fat %s in AM/PM milk recording and AMS recordings with only one sample. By testing for non-linearity of current effects and introducing new explanatory variables the aim is to increase the accuracy of the estimated 24-hour fat %.

=== Material and Methods ===
The data needed for the objective had to meet a number of criteria. The most important criteria were that the data comprised:

* differences in interval between milking times;
* different milking times;
* multiple samples per cow per herd test date;
* milking time and quantity of all milkings;

Only data of farms that use an AMS met all of these criteria. Therefore the research was conducted on data of all farms that used an AMS from January 20th 2001 until July 1st 2004. Records with only one sample per herd test date were excluded from the analysis.

In order to estimate as well as validate the new regression formula the each herd test date was assigned at random into two separate datasets. Dataset 1 was used for estimation and contained 371.528 samplings on 50.591 cows on 537 farms. Dataset 2 was used for validation and contained 371.885 milkings on 50.643 cows on 538 farms. Some characteristics of variables of both datasets are presented in Table 1.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" |'''''Table 1. Characteristics of variables in dataset 1 (estimation) and dataset 2 (validation).'''''
|-
| rowspan="2" |'''Variable'''
| colspan="2" |'''Dataset 1 (estimation)'''
| colspan="2" |'''Dataset 2 (validation)'''
|-
|'''Mean'''
|'''Std'''
|'''Mean'''
|'''Std'''
|-
|Sample milk amount (kg)
|10.1
|3.1
|10.1
|3.1
|-
|Sample fat (%)
|4.40
|0.76
|4.41
|0.76
|-
|Sample protein (%)
|3.49
|0.35
|3.49
|0.35
|-
|Time at sampling
|12.29
|7.24
|12.31
|7.24
|-
|Interval before sample (min)
|520
|154
|521
|155
|-
|Interval before prev. milking (min)
|526
|158
|527
|159
|}
</center>

=== Methods ===
The analysis started with the currently used regression formula which uses the effects: fat %, protein %, milk amount of sampling, interval before sampling, milk amount of the previous milking and interval before the previous milking (Peeters & Galesloot, 2002<ref name=":2" />). All these effects are considered to be linear. As an extra check of the data this regression formula was re-estimated and compared to the currently used regression formula. In order to estimate the regression formula first of all the 24-hour fat % was determined by using a weighted average of all milk samples for that cow on that herd test date.

Subsequently, a number of changes to the regression formula were tested for their effect on the accuracy of the 24-hour fat %. The changes that are tested are:

# non-linearity of the current effects;
# effect of time at sampling;
# effect of lactation stage;
# effect of parity;
# month of milk recording;

The effects were all tested in a similar way by plotting the residuals of the regression formula without the effect that is tested to the tested effect. Based on this plot a possible relation between residual and effect becomes clear and the best way of incorporating the effect is shown. The conclusion if an effect had a positive effect on the accuracy of the regression formula was based on the standard deviation of the difference between estimated and true 24-hour fat %. Also the correlation between the two fat %s and the b-factor (regression coefficient) of the linear regression between the two fat %s were considered.

=== Results ===
The regression coefficients of the re-estimated regression formula differed slightly from the estimates by Peeters & Galesloot (2002)<ref name=":1" />, probably due to the different dataset.

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %.
[[File:Imagefig1.png|center|thumb|''Figure 1a: Average residual per class for the variables sample fat %'']]
[[File:Imagefig1b.png|center|thumb|''Figure 1b: Sample protein %'' ]]
[[File:Imagefig1c.png|center|thumb|''Figure 1c : Interval before sampling'']]
[[File:Imagefig1d.png|center|thumb|''Figure 1d : Interval before previous milking'']]
[[File:Imagefig1e.png|center|thumb|''Figure 1e : Sample milk amount'']]
[[File:Imagefig1f.png|center|thumb|''Figure 1f: Milk amount before sampling'']]

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %. Of all variables, only fat % of the milk sample (Figure 1a) seemed to be linear. A 2nd order polynomial fitted the interval before the previous milking. The other variables, i.e. protein % of the milk sample, interval before sampling, milk amount of sample and milk amount of the previous milking were described by a 3rd order polynomial. For all variables except fat % of the sample higher order polynomials were found significant. This however was caused by the large amount of data and no longer a possible biological effect since it also had no effect on the accuracy of the estimation.

The effect of time of sampling showed a large amount of variability over time. Using a polynomial to fit the data was therefore difficult. Estimation of the effect by hourly intervals was a good alternative as is shown in Figure 2. Lactation stage had mainly an effect in the first 50 days of lactation as is shown by Figure 3. A 3rd order polynomial fitted the data properly.
[[File:Imagefig2.png|center|thumb|''Figure 2. Average residual per class for time of sampling (minutes after midnight).'']]
[[File:Imagefig33.png|center|thumb|''Figure 3. Average residual per class for lactation stage (days).'']]

The effects of parity and month of milk sampling were both considered as class variables. For parity the effects of parity 1 to 6 and 7 or higher were considered. Table 2 shows that mainly for the lower parities the estimated 24-hour fat % was overestimated. Also the months May to October, usually the pasture period, showed an overestimation of 24-hour fat %.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" |'''''Table 2. Effect of parity and month of sampling on estimated 24-hour fat % (*100).'''''
|-
|'''Parity'''
|'''Estimate'''
|'''Month of sampling'''
|'''Estimate'''
|-
|1
|<nowiki>-6.58</nowiki>
|January
|<nowiki>-0.24</nowiki>
|-
|2
|<nowiki>-3.56</nowiki>
|February
|<nowiki>-0.28</nowiki>
|-
|3
|<nowiki>-1.42</nowiki>
|June
|<nowiki>-0.54</nowiki>
|-
|4
|<nowiki>-0.48</nowiki>
|April
|<nowiki>-0.27</nowiki>
|-
|5
|<nowiki>-0.35</nowiki>
|May
|<nowiki>-2.07</nowiki>
|-
|6
|<nowiki>-0.35</nowiki>
|June
|<nowiki>-3.36</nowiki>
|-
|7+
|<nowiki>-0.00</nowiki>
|July
|<nowiki>-4.32</nowiki>
|-
|
|
|August
|<nowiki>-5.52</nowiki>
|-
|
|
|September
|<nowiki>-4.74</nowiki>
|-
|
|
|October
|<nowiki>-2.24</nowiki>
|-
|
|
|November
|<nowiki>-0.97</nowiki>
|-
|
|
|December
|<nowiki>-0.00</nowiki>
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" |'''''Table 3. Statistics of the difference between true and estimated 24-hour fat % for six regression formulas (current, re-estimated + five steps), each also including preceding steps.'''''
|-
|style="text-align: left;"|'''Regression'''
|'''Std.'''
|'''Min'''
|'''Max'''
|'''Cor'''
|'''b-factor'''
|-
|style="text-align: left;"|Current, re-estimated
|0.2856
|<nowiki>-1.840</nowiki>
|2.224
|0.898
|0.807
|-
|style="text-align: left;"|Non-linearity
|0.2820
|<nowiki>-1.890 </nowiki>
|2.198
|0.901
|0.812
|-
|style="text-align: left;"|Time of sampling
|0.2817
|<nowiki>-1.877 </nowiki>
|2.211
|0.901
|0.813
|-
|style="text-align: left;"|Lactation stage
|0.2803
|<nowiki>-1.883 </nowiki>
|2.196
|0.902
|0.814
|-
|style="text-align: left;"|Parity
|0.2794
|<nowiki>-1.887 </nowiki>
|2.179
|0.903
|0.816
|-
|style="text-align: left;"|Month of sampling
|0.2788
|<nowiki>-1.868 </nowiki>
|2.175
|0.903
|0.817
|}
</center>

Table 3 shows some statistics of the difference between the true and estimated 24-hour fat % based on dataset 2 (validation) of the different regression formulas. Each of the five changes to the regression formula had a (minor) positive effect on either the standard deviation of the difference between the true and estimated 24-hour fat % (Std.), the correlation (Cor) between the two fat %s, the b-factor of the linear regression between the two fat %s or a combination of the these. All changes together reduced the standard deviation with 2.4% from 0.2856 to 0.2788, increased the correlation from 0.898 to 0.903 and increased the b-factor from 0.807 to 0.817.

=== Conclusions ===
The regression formula to estimate the 24-hour fat % based on one milk sample was improved. Improvements were first of all considering non-linearity of the variables by using polynomials for protein % of the milk sample (3rd order), interval before sampling (3rd order), milk amount of sample (3rd order), milk amount of previous milking (3rd order) and interval before the previous milking (2nd order). Secondly, adding the effects of time of sampling (class variable), lactation stage (3rd order polynomial), parity (class variable) and month of sampling (class variable) gave a further reduction of the difference between true and estimated 24-hour fat %. The total reduction in standard deviation of the difference between true and estimated 24-hour fat % is 2.4% (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

== Appendix 3 - A unified Python implementation of standardized 305 day yield calculation methods ==
The ICAR guideline is translated into an open-source Python package that can serve as a reference implementation for 305-day yield calculation. In addition to implementing the methods described in the original guideline (with the exception of the multi-trait method, which will be added in future work), the package incorporates 14 lactation-curve models, including traditional parametric models, Bayesian fitting approaches, and an AI-based model. The package also provides tools to derive biologically relevant lactation characteristics such as time to peak, peak yield, cumulative yield, and persistency. The package is publicly available through PyPI and can be installed directly using pip install lactationcurve (van Leerdam et al., 2026). Extensive documentation was developed alongside the package to improve transparency and reproducibility [https://bovi-analytics.github.io/bovi/lactationcurve.html https://bovi-analytics.github.io/bovi/lactationcurve.html.]

Through a companioning website (https://tools.bovi-analytics.org<nowiki/>/), users can upload milk-recording data in CSV format, fit and visualize the implemented lactation-curve models, and compare different cumulative milk-yield methodologies on both test-day and fully daily-recorded lactations using metrics such as RMSE, Pearson correlation, MAPE, and MAE. Reference datasets are provided to allow organizations to benchmark their own calculations against alternative methodologies. In addition, downloadable PDF reports summarize the results through detailed statistics and scatterplots, both overall and stratified by parity.
</div>
</div>

Section 02 – Cattle Milk Recording

2026-07-22T17:36:51Z

Cmosconi: /* Procedure 1: Computing 24-hour Yields */

= Overview =
<div class="mw-collapsible mw-collapsed">
<div>
== Introduction ==
Information about milk production traits is very important for managing and breeding dairy herds. The milk recording process starts with the collection of animal identification, a calving date of milking cows, the amount of milk given and the date with time or time frame of a day. A milk sample may be taken. The obtained milk sample is analysed for milk constituents. The results of the analysis plus the data about milk yield and time of milking are stored in a database. Subsequently a number of parameters, cumulative yields and indices are calculated and stored in the database and, finally, reported to the farmer

This Section 2 of the ICAR Guidelines focuses on the milk recording process for dairy cattle.

== Scope ==
Figure 1 gives a pictorial summary of the main elements of this guideline.

In summary, this section of the ICAR Guidelines covers the milk recording process from the enrolment of a herd for milk recording, through to the delivery of information which a herd owner can use to assist in a range of decisions.
[[File:Scope of Section 2 - Dairy cattle milk recording..png|thumb|Figure 1. Scope of Section 2 -Dairy cattle milk recording.|center|524x524px]]

Not covered in this section are:
# Standards and guidelines for ICAR approval of milk recording devices. Please consult [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices|Section 11]] for this subject.
# Standards and guidelines for ICAR approval of ID devices. Please consult [[Section 10 – Identification Device Certification|Section 10]] for this subject.
# Standards and guidelines for preparation of milk samples and for quality assurance of milk analysis. Please consult [[Section 12 – Milk Analysis|Section 12]] for this subject.
# Standards and guidelines for in-line milk analysis on the farm. Please consult [[Section 13 – On-farm Milk Analysis|Section 13]] for this subject.

== Enrolment ==

Enrolment of new herds in the recording process should involve an agreement between the farmer and the recording organisation regarding technical and financial questions such as:

# General information about the recording programme itself, i.e.
#* Herd and cow identification.
#* Scope of recorded data, including database setup as required by the user.
#* Scheduling recording.
#* Data capture and processing.
#* Recording methods and intervals.
#* Milk measuring and meters.
#* Sampling and sample transport.
#* Reports (outcomes) and supporting decisions.
# Definition of supervision scheme and other quality assurance and plausibility checking steps.
# Fee structure and invoicing.
# Approval of technicians by milk recording organisations (MROs) so as to give them free access to farms for all recording and supervision actions.

In cases where the owner of the recorded cows or his employees carry out the recording itself, it is up to the organisation to decide upon, and provide for, any necessary training.

== Standard and Guidelines for Milk Recording ==
These standards and guidelines for milk recording are valid for all milking systems, including AMS where applicable.
====General Standards and Guidelines for milk recording====
#ICAR-approved (electronic) milk meters and sampling devices must be used on the recording day (see [https://wiki.icar.org/index.php/Section_11_%E2%80%93_Testing,_Approval_and_Checking_of_Measuring,_Recording_and_Sampling_Devices#Procedure_1:_Procedure_for_Application_for_Testing_of_Measuring,_Recording_and_Sampling_Devices_or_Sensor_Systems Procedure 1 of Section 11 - Guidelines for Testing, Approval and Checking of Milk Recording Devices]). The list of approved milk meters, jars and AMS and automatic milk sampler/tray combinations sampling devices can be found on the [https://www.icar.org/index.php/certifications/icar-certifications-for-milk-meters-for-cow-sheep-goats/ ICAR web page].
#Milk weights are recorded for each milking of the recording period. The measurement may be done using any of the ICAR approved recording devices, or by weighing. The minimum accuracy of the measurement is 0.2 kg.
#Where milk constituents are analysed, the equipment used must meet ICAR standards for accuracy. Please consult [[Section 12 – Milk Analysis|Sections 12]] and [[Section 13 – On-farm Milk Analysis|Section 13]] of the Guidelines for details.
#The accuracy of the equipment used for milk recording and sampling must be checked by an agency approved by the member organisations, on a regular and systematic basis using methods approved by ICAR. The list of methods is given in [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices#Procedure 6: Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices|Procedure 6 of Section 11]] - Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices.
#All analyses of the constituents of a milk sample must be carried out on the same milk sample.
#These samples should ideally represent the 24-hour milking period.
#If milk samples do not represent a 24-hour period, the results of milk analyses must be corrected to a 24-hour period by a method approved by ICAR (see [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]).
#In cases where the duration of recording deviates from 24 hours, the results must be converted into 24-hour yields. Only approved 24-hour yield calculation methods can be used. The appropriate methodology is described in [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]
#As date of recording, we recommend to use the date on which the last sample was taken. As alternative, the date of the first sample can be used.
#Calculation methods
##The quantities of milk and milk constituents shall be calculated according to one of the methods outlined in this section of the ICAR Guidelines (see [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Standard methods for calculating 24 hour yields]).
##Member organisations should keep the ICAR Secretariat informed about the calculation methods being used by the records processing operations in their organisation or country and shall be responsible for ensuring that the records are corrected and calculated as specified in this section of the ICAR Guidelines.
====Standards and Guidelines for milk recording using AMS====
This subsection covers systems where milk weights, milk quality or other traits of the cows are monitored constantly and automatically. This can be done in both automatic and manually operated milking systems.

Requirements:
*Animal identification is automatic and reliable. Farm transponders can also be used for automatic identification if they are linked to the cow’s official identification in farm software.
*All individual milkings must be recorded from all AMSs in the farm and transmitted to the recording database for calculation, interrupted milkings included.
*For official milk recording purposes, the data file obtained from electronic milk meters must contain the following: 1) Cow ID, 2) Milking time stamp, 3) Milk weight and 4) Sampling stamp to mark the milking where the sample comes from.
*All milkings within the recording period may be sampled, and in this case the samples should be analysed separately. Alternatively, a one-milking sample can be taken for each cow, followed by fat correction calculation.
*All cows in milk on the recording day have to be sampled. The sampling device must remain in operation until all cows are sampled. When the number of available sampling devices is smaller than the number of AMS units, sampling may need to be prolonged beyond one day to allow complete sampling of all cows. In that case, the sampling device has to be moved between AMS units.
*During sampling, the automatic sampler must be monitored to make sure there are vials left for the next cows.
*24-hour yield calculations must be carried out by a MRO, independently of the AMS manufacturer. This is done in order to guarantee harmonisation of calculation methods between the different brands of equipment and software.
*Data of all milkings over a given time period must be collected for the 24-hour milk yield calculation. A 96-hour data collection period is recommended.
Recommendations:
#Ideally, data of all milkings should be collected and used to compute lactation yield.
#Description of formats to exchange data recorded by an AMS can be requested from the manufacturer or the ICAR ADE data exchange standard for milking data can be used.
#In the case of milk recording method B (see [[Section 02 – Cattle Milk Recording#Recording|chapter 1.4 "Recording]]") with AMS, the milk recording organization should make sure that the farmer knows how to load or transfer data.
#Data can be extracted by: 1) manual operation by MRO Technician’s or Farmer (file extraction), 2) automated system and data transfer through an Application Programming Interface (API), 3) another data transfer and exchange system.
#Raw milk recording data from the AMS must be easily accessible for MRO data processing.
#For official milk recording purposes, the data file obtained from electronic milk meters may also contain the following: 1) Vial ID (this is obligatory with M sampling scheme), 2) Milking duration, 3) Milking speed, 4) Incomplete milking in automatic milking systems and 5) Other relevant data measured or reported by the equipment.
#Individual milkings should be tested for milk secretion rate in order to detect interrupted and unrecorded milkings, which in turn have an effect on the calculated 24-hour yields. If there is an interrupted milking or a milking that follows an interrupted milking at the beginning of the recording period, these two milkings must be excluded from the calculations. During the recording period they can be excluded but do not need to be.
#It is recommended to individually sample all milkings within the 24-hour recording period for 24-hour fat content calculation due to the high variability of milking frequency and milk fat content. In cases where sampling all milkings is not possible, please consult Chapter 2 of [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 - Computing 24-hour Yields] (for approved correction calculation methods).
#It is recommended to sample only milkings with a preceding interval longer than 4 hours.
====Authorisation to record====
It is recommended that professional milk recording technicians are trained and certified before they carry out recordings on their own. Ideally, such training includes a period of supervised work with a certified technician. Where such a certification system is in place, it is not allowed to record without an authorisation.

It is also recommended that frequent training is given to milk recording technicians on new technologies and equipment, safety instructions and data quality issues.

In B and C recording, farmers or their employees doing the practical recording need to be capable of operating the recording equipment correctly (e.g. milk meters, data capture tools) and are familiar with recording techniques.

It is recommended to have a conformation test from a certified recording agency and that frequent training take place.
====Cows to be recorded====
In a recorded herd, all milk-producing cows must be recorded. If a herd is divided into groups, all animals in the group have to be recorded on the same recording scheme. If different recording schemes are practiced on the farm all cows must be recorded according to the standards for recording and sampling intervals in table 3.

Acceptable reasons for missing data are discussed below, in 5.5. Missing results and/or abnormal intervals are reported [[Section 02 – Cattle Milk Recording#Missing results|here]].

===Identification (ID)===
====Herd ID====
Each herd in milk recording must be allocated a unique permanent identification number.
====Animal ID====
An official milk recording system must be based on a clearly identifiable and unique animal ID. It is recommended that one identification scheme for the whole country is used. Animal identification must also be in accordance with national and international regulation (e.g. EU member countries with EU legislation - 1760/2000 for cattle), and with relevant parts of currently valid ICAR Guidelines. The animal must be marked with an ICAR approved identification device or system. If the ID of imported animals is changed, the connection to the original ID must be maintained. Management numbers for cows can be used aside the official ID.
====Identification of the sample vial====
The sample, the milk weight and the cow ID must be linked at the milking.

Vials can be identified according to:
#Vial placement in the sampling unit.
#Cow or sample ID written on the vials.
#Barcoded vial with printed cow ID.
#Barcoded vial with cow ID registered at the milking.
#RFID vial with cow ID registered at the milking.
=====Sample identification without electronic equipment=====
Samples are identified according to their placement in the sampling unit. Additionally, sample or cow numbers can be written on the vials with a waterproof marker. If this marking is not done, there must be a sure and efficient way to identify sample No. 1 (e.g. different colour) and the sequence of other samples.

Each sampling unit must be connected to a list of samples where cow ID is given for each sample. Each transportation box also has to carry the relevant herd ID’s and, preferably, the sampling dates.
=====Barcoded vials=====
Samples are identified according to the barcode on the vial label.

If the label contains cow and/or herd ID, no electronic equipment is needed at the recording. The samples can be sent to the laboratory without accompanying sample lists or herd ID markings on the box.

If the label contains a random sample ID number, the cow ID must be connected with it on the farm. This is done with a barcode reader and computer programmes making the connection possible.
=====Vials with RFID=====
Samples are identified according to the RFID chip in the vial. This system requires the use of RFID readers and specific computer programmes creating a file where the cow and vial ID’s are connected.
=====Automatic sampling systems=====
In automatic milking systems (AMS), ICAR approved automatic samplers have to be used. Sample identification in these systems can be based on vial placement, barcode or RFID. The file with corresponding cow ID is in the management programme of the milking system. Data transfer is carried out with specific software and via a specific interface from the AMS to the MRO.
=====Sample ID in the laboratory=====
For impartiality and better quality, it is recommended that the samples are identified without cow ID and sent to the laboratory anonymously and the analysis results are merged afterwards in the data processing centre.
====Connection of the sample to milking and 24 h yield====
=====Sample and milk weight from the same milking=====
The ideal situation is that the sample and milk weight represent the same milking.
=====Sample from one milking, milk weight from two=====
A corrected analysis is routinely attached to the 24-hour yield.
=====Sample from one milking, milk weight from two or more, corrected by intervals=====
In this case, a 24-hour-yield is also combined with a one-milking sample, but the 24‑hour yield is obtained by correcting the recorded milkings according to the length of the preceding milking intervals. For example, if a cow has produced 20 kg milk in two milkings and the preceding intervals total 20 hours, her 24-hour yield is calculated as 20 kg * (24 h/20 h) = 24 kg. A corrected analysis is attached to this 24‑hour yield.
=====Sample from one milking or day, milk weight from several days=====
With electronic milk meters, it is possible to use the milk production from several days. This gives better accuracy of milk yield estimation; the highest accuracy with uncorrected milk weights is reached using a 4-day average. The problem is that the sample results become disconnected from the milk yield and a loss in fat and protein yield accuracy will occur. Ideally, fat and protein production should be connected to the recording day even in AMS.

In this case, there are three options to connect samples to the 24-hour yield:
#Milk weight is estimated from a longer measurement period but for fat and protein yield estimation only the milk yield on sampling day is used.
#Information only from the recording day for constituents in milk and milk yield estimation.
#Combination of multiple day milk yield with constituents from sampling. See ICAR procedures for using data from more than one day (Lazenby ''et al''., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>, estimation of fat and protein yield (Galesloot and Peeters , 2000)<ref name=":1">Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>.
The analysis data are merged with milk weights in the laboratory or data processing centre and the date of the analysis must be known.

=== Traits to be recorded ===

==== Definition of milking speed and box time ====

===== Introduction =====
Automated Milking Systems (AMS) do measure many traits. The definition of these traits might be different per brand of AMS. Data of these traits is often used by e.g. milk recording organisations, herdbooks or management software providers. When organisations store these data in their databases and use for certain services, it is important to know how these traits are defined.

These definitions could be used by milk recording organisations etc. to take into account differences between traits measured by different brands of AMS. These definitions could also be used by manufacturers of AMS to take into account for product development, to get more alignment in trait definitions between different brands of AMS.

Aim of this document is to propose a harmonized definition of some traits measured by AMS.

At this stage, the traits milking speed and box time are taken into account. Traits related to teat coordinates are described in Section 5 (Conformatoin Recording) of the ICAR guidelines.

==== Average milking speed ====
Definition = AverageMilkingSpeed (gr/min) = {TotalMilkYield / TotalMilkingTime}

* Total milk yield (kg) = Sum of all quarter level milk yields (kg)
* Total milking time = Last Take-off time (of any teat) - Begin of milk flow (of any teat)

Recommendations for manufacturers:

* Exclude any pre-treatment time from milking time.
* Provide take-off settings (threshold in gr/min at take-off, user-defined or default) and settings for the beginning of the measurement period, as milking time will be influenced by take-off settings and by the definition of the beginning of the milk flow.

Recommendations for data users:

* Don't report milking sessions with kick-off´s, interrupted and re-attached milkings because milking time will vary for these milkings.

==== Box time ====
Different types of box time:

* Milking
* Feed-only
* Pass-through
* Selection
* Training

Definition = {End box time - Begin box time} (HH:MM:SS)

* Begin box time = datetime of recognition of animal
* End box time = datetime when cow has exited the box (which might be different from opening of the gate), best to detect when cow has actually left the box

Additional data is needed to understand the status and completeness of the milking visit (Wethal and Heringstad, 2019). Registered issues during the milking are e.g.

* ff: at least 1 teat cup kicked off
* TeatNotFound: unable to find at least 1 of the teats for milking
* IncompleteMilking/FailedMilking: Minimum of 1 teat was registered as incompletely milked.
* The expected milk yield for a milking session depends on previous milkings. Settings like yield less than 80% of expectation for a teat, the milking session would be recorded as having an incompletely milked teat.
* Manual interaction like teat manually attached or milking finished manually.

Recommendations for manufacturers:

* Make the codes available that express if a milking was successful and the cause if the milking was not successful.
* Uniform names and definitions for interrupted, incomplete or failed milkings as well.

Recommendations for data users:

* Check the availability of a code that expresses if a milking was successful and the cause if the milking was not successful. The meaning of the code can be used to consider if the box time record has to be used for the intended purpose or not.
* To check if there is any extra box time due to feeding concentrates, e.g. through user specific settings such as 'PriorityFeeding'.

=== Traits to be recorded ===
In official milk recording, the following data have to be recorded, wherever available:

# Identification of each cow in the herd, even if they remain in the herd for a very short time.
# Birth date, sex, breed and parents of each animal when known.
# All services and embryo flushings and transfers: date, recipient, sire, dam of the embryo.
# All animal deaths and movements between farms and owners.
# Recording dates and locations.
# Milk yields for each cow and recording date.
# Fat content in milk for each cow and sampling date.

It is recommended to record also the following:

# Protein content in milk for each cow and sampling date.
# Milk somatic cell count for each cow and sampling date.
# Other results obtained from milk analysis.
# Milking duration and milking speed where possible.
# Milking times during recording.
# Recording methods and respective symbols used in records.
# Information about cow during the rearing period.

=== Recording method ===
The recording method for the herd consists of using five different symbols for:

# Responsibility for the practical recording.
# Sampling scheme.
# Recording interval.
# Sampling interval (if different from the above).
# Number of milkings per day (especially any deviation from 2x milking).

The symbols in Table 2 should be used:<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Symbols for milk recording schemes.''
|- style="background-color:#efefef; text-align:center;"

|'''Responsibility for recording'''
|'''Sampling scheme'''
|'''Recording interval (weeks)'''
|'''Sampling interval (weeks)'''
|'''Number of milkings per day'''
|-
| style="text-align:center;" | A
| style="text-align:center;" | P
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | B
| style="text-align:center;" | E
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | C
| style="text-align:center;" | Z
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" |
| style="text-align:center;" | T
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" |
| style="text-align:center;" | M
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:center;" | R x
|-
| style="text-align:center;" |
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | S x
|}
</center>

As an example: Recording method is CP36, 2x means that this is a recording where records/ samples are taken partly by the owner (farmer), and partly by a technician from the MRO, where the recording frequency is every 3 weeks, where the sampling frequency is every 6 weeks, and where the number of milkings per day is 2. If a national nomenclature system is used, it should be possible to transfer this system into ICAR nomenclature.

The reference milk recording method is by a representative of the recording organisation, measuring and sampling every four weeks, with proportional sampling and two milkings per day (AP44, 2x).

Recording other than by the reference method must be indicated using the appropriate symbols.

It is recommended that a limit is set for changing the recording method e.g. so that normally it is only possible to change the method twice per year.

It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

In the next sections the symbols are explained:
====Responsibility for the recording====
This symbol indicates who is responsible for measuring the milk yields and taking samples in the herd.
#Representative of the MRO (Method A; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Farmer or his/her representative (Method B; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Mixed responsibility (Method C; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
====ICAR Standards for sampling schemes====
=====Proportional sampling (P)=====
Samples and milk weights are taken at each milking during the recording day. The sampled amount corresponds to the milk yield of each milking. This is achieved by the use of a pipette in equal number of pipetting at each milking or of a specially designed tool which ensures proportional sampling to create one mixed sample. This is the default sampling scheme with no necessary correction to the analysis results, all other schemes must be reported.
=====Equal measure sampling (E)=====
Samples and milk weights are taken at each milking during the recording day. The amount of the sample is measured to be equal at each milking and mixed into one sample. The analysis results for fat should be corrected if one of the milking intervals is shorter than 10 or longer than 14 hours.
=====Multiple sampling (M)=====
Samples are taken at more than one milking during the recording day while milk weights are taken at each milking or over several days. Samples from different milkings are not mixed but they are kept in distinct vials so that each cow has at least two samples. The analysis results must be corrected to correspond to the 24-hour fat and protein yields. For example: a cow is milked 3x during 24 hours and 2 or 3 separate samples are taken, kept and analysed in different vials. This is the gold standard for AMS. It produces the most accurate results but is more expensive.
=====One-milking sampling with milk weights from more than one milking (Z)=====
Samples are taken from one milking during the recording day while milk weights are taken at each milking or over several days. The analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Alternated one-milking recording (T)=====
Samples and milk weights are taken during one milking, alternating between morning and evening milkings. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Constant one-milking recording (C)=====
Samples and milk weights are taken during one milking, constantly during morning or evening milking. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====In-line analysis recording (I)=====
Milk is not sampled but its constituents are continuously analysed by a stationary analyser.
====ICAR Standards for recording and sampling intervals====

<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Standards for recording and sampling intervals.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| rowspan="2" style="text-align:center;" |'''Recording or sampling interval (weeks)'''
| rowspan="2" style="text-align:center;" |'''Minimum number of recordings or samplings per year'''
| colspan="2" style="text-align:center;" |'''Interval between recordings or samplings (days)'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| rowspan="10" style="text-align:center;" |Reference method
| style="text-align:center;" |1
| style="text-align:center;" |44
| style="text-align:center;" |4
| style="text-align:center;" |10
|-
| style="text-align:center;" |2
| style="text-align:center;" |22
| style="text-align:center;" |10
| style="text-align:center;" |18
|-
| style="text-align:center;" |3
| style="text-align:center;" |15
| style="text-align:center;" |16
| style="text-align:center;" |26
|-
| style="text-align:center;" |4
| style="text-align:center;" |11
| style="text-align:center;" |22
| style="text-align:center;" |37
|-
| style="text-align:center;" |5
| style="text-align:center;" |9
| style="text-align:center;" |32
| style="text-align:center;" |46
|-
| style="text-align:center;" |6
| style="text-align:center;" |8
| style="text-align:center;" |38
| style="text-align:center;" |53
|-
| style="text-align:center;" |7
| style="text-align:center;" |7
| style="text-align:center;" |44
| style="text-align:center;" |60
|-
| style="text-align:center;" |8
| style="text-align:center;" |6
| style="text-align:center;" |50
| style="text-align:center;" |70
|-
| style="text-align:center;" |9
| style="text-align:center;" |5
| style="text-align:center;" |55
| style="text-align:center;" |75
|-
| style="text-align:center;" |Daily
| style="text-align:center;" |310
| style="text-align:center;" |1
| style="text-align:center;" |3
|}
</center>

====ICAR standards for number of milkings per day====

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 3. Symbols for number of milkings per day.''
|- style="background-color:#efefef; text-align:center;"
|'''Number of milkings per day'''
|'''Symbol'''
|-
| style="text-align:center;" | Once per day milking
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | Two milkings
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | Three milkings
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" | Four milkings
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" | Continuous milking (e.g. AMS)
| style="text-align:center;" | R x
|-
| style="text-align:center;" | Regular milkings not at the same times on each day (e.g. 10 milkings per week)
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" | Shown as the average number of milkings per day.
| style="text-align:center;" |
|-
| style="text-align:center;" | Animals that are both milked and suckled. (Number of times milked to prefix the S)
| style="text-align:center;" | S x
|}
</center>

Where a herd is dry for a period of the year, the minimum number of recordings should be adjusted proportionately to the production period.

Minimum number of herd recordings should be at least 85% of the normal number of recordings.

=== Missing results and/or abnormal intervals ===
{{anchor|Missing_results}}A recorded 24-hour yield is the best estimate of the yield and the constituents of the milk, weighed, sampled and recorded within 24 hours on the day of recording.
#When herds are normally milked at intervals such that the recording day is other than 24 hours, the yields shall be adjusted to a 24-hour interval using the following procedure (or other procedures approved by the ICAR):
#*Divide 24 by the interval, then multiply by the yield. For example:
#**For a 25 hour interval (24/25) x 35 kg = 33.6 kg
#**For a 20 hour interval (24/20) x 35 kg = 42.0 kg
#A recording is a set of daily test values for a given animal on a given day of recording, one or some or all of them can be missed (missing values)
#Missing values can be due to:
#*Out of range.
#*Sickness.
#*Disaster.
#*No sample analysis results.
#The number of the official and complete (milk, fat and protein) recordings in the lactation or other accumulated yield should be reported.
#Permitted range of the daily recorded values is given in Table 5. Outside of these ranges, the daily recorded<ref>'''Note:''' High fat breeds have breed average higher than 5.0 for fat %.</ref> value will be considered as a missing value.

<center>
{| class="wikitable"
! colspan="7" style="text-align:left;" | ''Table 5. Permitted range of the daily recorded values.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| colspan="2" style="text-align:center;" |'''Milk (kg)'''
| colspan="2" style="text-align:center;" |'''Fat %'''
| colspan="2" style="text-align:center;" |'''Protein %'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| style="text-align:center;" | Main Dairy Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 1.5
| style="text-align:center;" | 9.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 7.0
|-
| style="text-align:center;" | High Fat1 Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 2.0
| style="text-align:center;" | 12.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 9.0
|}
</center>1Note: High fat breeds have breed average higher than 5.0 for fat %The true daily recorded values collected from animals labelled by the farmer as sick, injured or under treatment must be used in the computation of the lactation record unless the milk yield is less than 50% of the previous milk yield or less than 60% of the predicted yield. In such a case, the whole set of daily recorded values may be considered as missing.

Estimates of the missing values of a daily recording can be computed by using interpolation procedures or by more sophisticated procedures approved by ICAR

== Samples ==

=== Representative sample ===
The milk sample has to represent the complete milking linked to it. This is achieved by mixing the milk thoroughly or pouring it into another vessel right before sampling.

Sampling scheme P requires using a pipette for making the sample proportional between different milkings.

With sampling scheme E, it is advisable to use a measuring cup to make sure the sample parts actually are equal.

Immediately after sampling, the vials have to be preserved, capped, shaken and marked. Samples should be stored cool and dark.

=== Transport ===
Samples should be transported for analysis to a laboratory as soon as possible after sampling.

The samples need to be packed for transport and handled during transport in a manner that guarantees that sample IDs are not compromised or mixed. It is also recommended to protect the packages from external interference.

The packing material must be clean and disposable or easy to clean.

During transportation, it is recommended that the temperature of the samples stays below +10°C.

== Database ==
Storing the recorded data in a milk recording database is an indispensable part of the recording. It is recommended to use the quickest possible means to store the data in the database in order to ensure up-to-date breeding values and management applications. Where computerised data capture is possible, it should not take more than five days after the recording to have the complete recording data set in the database.

The application of the Guidelines in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield], together with other parts of the Guidelines, ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

The guidelines on storage of data collected by the milk recording process are:

# For every recording, cow identification (ID), 24-hour milk yield or individual milk yields with a minimum of 0.2 kg (or the equivalent thereof) milk accuracy and recording date have to be stored.
# Where possible, it is advisable to store each milking separately. The data stored can include milk yield, time and date of milking, and milking scheme.
# Analysed results of the milk sample are stored, namely: sample ID, fat content (or percentage), sample status, sample type. Optional data can be stored on protein and/or lactose content, somatic cell count and additional analyses.
# Analysis results can be linked to one or more milkings of the cow.
# In case of storage or performance problems it might be necessary to remove old data of individual cow milkings from the database.
# Recording day information is the yield over 24 hours and should at least be kept in the database for the current lactation and the previous lactation.
# If recording day information is changed after batch processing it should be marked with a user-ID and time stamp.
# Yields are stored in kg or lbs or, in the case of fat and protein contents, in percent units.

The necessary additional information about how the results have been obtained include:

# Who did the recording (certified technician, farmer etc.).
# Herd and/or cow milking frequency.
# How many milkings were measured.
# How many milkings were sampled.
# Sampling scheme when sampling.
# Daily yield calculation method used.
# Recording and sampling intervals.
# It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

Basic checks for recording data:

# Farm (herd) ID: identified by a unique key.
# Animal ID: has to be unique in database.
# Format of animal ID: compliant to international standards of identification and registration.
# Recording date: less than or equal to today, greater than last recording date.
# Milk yield: stored with one decimal.
# 24 hour milk yield within range ( Table 5).
# Fat and protein content: e.g. within a range of +/- 3 standard deviation of population average (Table 5).
# Calving date: greater than birthday of cow (e.g. greater than birthday of cow + 20 months).
# Calving date: less than or equal to today.
# Sample analysis

This section of the ICAR Guidelines examines how observations are performed on farms and how data are collected, analysed and reported back to farmers. It forms an integral part with other sections of the ICAR Guidelines. It ensures that samples are analysed to the relevant degree of accuracy for the purposes of milk recording, breeding value prediction and other areas of usage. ICAR members operate in a range of situations, ranging from places with almost fully automated recording systems to areas with no roads and electricity. Therefore, the guidelines only demand standards that can be followed, irrespective of production situations and recommend more advanced options, where possible or required. Under the guidelines some practices might not be permitted while other practices are tolerated but not recommended.

== Yield calculations ==
This section covers 24-hour yields and accumulated yields for milk, fat, protein and somatic cells. It also describes the procedure for acceptance of new methods not previously mentioned in the guidelines.

The basic requirements for all calculation methods are that rounding shall only take place at the last step of the computation.

=== Lactation period ===

==== Commencement of the lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, is considered to commence is:

# The day that the cow calves (calving date), or
# In the absence of a calving date, the best estimate of the day that the cow commenced milk production.

A (valid) calving is defined as a parturition taking place:

# After the mid-point of the gestation period if a service has been recorded, or,
# After at least 75% of the normal gestation period has elapsed since the previous calving recorded if no service event has been recorded.

Any parturition falling outside the above definition shall be recorded as an abortion and shall not start a new lactation period.

For cows of dairy breeds the normal gestation length shall be deemed to be 280 days unless more specific breed information is available for use.

If the first recording is done on the calving date or within the first 4 days after calving, the milk yield and constituents at the first recording should not form part of the official lactation record, especially for automated milking systems (AMS) with multiple recorded days.

==== Completion of lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, has been completed is or:

# The day that the cow ceases to give milk (goes dry) or
# The day the cow gives less than 3.0 kg/day or 1.0 kg/milking in a recording (unless recorded sick) or
# When it is common practice not to record the dry-off date, the day of the midpoint between the last recording with the cow in milk and the first recording day with the animal dry may be assumed to be the dry-off date.

The lactation period ends on whichever date above occurs first.

Cows may be recorded as absent or sick on the recording day, without the lactation period being defined as terminated.

=== Production period ===
In the case where yield records are calculated on the basis of a period of production, usually a year, the record should be expressed as a ‘production period record‘ (symbol PP).

The production period begins the day after the end of the previous production period and ends as defined by the length (in days) of the production period.

=== Additional notes ===
For any ICAR method the interval between two consecutive recordings must routinely fulfil the value for the acceptable range on the herd level.

If the first recording occurs within 14 days from calving, then no adjustment is required to the first recorded value when computing the accumulated record. If the first recording occurs 15 to 95 days from calving, then an adjustment procedure may be applied.

If the 305th day of a lactation falls before the last recording, the interpolation method should be used also for the last period to compute the yields.

=== Standard methods for calculating 24 hour yields ===
The ICAR approved methods are presented in '''[https://www.icar.org/Guidelines/02-Procedure-1-Computing-24-Hour-Yield.pdf Procedure 1 of Section 2]'''. They include:

1. Methods for calculating daily yields from AM/PM milkings:

# Method of Delorenzo and Wiggans (1986)<ref>Delorenzo, M.A., and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. [https://www.journalofdairyscience.org/article/S0022-0302(86)80678-6/pdf J Dairy Sci 69; 2386]</ref>
# Method of Liu et al. (2019). Please note that in 2022 the method of Liu et al. (2000)<ref name=":0">Liu, Z., R. Reents, F. Reinhardt and K. Kuwan. 2000. Approaches to Estimating Daily Yield from Single Milk Testing Schemes and Use of a.m.-p.m. Records in Test-Day Model Genetic Evaluation in Dairy Cattle. [https://www.journalofdairyscience.org/article/S0022-0302(00)75161-7/pdf J. Dairy Sci. 83:2672-2682].</ref> has been updated to the method of Liu et al. (2019). We recommend to organisations that currently have implemented the method of Liu et al. (2000)<ref name=":0" /> to update to method of Liu et al. (2019).
# Method of Kyntäjä et al. (2021)<ref name=":3">1. Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. [https://www.icar.org/Documents/technical_series/ICAR-Technical-Series-no-25-Virtual-Meeting/Kyntaja.pdf ICAR Technical Series no. 25: 171-175.]</ref>

2. Methods to estimate 24h yield from Automatic Milking Systems:

# Using data on more than one day (Lazenby et al., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Using data on 1 day (Bouloc et al., 2002)<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Estimation of fat and protein yield (Galesloot and Peeters, 2000)<ref>Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>
# Sampling period (Hand et al., 2004<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D.F. 2004. Comparison of Protocols to Estimate 24 Hour Percent Fat and Protein. Presented at 34th ICAR session, Sousse, Tunisia, June, 2004. Proceedings of the 34th ICAR Meeting EAAP Publication No. 113:219-224</ref>; Bouloc et al., 2004)

3. Standard methods to estimate 24h yield from electronic milk meters:

# Estimation of 24-hour milk yield
# Using data on more than one day (Hand et al., 2006)<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. [https://doi.org/10.3168/jds.S0022-0302(06)72240-8 J. Dairy Sci. 89:1723-1726]</ref>
# Estimation of 24-hour fat and protein yield

=== Standard methods for calculating accumulated yields ===
The ICAR approved methods are presented in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_2_%E2%80%93_Computing_of_Accumulated_Lactation_Yield Procedure 2 of Section 2]. They include:

# Test Interval Method (TIM) (Sargent, 1968)<ref>Sargent, F.D., V.H. Lyton, and O.G. Wall, Jr . 1968. Test interval method of calculating Dairy Herd Improvement Association records. [https://doi.org/10.3168/jds.S0022-0302(68)86943-7 J. Dairy Sci. 51:170].</ref>
# Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987)<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. [https://doi.org/10.1016/0301-6226(87)90049-2 Livest. Prod. Sci. 17:l].</ref>
# Best prediction (VanRaden, 1997)<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. [https://doi.org/10.3168/jds.S0022-0302(97)76268-4 J. Dairy Sci. 80:3015-3022].</ref>
# Multiple-Trait Procedure (MTP) (Schaeffer and Jamrozik, 1996)<ref>Schaeffer, L.R. and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. [https://doi.org/10.3168/jds.S0022-0302(96)76578-5 J. Dairy Sci. 79:2044-2055.]</ref>

=== Procedure to approve new methods ===

# All parties interested in seeking approval for any new accumulated yield calculation method will notify the ICAR Secretariat and provide a description of the proposed method.
# These parties will provide a detailed report including statistical details, scientific references and other relevant data to the ICAR Dairy Cattle Milk Recording Working Group.
# The ICAR Dairy Cattle Milk Recording Working Group will then consider the proposal and recommend that it be conditionally approved, approved or rejected.
# The final steps will consist of approval by the General Assembly and publication in the guidelines. .

== Reporting ==
This subsection covers reports, data files, statistics and calculated key figures provided to farmers for breeding and management purposes.

It is recommended that farmers are given reports after each recording and at the end of the recording year or another longer recording period. These reports should contain data on both cow and herd level. In bigger herds, it is also advisable to present results by management groups or otherwise chosen cow groups within the herd. The reporting may be done on paper, through web pages and/or in the form of data files or electronic reports.

Where data files are distributed or direct access given to the results in the database, care must be taken that data ownership is clearly defined. This also includes defining who has access to data and how this access can be authorised.

ICAR members are advised to prepare annual statistics in a reasonable timeframe after closing the recording year. The minimum data requirements are what is needed for the ICAR [https://my.icar.org/stats/list Dairy Cattle Yearly Enquiry on-line database].

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 5. Examples of key figures for herd to be used by farmers and other users.''
|- style="background-color:#efefef; text-align:center;"
|style="text-align:left |'''Key figure'''
|style="text-align:left |'''Explanation'''
|-
| style="text-align:left;" | 12-month rolling average yield
| style="text-align:center;" | Total milk, fat and protein produced during the 365 (366) days preceding the recording divided by the average number of cows for the same period.
|-
| style="text-align:left;" | Average 305-day yield
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations finished during the reporting period divided with the number of finished 305-day lactations.
|-
| style="text-align:left;" | Average 305-day yield within a period
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations during the reporting period divided with the average number of cows on a 305-day lactation within the reporting period.
|-
| style="text-align:left;" | Average annual yield
| style="text-align:center;" | Total milk, fat and protein produced during the recording year divided by the average number of cows for the same recording year.
|-
| style="text-align:left;" | Average calving interval
| style="text-align:center;" | The average preceding intervals of all calvings second and more during the reporting period.
|-
| style="text-align:left;" | Average fat, protein or lactose contents in milk
| style="text-align:center;" | Total fat, protein and lactose yields divided by the total milk yield, usually expressed with two decimals.
|-
| style="text-align:left;" | Average lactation yield
| style="text-align:center;" | Total milk, fat and protein produced within lactations of any length finished during the reporting period divided with the number of finished lactations.
|-
| style="text-align:left;" | Average lactation yield within a period
| style="text-align:center;" | Total milk, fat and protein produced during the reporting period divided with the average number of cows in milk within the reporting period.
|-
| style="text-align:left;" | Average number of cows
| style="text-align:center;" | Average number of cows in the herd (or group) on a given day during the reporting period. Usually expressed with one decimal.
|-
| style="text-align:left;" | Average somatic cell count
| style="text-align:center;" | The average of all individual cow somatic cell counts weighted for individual milk yields.
|-
| style="text-align:left;" | Daily milk, fat and protein yields
| style="text-align:center;" | 1) Total daily milk, fat and protein yields divided by number of cows, or 2) Total daily milk, fat and protein yields divided by number of cows in milk.
|-
| style="text-align:left;" | Energy Corrected Milk (ECM)
| style="text-align:center;" | Calculated according to a national standard.
Example from the Nordic countries:

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + milk yield, kg * 0.7832)/3.14

or, if lactose has been analysed

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + lactose yield * 16.54 + milk yield, kg * 0.0207)/3.14.

From solids expressed as %:

ECM = [(fat content, % * 383 + protein content, % * 242 + 783.2)/3140]* milk yield, kg

or, if lactose has been analysed

ECM = [(fat content, % * 383 + protein content, % * 242 + lactose content, % * 165.4 + 20.7)/3140]* milk yield, kg.
|-
| style="text-align:left;" | Number of lactations
| style="text-align:center;" | Total number of finished lactations in the herd (or group) during the reporting period.
|-
| style="text-align:left;" | Reporting period
| style="text-align:center;" | The period presented in the given report. The most usual options are: one day, one recording interval, lactation, rolling 365 days, recording or calendar year, and the cow’s lifetime.
|}
</center>

== Decisions ==

As a result of the recording process and reports prepared on the basis of its results, decisions can be made on one or more of the following:

=== Short term impact: day-to-day management decisions taken on farms ===

# Decisions about bulk milk quality.
# Feeding decisions - daily diet based on group or individual performance.
# Pasture management decisions.
# Grouping decisions - placing cows in different management or feeding groups.
# Culling decisions - decisions on the sale or slaughter of cattle.
# Mating decisions.
# Decisions regarding programmes of certification for milk and milk products.
# Decisions based on data flow from MRO’s to farms and vice versa.

=== Medium-term impact ===

# Farmers’ decisions based on advisory services, veterinarians, independent experts and other services.
# Decisions about production planning on farms (herd development).

=== Long-term impact ===
# Breeding programme and selection decisions - breeding partners informed by genetic evaluation ([[Section 09 – Dairy Cattle Genetic Evaluation|Section 9)]] based on milk recording results.
# Decisions based on herd book and breeder association activities and deciding on business actions related to breeding animals, i.e. in some countries animal recording data are required for international trade with breeding animals.

=== Strategic decisions ===
# Research programmes concerning management, recording and breeding.
# Political decisions about possible subsidies in dairy cattle breeding at the governmental level and implementing measurements according to agriculture policy.

== Quality control ==
This Section together with other parts of the Guidelines ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

=== Bulk tank data comparison ===
It is a recommended practice to compare milk recording data with dairy deliveries and bulk tank milk contents. This can be done on the recording day or over a longer period of time. The calculation is done as follows:

# Comparison ratio = Total recorded milk yield, kg /Total milk produced, kg. This comparison is used where there is a reliable estimate of the farm use of milk.
# Quick comparison ratio = Total recorded milk yield, kg/ Total milk delivered, kg. This comparison is used where farm use of milk is not estimated.
# Content comparison = Recorded average fat / Bulk tank average fat
# Comparison ratio for fat = Total recorded fat yield, kg/ Total fat produced, kg
# Total recorded milk yield, kg = Ʃ (Individual milk yield, kg)
# Total milk delivered, kg = Total milk delivered, litres * milk density kg/litre
# Total milk produced, kg = (Total milk delivered, litres + Milk used or discarded on the farm, litres) * milk density kg/litre
# Total fat produced, kg = Total milk produced, kg x (Bulk tank fat percent/100)
# Recorded average fat = Ʃ [Individual milk yield kg x (Individual fat percent/100)]/Ʃ (Individual milk yield, kg)

The recommended acceptable range for comparison ratios is 0.95 - 1.05, and for quick comparison ratios 0.90 - 1.00, with due regard to herd size.

=== One day bulk tank data comparison ===
Milk yields and fat yields or contents are compared on the recording day. Comparing the contents is routinely possible where every delivery is sampled or by taking a bulk tank sample (see point [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Bulk_tank_data_comparison 1.10] above for how the comparison is done.)

=== Bulk tank data comparison over a longer period ===
Milk yields and fat yields or contents are compared over a longer period of time, e.g. 4 months or 12 months. This option requires a routine to obtain the applicable data from the dairies or milk buyers. Farm use of milk may be taken into account where applicable.

=== Bulk tank sample ===
Bulk tank samples can be used to verify the milk contents analysis obtained in milk recording. A sample is taken from a well-mixed bulk tank on the recording day. It must represent the milk of the whole 24-hour period. Bulk tank fat and protein contents are then compared to the weighted averages of the fat and protein percent obtained from milk recording. Normally, the difference between the values should not be more than 5%.

=== Supervised or repeated recording ===
Supervised recording is a tool designed to verify that individual cow records are reliable. It is based on repeating the herd recording as soon as possible after the original recording, and the obtained results are compared with the original recording. It is obligatory for ICAR Certificate of Quality (CoQ) holders to practice regular supervision, irrespective of recording methods used.

It is recommended that the supervised recording will follow immediately after the original recording, but for a good reason it can be postponed for up to 7 days.

The farmer and any other staff doing the original recording must not know that a supervised recording will follow. The technician who performs the supervised recording should not be the same person who did the original recording.

Usually supervised recording is done by recording the whole herd again, using the same sampling scheme and recording method (or a reference method) as in the previous recording. When herd size exceeds 200 cows, it is also allowed to do a supervised recording to selected, or randomised groups of animals in the herd.

Choosing the herds for supervised recording may be random or based on preselection. Traits for this preselection may include high yield, great increase in yield, presence of bull dams in the herd, and general suspicions about the correctness of herd results.

The traits compared in supervised recording must include milk and fat. Comparing protein is also recommended.

=== Supervision - example of comparison calculations ===

# Milk, fat and protein yields per cow are calculated for both the original and the supervised milking.
# Individual cow records where results between supervised recording and the original recording differ outside the norms might be excused where a good explanation can be given for exclusion (illness, heat, missed milking)
# Deviations (%) are calculated for each cow and yield constituent according to the formula: deviation = (supervised yield/unsupervised yield)*100-100
# Herd averages of the absolute values for each yield constituent are calculated.
# If the supervised recording occurs within 2 days of the original recording, the acceptable difference in herd averages are 7% for milk and protein and 9% for fat.
# If the supervised recording occurs between 3 and 7 days after the original recording, the acceptable difference of the aforementioned herd averages are 9% for milk and protein and 12% for fat.

The limits mentioned in these examples are typically applied by some of the member organisations, and are not meant to be understood as exact norms. Such norms should be laid down by each member organisation.

=== Evaluation of recording data ===
It is recommended that data quality is evaluated for each herd recording day. When such an evaluation is applied, the following features of the data have to be included:

# Person responsible for the recording.
# ICAR approval and calibration status of the recording equipment if owned by the farmer.
# Number of herd recordings per time period and/or recording interval.
# Number of herd samplings per time period and/or sampling interval.

The following features are also recommended to be included if possible:

# Deviation of milk and fat yields from dairy deliveries.
# Deviation of milk and fat yields from previous or predicted yields.
# Standard deviation of individual cow records.
# Number of recorded and/or sampled milkings within the recording day.
# Number of cows missed or not recorded in the recording.
</div>
</div>
= Procedures =
== Procedure 1: Computing 24-hour Yields ==

=== Methods to calculate 24-hour yield for milk yield and fat percentage from a single milking ===

==== Method of Delorenzo & Wiggans (1986)<ref>Delorenzo, M.A. and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. J. Dairy Sci. 69: 2386-2394.</ref> ====
Daily milk (DMY) and fat yield (DFY) estimates are based on measured yield and milking frequency. An adjustment factor accounts for differences in the average milking interval (expressed in decimal hours) between the preceding milking and the measured milking, and the time of day of the measured milking (started in a.m. or p.m.). For 2X milking, an additional adjustment is applied to milk yield for the interaction between milking interval and stage of lactation, with mid lactation (158 DIM) set to zero. Milking interval does not affect protein and solids non fat (SNF) percentages and so the percentages for the sampled milking are used for test-day estimates. Protein yield is calculated from the measured percentage and the adjusted milk yield.

The prediction of DMY and DFY from single milking on morning or evening in herds milked twice a day requires factors, that are the reciprocal of the proportion of total yield expected from single milkings in relation to the milking interval.

We propose to derive these coefficients (intercept, slope, etc.) for each country separately.

===== Adjustment of milking interval =====
The milking interval is the interval between milking time for the observed milking and the milking time preceding the observed milking. The milking interval is divided into 15-minutes classes. Factors for milk and fat yields may be calculated to each class using Equation 1:

''Equation 1. Factors for milk and fat yields.''
[[File:Equation 1.png|none|thumb|397x397px]]

===== Adjustment of lactation stage =====
Because the lactation stage of the cow has an influence on the effect of different milking intervals on milk production a second adjustment is made for every interval class through a covariate of days in milk as addition:

Covariate x (days in milk - 158)

===== Estimating sample day yields =====
Formulas for prediction sample day yields and percentages in herds with two milkings are:

''Equation 2. Equation for predicting 24-hour milk yield.''
[[File:Equation2.png|none|thumb|428x428px]]

''Equation 3. Equation for predicting 24-hour fat percentage.''
[[File:Equation3.png|none|thumb|431x431px]]

''Equation 4. Equation for predicting 24-hour fat yield.''
[[File:Equation4.png|none|thumb]]

''Equation 5. Equation for predicting 24-hour protein yield.''
[[File:Equation5.png|none|thumb|316x316px]]

===== Calculation examples =====

====== Practical Application ======
Two sets of factors are available for estimating DMY from a single milking, each for morning or evening milking sampling. The factors are calculated from the formula as described above and given in Table 1.
<center>
{| class="wikitable"
| colspan="5" align="left" |'''''Table 1. Factor of milk yield and covariate for herds milked twice a day.'''''
|- style="background-color:#efefef;"
| rowspan="2" align="center" |'''Length of milking interval in hours (minutes in decimal)'''
| colspan="2" align="center" |'''Morning milking'''
| colspan="2" align="center" |'''Evening milking'''
|- style="background-color:#efefef;"
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
|-
| align="center" |< 9.00
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.594
| align="center" |0.00378
|-
| align="center" |9.00-9.24
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.534
| align="center" |0.00485
|-
| align="center" |9.25-9.49
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.477
| align="center" |0.00486
|-
| align="center" |9.50-9.74
| align="center" |2.411
| align="center" |0.00716
| align="center" |2.423
| align="center" |0.00511
|-
| align="center" |9.75-9.99
| align="center" |2.359
| align="center" |0.00726
| align="center" |2.370
| align="center" |0.00473
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |10.00-10.24
| align="center" |2.310
| align="center" |0.00458
| align="center" |2.321
| align="center" |0.00337
|-
| align="center" |10.25-10.49
| align="center" |2.262
| align="center" |0.00399
| align="center" |2.273
| align="center" |0.00214
|-
| align="center" |10.50-10.74
| align="center" |2.217
| align="center" |0.00294
| align="center" |2.227
| align="center" |0.00000
|-
| align="center" |10.75-10.99
| align="center" |2.173
| align="center" |0.00223
| align="center" |2.183
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |11.00-11.24
| align="center" |2.131
| align="center" |0.00000
| align="center" |2.140
| align="center" |0.00000
|-
| align="center" |11.25-11.49
| align="center" |2.091
| align="center" |0.00000
| align="center" |2.099
| align="center" |0.00000
|-
| align="center" |11.50-11.74
| align="center" |2.052
| align="center" |0.00000
| align="center" |2.060
| align="center" |0.00000
|-
| align="center" |11.75-11.99
| align="center" |2.014
| align="center" |0.00000
| align="center" |2.022
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |12.00
| align="center" |2.000
| align="center" |0.00000
| align="center" |2.000
| align="center" |0.00000
|-
| align="center" |12.01-12.24
| align="center" |1.978
| align="center" |0.00000
| align="center" |1.986
| align="center" |0.00000
|-
| align="center" |12.25-12.49
| align="center" |1.943
| align="center" |0.00000
| align="center" |1.951
| align="center" |0.00000
|-
| align="center" |12.50-12.74
| align="center" |1.910
| align="center" |0.00000
| align="center" |1.917
| align="center" |0.00000
|-
| align="center" |12.75-12.99
| align="center" |1.877
| align="center" |0.00000
| align="center" |1.884
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |13.00-13.24
| align="center" |1.846
| align="center" |0.00000
| align="center" |1.852
| align="center" |-0.00190
|-
| align="center" |13.25-13.49
| align="center" |1.815
| align="center" |0.00000
| align="center" |1.822
| align="center" |-0.00231
|-
| align="center" |13.50-13.74
| align="center" |1.786
| align="center" |-0.00167
| align="center" |1.792
| align="center" |-0.00308
|-
| align="center" |13.75-13.99
| align="center" |1.757
| align="center" |-0.00258
| align="center" |1.763
| align="center" |-0.00339
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |14.00-14.24
| align="center" |1.730
| align="center" |-0.00347
| align="center" |1.736
| align="center" |-0.00509
|-
| align="center" |14.25-14.49
| align="center" |1.703
| align="center" |-0.00363
| align="center" |1.709
| align="center" |-0.00471
|-
| align="center" |14.50-14.74
| align="center" |1.677
| align="center" |-0.00332
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |14.75-14.99
| align="center" |1.652
| align="center" |-0.00316
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |≥ 15.00
| align="center" |1.628
| align="center" |-0.00235
| align="center" |1.683
| align="center" |-0.00454
|}
</center>

For estimating daily fat percentage there is only one table independent of morning or evening sampling – refer to Table 2.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" |'''''Table 2. Factor of fat percentage for herds milked twice a day.'''''
|- style="background-color:#efefef;"
|'''Length of milking'''

'''interval in hours'''
|'''Fat (percentage'''

'''factor)'''
|-
|< 9.00
|0.919
|-
|9.00-9.24
|0.927
|-
|9.25-9.49
|0.934
|-
|9.50-9.74
|0.941
|-
|9.75-9.99
|0.948
|-
|
|
|-
|10.00-10.24
|0.955
|-
|10.25-10.49
|0.961
|-
|10.50-10.74
|0.968
|-
|10.75-10.99
|0.974
|-
|
|
|-
|11.00-11.24
|0.980
|-
|11.25-11.49
|0.986
|-
|11.50-11.74
|0.992
|-
|11.75-11.99
|0.997
|-
|
|
|-
|12.00
|1.000
|-
|12.01-12.24
|1.003
|-
|12.25-12.49
|1.008
|-
|12.50-12.74
|1.013
|-
|12.75-12.99
|1.018
|-
|
|
|-
|13.00-13.24
|1.023
|-
|13.25-13.49
|1.028
|-
|13.50-13.74
|1.033
|-
|13.75-13.99
|1.037
|-
|
|
|-
|14.00-14.24
|1.042
|-
|14.25-14.49
|1.046
|-
|14.50-14.74
|1.050
|-
|14.75-14.99
|1.054
|-
|≥ 15.00
|1.058
|}
</center>

Milking-interval factors are calculated using Equation 1, where the intercept and slope are as in Table 3.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 3. Slope and intercept for milk yield and fat yield.'''''
|- style="background-color:#efefef;"
| rowspan="2" |'''Trait'''
| colspan="2" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started in a.m.'''
|'''For measured milking started in p.m.'''
|-
|Milk yield
|0.0654
|0.0634
|0.0363
|-
|Fat yield
|0.1965
|0.1939
|0.0254
|}
</center>
The milking interval has no significant influence on protein percentage. Therefore, the protein percentage of the sampled milking is used as the daily protein percentage.

====== Calculation of daily yields from morning milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Data for a cow from morning milking.'''''
|-
|Begin of recording:
|6:15
|(Morning milking)
|-
|Start of preceding milking:
|17:25
|
|-
|Length of milking interval:
|12 hours 50 minutes
|(Expressed as decimal 12.83)
|-
|Milk results at morning:
|12,0
|Milk-kg
|-
|
|4,12
|Fat-percentage
|-
|
|3,45
|Protein-percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 5. Factors for morning milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.877
|-
|The covariate is
|0
|-
|The factor for fat percentage from Table 2 is
|1.018
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 6. Example calculations for morning milking.'''''
|-
|The sample-day milk yield:
|1.877 x 12,0 kg + 0 x (120 - 158) = 22,5 kg
|-
|The sample-day fat percentage:
|1.018 x 4,12 = 4,19
|-
|The sample-day fat yield:
|22,5 kg x 0,0419 = 0,94 kg
|-
|The sample-day protein yield:
|22,5 kg x 0,0345 = 0,78 kg
|}
</center>

====== Calculation of daily yields from evening milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 7. Data for a cow from evening milking.'''''
|-
|Begin of recording:
|16:48
|Evening milking
|-
|Start of preceding milking:
|6:35
|
|-
|Length of milking interval:
|13 hours 47 minutes
|Expressed as decimal 13.78
|-
|Milk results at evening:
|14,0
|Milk kg
|-
|
|4,00
|Fat percentage
|-
|
|3,40
|Protein percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 8. Factors for evening milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.763
|-
|The covariate is
|<nowiki>-0,00339</nowiki>
|-
|The factor for fat percentage from Table 2 is
|1.037
|}
{| class="wikitable"
| colspan="2" |'''''Table 9. Example calculations for evening milking.'''''
|-
|The sample-day milk yield:
|1.763 x 14,0 kg - 0,00339 x (120 - 158) = 24,8 kg
|-
|The sample-day fat percentage:
|1.037 x 4,00 = 4,15
|-
|The sample-day fat yield:
|24,8 kg x 0,0415 = 1,03 kg
|-
|The sample-day protein yield:
|24,8 kg x 0,0340 = 0,84 kg
|}
</center>

====== Alternate recording of components and milk yield at both milkings ======
For this plan only the sample-day fat yield has to be calculated with regard to milking interval. The milk yield is the sum of evening and morning milk results.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 10. Example data for a cow from both milkings.'''''
|-
|Begin of recording evening:
|17:25
|
|-
|Milk results at evening:
|10:00
|Milk kg (only milking-yield)
|-
|Begin of recording morning:
|6:15
|
|-
|Milk results at morning:
|12:00
|Milk kg
|-
|
|4:20
|Fat percentage
|-
|
|3:50
|Protein percentage
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 11. Factor for fat percentage.'''''
|-
|Length of milking interval:
|12 hours 50 minutes (expressed

as decimal 12.83)
|-
|The factor for fat percentage from Table 2 is
|1.018.
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 12. Example calculation of daily yields.'''''
|-
|The sample-day milk yield:
|10,0 kg + 12,0 kg = 22,0 kg
|-
|The sample-day fat percentage:
|1.018 x 4,20 = 4,28
|-
|The sample-day fat yield:
|22,0 kg x 0,0428 = 0,94 kg
|-
|The sample-day protein yield:
|22,0 kg x 0,0350 = 0,77 kg
|}
</center>

====== Calculation for 3X Milking ======
For 3X herds, a single milking or two consecutive milkings may be weighed. The sample may be collected at one or both of these milkings. Stage of lactation × milking interval adjustments are not used for greater than 2× milking. These AM/PM factors for estimating daily yields in 3X herds should not be confused with factors that adjust 3X records to a 2X basis. Milking-interval factors are calculated using the same formula with the intercept and slope as in Table 13.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" align = "left" |'''''Table 13. Slope and intercept factors for 3X milking.'''''
|- style="background-color:#efefef;"
| rowspan="2" | '''Trait'''
| colspan="3" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started between 2 a.m. and 9:59 a.m.'''
|'''For measured milking started between 10 a.m. and 5:59 p.m.'''
|'''For measured milking started between 6:00 p.m. and 1:59 a.m.'''
|-
|Milk yield
|0.077
|0.068
|0.066
|0.0329
|-
|Fat yield
|0.186
|0.186
|0.182
|0.0186
|}
</center>
When two milkings are included for sampling, the intercepts and intervals for both milkings are included in determining a factor for calculated estimated milk yield that is applied to the total yield from both milkings as in Equation 6.

''Equation 6. Milking interval factor for 3X milking.''
[[File:Equation6.png|none|thumb|536x536px]]
Milk and fat percent factors are calculated separately based on the number of milkings weighed or sampled.

====== Calculation for 4X - 6X Milking ======
The intercept terms for calculating 3X factors (0.077, 0.068, and 0.066) are multiplied by the factor [3 / (milkings per day)] for use in calculating factors for milking frequencies greater than 3X.

==== Method of Liu et al. (2019) ====
A multiple regression method (MRM) is used for estimating 24-hour daily milk yield (DMY), daily fat yield (DFY) and daily protein yield (DPY) based on partial yields from either morning (AM) or evening (PM) milking. Fat percentage (DFP) or protein percentage (DPP) on a 24-hour daily basis are then derived using the estimated 24-hour daily yields. The MRM can be used as a reference method for estimating daily yields and component percentages.

The method of Liu et al. (2019) is an updated version of the method of Liu et al. (2000). The model is only used for farms with 2 time milkings during 24 hours.

The following formula is used to estimate DMY, DFY, DPY based on partial yields (PMY, PFY,PPY) from either morning (AM) or evening (PM) milking:

''Equation 7. Model for predicting 24-hour yield.''

''yijk = a + bijk * xijk''

where:

yijk is the estimated 24-hour daily yield (DMY, DFY or DPY);

xijk is AM or PM partial daily yield on a test day (PMY, PFY, or PPY).

Subscript '''''i''''' represents class of parity effect with 2 levels: first and higher parities.

Subscript '''''j''''' represents class of length of preceding milking interval with 8 levels for AM milking: < 720 minutes, < 740 minutes, < 760 minutes, < 780 minutes, < 800 minutes, < 820 minutes, < 840 minutes, >= 840 minutes and 8 levels for PM milking: < 600 minutes, < 620 minutes, < 640 minutes, < 660 minutes, < 680 minutes, < 700 minutes, < 720 minutes, >= 720 minutes.

Subscript '''''k''''' represents class of lactation stage with 7 classes: < 60 days, < 120 days, < 180 days, < 240 days, < 300 days, < 360 days, >= 360 days.

'''''a''''' is the estimated intercept for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

'''''b'''''ijk is the estimated slope for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

The factors for '''''a''''' and '''''b'''''ijk can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Appendix_1_-_Adjustment_factors_to_calculate_24-hour_yields_using_the_Liu_method Appendix 1].

For a given yield trait a total number of 112 formulae are to be estimated for calculating 24-hour daily yield based on partial yield from either AM or PM milking. Component percentage for fat (DFP) and protein (DPP), on a 24-hour basis is calculated by dividing estimated fat or protein yield by estimated daily milk yield:[[File:Imagefinal.png|center|thumb|339x339px]]

===== Calculation example with method of Liu et al. (2019) =====
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" align = "left" |'''''Table 14. Data from an evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="6" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="6" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="6" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow'''

'''ID'''
|'''Calving date'''
|'''Lactation number'''
| colspan="2" |'''Milk yield (kg)'''
|'''Fat content (%)'''
|'''Protein content (%)'''
|'''Fat yield (kg)'''
|'''Protein yield (kg)'''
|'''Index1'''
|-
|A
|01.01.2020
|1
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1132
|-
|B
|01.01.2020
|2
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1232
|-
|C
|27.03.2020
|1
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1131
|-
|D
|27.03.2020
|2
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1231
|-
|
|
|
|
|
|
|
|
|
|
|}
'''1''' Index is marked in the Appendix table.
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 15. Calculation of 24-hour daily yield and components for evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="3" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="3" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="3" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow ID'''
|'''DMY (kg)'''
|'''DFY (kg)'''
| colspan="2" |'''DPY (kg)'''
|'''DFP (%)'''
|'''DPP (%)'''
|-
|A
|3,47396+25,0

<nowiki>*</nowiki> 1,98268 = 53,0401 ≈ '''53,0'''
|0,2135+0,995

<nowiki>*</nowiki> 1,68050 = 1,8855975
| colspan="2" |0,10471+0,8325* 1,99092 = 1,7621509
|1,8855975 / 53,04096*100

≈ '''3,55'''
|1,7621509 / 53,04096*100

≈ '''3,32'''
|-
|B
|4,15080+25,0* 1,98520 = 53,7808 ≈ '''53,8'''
|0,3635+0,995

<nowiki>*</nowiki> 1,47515 = 1,8312743
| colspan="2" |0,13952+0,8325* 1,97074 = 1,7801611
|1,8312743 / 53,7808*100

≈ '''3,41'''
|1,7801611 / 53,7808*100

≈ '''3,31'''
|-
|C
|2,80244+33,1

<nowiki>*</nowiki> 2,02183 = 69,72501 ≈ '''69,7'''
|0,17663+1,3339 * 1,72438 = 2,4767805
| colspan="2" |0,11078+1,1122 * 1,96422 = 2,2953855
|2,4767805 / 69,725013*100

≈ '''3,55'''
|2,2953855 / 69,725013*100

≈ '''3,29'''
|-
|D
|3,85525+33,1 * 2,00429 = 70,19725 ≈ '''70,2'''
|0,27991+1,3339 * 1,62403 = 2,4462036
| colspan="2" |0,12863+1,1122* 1,98973 = 2,3416077
|2,4462036 / 70,7197249*100 ≈ '''3,48'''
|2,3416077 / 70,7197249*100 ≈ '''''3,34'''''
|-
|
|
|
|
|
|
|
|}
</center>
'''Note''' that intercepts and slopes of the applied regression formulae are underscored.

===== Fat correction for equal measure sampling =====
With Equal measure sampling, it is advisable to use Equation 8 (or the like) to correct fat contents:

Equation 8. Fat correction for equal measure sampling.

Fat, % = Analysed fat, % + 0.69 – 1.3 x (morning milk/ 24-hour milk)

The relation of morning milk to 24-hour milk is to be calculated to at least four decimals.

==== 1.1 Method of Kyntäjä & Nokka (2021)<ref name=":3" />: 24-hour correction factors for fat percentage ====
This method can be applied to calculate 24-hour correction factors for fat percentage, in case the milk recording is based on two milkings, with at least one known milk yield and one sample. A 24-hour recording day is assumed.

The conventional way to calculate correction factors is based on a data set where all milkings have been recorded and analysed separately. This approach requires a lot of effort and extra analysis, and is not cheap to organise. Organisations that have access to a large number of records may be able to use those data to calculate correction factors even if they have no extra analysis.

Requirements for the data set:

# The data set has to be large enough. Every single factor needs to be based on at least 10,000 or, even better, 100,000 observations.
# Each individual data set must contain at least one preceding milking interval, milk weight, and analysed sample. If it contains more milk weights, intervals etc. that is even better. It is also good to include breed, lactation number, days in milk and other data that may have an effect on the factors.

===== Calculation example of the method of Kyntäjä & Nokka (2021)<ref>Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. ICAR Technical Series no. 25: 171-175.</ref> =====

====== The accumulated data set ======
Since 2003, Finland had accumulated a data set of 7.5 million recordings with data on the time of the sampled and preceding milking as reported by the farmer, the lab analysis results, and the 24-hour milk yield. Grouped according to the preceding interval, the analysed fat content gives a nice sigmoid curve with the highest fat content found after a 540 to 630 minutes’ interval (9 to 10.5 hours) and the lowest at 810 to 930 minutes (13.5 to 15.5 hours).
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 16. Average analysed milk fat percentage by preceding interval class, 2003 – 2020.'''''
|- style="background-color:#efefef;"
|'''Interval before'''

'''Sampling (minutes)'''
|'''Number of samples'''
|'''Median interval in the class'''
|'''Average fat content analysed (%)'''
|-
|<510
|93,577
|495
|4.20
|-
|510-539
|19,523
|525
|4.70
|-
|540-569
|111,268
|555
|4.79
|-
|570-599
|253,807
|585
|4.83
|-
|600-629
|1,461,587
|615
|4.75
|-
|630-659
|919,968
|645
|4.66
|-
|660-689
|1,168,683
|675
|4.56
|-
|690-719
|223,877
|705
|4.42
|-
|720-749
|517,447
|735
|4.28
|-
|750-779
|212,428
|765
|4.16
|-
|780-809
|924,014
|795
|4.12
|-
|810-839
|698,463
|825
|4.09
|-
|840-869
|1,104,778
|855
|4.07
|-
|870-899
|154,561
|885
|4.05
|-
|900-929
|77,024
|915
|4.07
|-
|>929
|26,977
|945
|4.13
|}
</center>

The results were also divided into subgroups according to lactation number, phase of lactation, and breed. The effect of the preceding milk interval on milk fat seems to be bigger with older cows and in the beginning of lactation. It was also bigger with Ayrshire cows as compared with Holsteins. At this point, however, the decision was made not to take these factors into account when calculating new correction factors.

====== Calculation of new factors ======
The results above were turned into a simple set of correction factors, dependent solely on the preceding interval. In order to do this, two assumptions were made:

# A 24-hour recording day was assumed. This way, we can deduce the second milking interval from the one we know and mirror the fat percent for that milking.
# Milk secretion rate was assumed to be constant around the 24-hour period. This allows us to deduce the share of the 24-hour yield produced at each milking.

These assumptions allow us to create the new correction factors by mirroring the milk yield and milk fat content in the milking whose actual data we have not got. This way, we get the following formula:

Equation 9. Correction factor.
[[File:Equation9.png|none|thumb|545x545px]]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left" |'''''Table 17. Calculation of the mirrored milking and the correction factors'''''
|- style="background-color:#efefef;"
|'''Interval before sampling (minutes)'''
|'''Average fat in the sampled milking (%)'''
|'''Share of 24-hour milk in the sampled milking'''
|'''Mirrored interval (minutes)'''
|'''Average fat in the mirrored milking (%)'''
|'''Calculated 24-hour average fat(%)'''
|'''Correction factor'''
|-
|<510
|4.21
|0.34
|>929
|4.14
|4.16
|0.989
|-
|510-539
|4.77
|0.36
|900-929
|4.08
|4.33
|0.907
|-
|540-569
|4.82
|0.39
|870-899
|4.05
|4.35
|0.903
|-
|570-599
|4.84
|0.41
|840-869
|4.07
|4.38
|0.906
|-
|600-629
|4.76
|0.43
|810-839
|4.09
|4.37
|0.919
|-
|630-659
|4.66
|0.45
|780-809
|4.12
|4.36
|0.936
|-
|660-689
|4.56
|0.47
|750-779
|4.16
|4.35
|0.953
|-
|690-719
|4.43
|0.49
|720-749
|4.29
|4.36
|0.984
|-
|720-749
|4.29
|0.51
|690-719
|4.43
|4.36
|1.016
|-
|750-779
|4.16
|0.53
|660-689
|4.56
|4.35
|1.046
|-
|780-809
|4.12
|0.55
|630-659
|4.66
|4.36
|1.059
|-
|810-839
|4.09
|0.57
|600-629
|4.76
|4.37
|1.070
|-
|840-869
|4.07
|0.59
|570-599
|4.84
|4.38
|1.076
|-
|870-899
|4.05
|0.61
|540-569
|4.82
|4.35
|1.073
|-
|900-929
|4.08
|0.64
|510-539
|4.77
|4.33
|1.062
|-
|>929
|4.14
|0.66
|<510
|4.21
|4.16
|1.006
|}
</center>

=== Methods to calculate 24-hour yields in Automatic Milking Systems ===

==== General remarks about calculation of 24-hour milk yield ====
It is characteristic for AMS systems that individual cows set their own milking rhythm, thus making it largely irrelevant to use the traditional model of measuring milk yields and sampling at all milkings in the herd during the recording day. In order to determine how much an individual cow’s real 24-hour milk, fat and protein yield is, more complex calculations are required, especially with milk fat that varies considerably from milking to milking. For protein content and cell counts, no correction is needed for a one-milking sample.

The basic idea with calculating a 24-hour milk yield from AMS data is that milk yields per milking are converted into milk yield per time unit (minute or hour) during the preceding interval. This milk yield per time unit is then converted into milk yield in 24 hours. In order to do this, the data set must also contain time stamps for each milking.

How many milkings or how long a measurement period is used for creating 24-hour yields depends on the milk recording organisation. The fewer milkings are used the more random variance there will be in the individual cow milk yields. The absolute minimum is two milkings with preceding intervals, while a measuring period of 96 hours is recommended.

The sampled milking must always be inside the milk yield measurement period. For the calculation of fat and protein yields, it is recommended to use only those milk yields that are from the same period or day. With Z sampling, the 24-hour fat and protein yields may be calculated based on a shorter measurement period than what is used for calculating the 24-hour milk yields.

==== Calculation of milk yield using data of several days (Lazenby ''et al''., 2002<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Automatic Milking Systems (AMS). The average of most recent milk weights can be calculated using a number of preceding milkings or a number of preceding days. If number of milkings is used, the optimal estimate of the milking rate is obtained using an average of current milking together with the 12 most recent milkings back in time. The optimal estimate is the maximum value of the difference curve at which the correlation with the ‘true’ 24-hour milk yield is greatest and the variance across milkings is minimized. If number of days is used, the optimal estimate of the milking rate is obtained using an average of all milkings occurred in the last 96 hours (4 most recent days). In Table 18 the percent of maximum difference for various number of milkings and days is reported. The optimal estimate is independent from stage of lactation and parity.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 18. Percent maximum for different number of days and milkings.'''''
|- style="background-color:#efefef;"
|'''Days'''
|'''Percent Max.'''
|'''Current milking'''

'''+ most recent milkings'''
|'''Percent max.'''
|-
|1
|49.38
|10
|97.85
|-
|2
|77.26
|11
|99.08
|-
|3
|92.34
|12
|99.70
|-
|4
|98.91
|13
|99.81
|-
|5
|98.50
|14
|99.40
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table19.png|center|thumb|911x911px]]
Therefore, 24-hour yield estimation using most recent milkings (1+12) is computed using Equation 10.

''Equation 10. 24-hour yield estimation using 12 previous milkings from AMS.''
[[File:Equation10.png|none|thumb|527x527px]]
and, 24-hour yield estimation using all milkings occurred in the last 96 hours (most recent 4 days), all milking in the last 4 days are included is computed using Equation 11.

''Equation 11. 24 hours yield estimation using milkings from the last 96 hours from AMS''
[[File:Equation11.png|none|thumb|534x534px]]

===== Advantages and disadvantages of this method =====
In terms of Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between milk weights and contents may arise if contents are recorded on one day only. Moreover, some cows may begin or finish their lactation during the period of recording. In this case the computation of milk yield must be adapted. The number of data that need to be validated is higher (for instance, contents have short interval between two milkings).

==== Calculation of milk yield using data on 1 day (Bouloc ''et al''., 2002<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
When the number of milkings is reduced to milkings obtained during one day only, the accuracy of the estimation of the true performance is the same as classical milk recording methods with the same interval between two test days. For instance, Milk Yield estimated from all the milkings recorded during 24 hours, and with an interval between two test days of four weeks has the same accuracy as A4.

==== Calculation of fat and protein yield (Galesloot & Peeters, 2000<ref name=":1" />) ====
Calculation of fat and protein percent must be based on milk weights at time of sampling. The 24-hour protein percentage can be predicted by the protein percentage of the sample without adjustment. However, the 24-hour fat percentage is more difficult to predict, as levels of fat percent are inversely proportional to the amount of milk yield. It is important then to have a close connection between time of samples and actual milk yields.

The Peeters and Galesloot method is a multiple linear regression model for estimating 24-hour fat percent and yields from one-sampled milking during the AMS sampling period. Six different statistical models were tested. This method takes into account fat percent, protein percent, milk weight and milking interval of the sampled milking, milking interval and milk weight of the previous milking (simple model). Another model, based on six different classification of variables (Ca - Cf) such as, time of sampled milking, interval preceding the sampled milking, ratio of fat to protein percent, parity, lactation stage, can be applied (complex model).

===== Simple model =====
24-hour Fat% = b0 + b1* Fat%(n) + b2* Prot%(n) + b3* Int(n) + b4* Int(n-1) + b5* Milk(n) + b6* Milk (n-1) + e

b0= Intercept, b1 to b6 = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, e = Residual effect.

===== Complex model =====
24-hour Fat%i = b0i + b1i* Fat%(n) + b2i* Prot%(n) + b3i* Int(n) + b4i* Int(n-1) + b5i* Milk(n) + b6i* Milk(n-1) + ei

b0i = Intercept, b1i to b6i = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, ei = Residual effect

i = subclass of classification for class variables Cx for x = a, b, c, d, e, f

Ca = Day Time of sampled milking (h) 0-5.59, 6.00-11.59, 12.00-17.59, 18.00-23.59

Cb = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440

Cc = Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

Cd = Parity 1, 2, ≥ 3

Ce = Lactation stage 1-99, 100-199, ≥200

Cf = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440 and Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

The best prediction of 24-hour fat percent and 24-hour fat yields from this method, includes fat percent, protein percent, milk weight and milking interval of the sampled milking, milk weight and milking interval of the preceding milking and the interaction between milking interval, the ratio of fat to protein percent of the sampled milking (complex model corresponding to Cf classification).

The Peeters and Galesloot method has been updated by Roelofs et al. (2006)<ref>Peeters, R. and P. J. B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. J Dairy Sci. 85:682-688.</ref>. The Roelofs method is described in [[Section 02 – Cattle Milk Recording#Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme|Appendix 2]] of this Section.

N.B. This method has been developed by CRV. CRV has available a set of parameters, estimated with this method. For more information about costs and advice on application of this method, please contact CRV. ICAR has no benefit from the application of this method or any other method described in these guidelines.

==== Calculation example of 24-hour fat and protein yields with sampling scheme M ====
With this method, all milkings in a 24-hour recording period must be sampled. The obtained separate analysis results are then used to compute a 24-hour yield of milk solids, and a weighted average of their content.

Individual milkings (last 96 hours) and recording day contents:
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left" |'''''Table 20. Calculation of 24-hour fat and protein contents with sampling scheme M.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY/MM/DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat%'''
|'''Protein%'''
|-
|1
|2021/09/09
|20:45
|525
|13.7
|26.1
|
|
|-
|2
|2021/09/10
|5:30
|617
|16.0
|25.9
|
|
|-
|3
|2021/09/10
|15:47
|720
|18.7
|26.0
|
|
|-
|4
|2021/09/11
|3:25
|645
|16.8
|26.0
|
|
|-
|5
|2021/09/11
|14:10
|899
|18.3
|20.3
|
|
|-
|6
|2021/09/11
|23:27
|557
|14.6
|26.2
|
|
|-
|7
|2021/09/12
|10:51
|684
|17.4
|25.4
|4.53
|3.17
|-
|8
|2021/09/12
|19:44
|533
|14.1
|26.5
|4.92
|3.18
|-
|9
|2021/09/13
|1:35
|351
|9.9
|28.2
|5.92
|3.07
|}
</center>

For example, calculation of fat% on recording day:

24-hour Fat% = (9.9 kg milk x 5.92% fat + 14.1 kg milk x 4.92 % fat + 17.4 kg milk x 4.53 % fat) / (9.9 + 14.1 + 17.4) kg milk = 5.00 %

To calculate the 24-hour fat yield, the calculated 24-hour milk yield is multiplied by the fat content thus obtained (5.00 %).

The same method is used for protein, somatic cell count, urea, lactose and other milk constituents.

Estimation of milk contents: It is recommended to set the robot not to take samples if the preceding milking of the individual cow is not more than 4 hours earlier. If such milkings occur the milk sampled from them is not suitable for 24-hour fat calculation.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left"|'''''Table 21. Calculation of 24-hour fat and protein contents with sampling scheme M where one milking interval was shorter than 4 hours.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY-MM-DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat %'''
|'''Protein%'''
|-
|1
|2021/11/12
|20:05
|590
|15.4
|26.4
|
|
|-
|2
|2021/11/13
|6:31
|626
|16.3
|26.0
|
|
|-
|3
|2021/11/13
|17:12
|641
|17.1
|26.7
|
|
|-
|4
|2021/11/14
|4:40
|688
|17.5
|25.4
|
|
|-
|5
|2021/11/14
|15:11
|631
|16.4
|26.0
|
|
|-
|6
|2021/11/15
|2:25
|674
|16.5
|24.5
|
|
|-
|7
|2021/11/15
|9:47
|452
|10.8
|23.9
|
|
|-
|8
|2021/11/15
|18:30
|523
|13.6
|26.0
|4.71
|3.36
|-
|9
|2021/11/15
|21:15
|165
|3.1
|18.8
|5.161
|3.481
|-
|10
|2021/11/16
|7:49
|634
|16.5
|26.0
|4.47
|3.21
|}
1 Time between two consecutive milkings shorter than 4 hours, data not taken into account for calculation of milk contents.
</center>

Calculation of the fat content of milk during the recording day:

24-hour Fat% = (16.5 kg milk x 4.47 % fat + 13.6 kg milk x 4.71 % fat) / (16.5 kg + 13.6 kg) = 4.57 %

The same method is used for protein, somatic cells, urea, lactose and other milk constituents.

=== Methods to calculate 24-hour yields from electronic milk meters ===

==== Using data on more than one day (Hand ''et al''., 2006<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. J. Dairy Sci. 89:1723–1726.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Electronic Milk Meters. The average of most recent milk weights can be calculated using a number of preceding days. Table 22 reports the concordance correlations for a range of multiple-day averages. As soon as at least the 3 preceding days are used in the calculation, the concordance correlation reaches a high value of at least 0.981. There are no significant differences between 3, 4, 5, 6 and 7-day averages. The correlations are independent from stage of lactation and parity. Thus, 24-hour yields can be the average of from 3 to 7 daily milkings previous to the test day when fat and protein samples were taken.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 22. Concordance correlations for different multiple-day averages.'''''
|- style="background-color:#efefef;"
|'''Multiple-day average'''
|'''Concordance correlation'''
|-
|1
|0.957
|-
|2
|0.975
|-
|3
|0.981
|-
|4
|0.981
|-
|5
|0.982
|-
|6
|0.981
|-
|7
|0.981
|-
|10
|0.979
|-
|14
|0.977
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table20.png|center|thumb|923x923px]]

Therefore, 24-hour yield estimation averaging over 5 days is given by Equation 12.

''Equation 12. 24-hour yield estimation averaging over 5 days.''
[[File:Equation12.png|center|thumb|601x601px]]

===== Advantages and disadvantages of this method =====
Concerning Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between Milk weights and contents have been shown. The estimation bias increases proportionally to the number of days use to compute the 24-hour average. Thus, this method is recommended only if milk weight is the only variable of interest. If milk contents are of interest then the milk weight should be calculated using the milkings from the same day of sampling.

==== Estimation of 24-hour fat and protein yield ====
Fat and protein yields should be determined from the 24-hour yield on the day of sampling, and not the averaged value.

=== Calculation of daily fat percentage from single samples by Gerke et al., 2025 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Gerke.xlsx here]

Constant access to the automatic milking system (AMS) leads to varying milking frequency of cows and subsequently varying milking interval lengths (MI) and milk yield (MY) of single milkings. This influences milk production and can result in variable milk composition in individual milkings during the day. Therefore, the fat percentage from one sampled milking must be adjusted before it can be used as a daily value. The method described specifies the data required and the calculation procedure for deriving a corrected 24 h milk fat percentage from a single sample on test day (TD) in AMS herds.

==== Model specification ====
The multiple linear regression includes transformation, interaction, and polynomial parameters to model non-linearity and thereby improve prediction accuracy. Beside F% of a single milking (''m'') on TD, the model focused on lactation characteristics and milk recording data of up to 4 preceding milkings. With milking intervals ranging between 4 and 20 hours, the method can be applied to milk recording samples from cows with 2 or 3 milkings whose milking intervals lengths (MI) before sampling accumulate to less than 24 h.

The functional form of the model described below specifies the data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample:[[File:Image A.png|center|thumb|636x636px|'''Data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample''']]
</div>where:

DF% = estimated 24 h fat percentage on TD

''m'' = sampled milking on TD

''m-x'' = x milkings before the milking where the sample was taken (x: 1-3)

F% = fat percentage of the sampled milking ''m''

MY(''m'') = milk yield (kg) of ''m''

MI(''m'') = length of time interval (min) preceding the sampled milking ''m''

MY(''m''-x) = milk yields of the 1-3 preceding milkings of ''m''

MI(''m''-x) = milking interval length corresponding to MY(''m''-x)

DIM = days in milk on TD ranging between 5 and 330 d

Parity = parity class (e.g primiparous = 1 and multiparous = 0)

Daytime = time-of-day group of ''m'' (e.g. morning/noon/evening)

e = residual error

The method and its implementation are described in detail by Gerke et al. (2025).

==== Calculation and examples ====
The mathematical notation, with the corresponding regression coefficients in Table 1 for calculating the daily fat percentage (DF%):[[File:Calculating the daily fat percentage (DF%).jpg|center|Calculating the daily fat percentage (DF%)|thumb|511x511px]][[File:Calculating the daily fat percentage (DF%) 2.jpg|center|frame|'''Table 1. Coefficients for regression formula.''']]
</div>
[[File:Example data required for estimating 24 h fat percentage (DF%).jpg|alt=Example data required for estimating 24 h fat percentage (DF%)|center|frame|'''Table 2.''' '''Example data required for estimating 24 h fat percentage (DF%)''']]
Based on the data assembled on TD (Table 2), the corrected 24 h fat percentage (DF%) can be calculated using the mathematical formula und its corresponding coefficients listed in Table 1 as shown in the following examples:
[[File:Corrected 24 h fat percentage.jpg|alt=Corrected 24 h fat percentage|center|thumb|661x661px|'''Corrected 24 h fat percentage''']]

=== Reference ===
Gerke, J. S., Kammer, M., Werner, A., Köstler, R., Piepenburg, J., Mayerhofer, M., … Duda, J. (2025). Estimating daily fat percentage from single samples in herds with automatic milking system using a regression model. ''Livestock Science'', ''293'', 105649. doi: 10.1016/j.livsci.2025.105649

=== Calculation of daily fat percentage from single samples by Jenko et al., 2008, 2010 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Jenko.xlsx here]

This method estimates daily milk yield (DMY), daily fat yield (DFY), and daily protein yield (DPY) in the alternate one-milking recording (T) scheme. Daily fat percentage (DFP) and daily protein percentage (DPP) are then derived from the daily yield (DY) estimates. Utilizing this method allows us to remove the risk of underestimating high and overestimating low DY and contents.

The following formula is used to estimate the DY from the partial yield (PY) and the estimated PY/DY ratio (y):

DY=PYi/yi

where the subscript i is either morning (a.m.) or evening (p.m.).

The value of y is calculated based on the milking interval in minutes (MI), estimated intercept (µ) and regression coefficients (b1 and b2) for yield traits in a.m. or p.m. milking using the following equations for DMY and DPY:

'''Equation 1. Model for milk yield and protein yield.'''

yi = µ + b1 × MI

and for DFY

'''Equation 2. Model for fat yield.'''

yi = µ + b1 × MI + b2 × MI2

The intercept and regression coefficients can be either estimated from the data with records from both a.m. and p.m. milking or the estimates from Table 1 can be applied.

'''Table 1. Intercept and regression coefficients for calculation of daily yield.'''
{| class="wikitable"
|'''Daily yield'''
|'''Milking'''
|'''µ'''
|'''b1'''
|'''b2'''
|-
|DMY
|a.m.
|0,1081000000
|0,0005503000
|
|-
|
|p.m.
|0,0884200000
|0,0005683000
|
|-
|DPY
|a.m.
|0,1124000000
|0,0005419000
|
|-
|
|p.m.
|0,0966400000
|0,0005593000
|
|-
|DFY .
|a.m.
|0,5903000000
|<nowiki>-0,0005093000</nowiki>
|0,0000005377
|-
|
|p.m.
|0,1574000000
|0,0006705000
|<nowiki>-0,0000002744</nowiki>
|}
Finally, daily fat percentage (DFP) and daily protein percentage (DPP) are calculated from the estimated DY:

DFP=DFY/DMY × 100

DPP=DPY/DMY × 100

==== Calulation example with method of Jenko et al. (2008, 2010) ====
Example of the calculations of daily yields from morning milking and evening milking is presented in tables 3 and 4. Data from the Delorenzo and Wiggans method is used in the calculations (Table 2).

'''Table 2. Data for morning and evening milking.'''
{| class="wikitable"
|'''Milking'''
|'''a.m.'''
|'''p.m.'''
|-
|Beginning of recording
|06:15
|20:22
|-
|Start of preceding milking
|17:25
|06:35
|-
|Milking interval (min)
|770
|827
|-
|'''Milking results'''
|
|
|-
|Milk (kg)
|12,00
|14,00
|-
|Protein (%)
|3,45
|3,40
|-
|Fat (%)
|4,12
|4,00
|}

'''Table 3. Calculation of partial yield (PY) and calculation of y value.'''
{| class="wikitable"
|Trait
|Milking
|PY (%)
|PY (kg)
|y
|-
|Milk
|a.m.
|
|12,00
|0,1081000000 + 0,0005503000 x 770 = 0,531831
|-
|
|p.m.
|
|14,00
|0,0884200000 + 0,0005683000 x 827 = 0,558404
|-
|Protein
|a.m.
|3,45
|12,00 / 3,45 = 0,41
|0,1124000000 + 0,0005419000 x 770 = 0,529663
|-
|
|p.m.
|3,40
|14,00 / 3,40 = 0,48
|0,0966400000 + 0,0005593000 x 827 = 0,559181
|-
|Fat
|a.m.
|

4,12
|12,00 / 4,12 = 0,49
|0,5903000000 -0,0005093000 x 770 + 0,0000005377 x 7702 = 0,516941
|-
|
|p.m.
|

4,00
|12,00 / 4,00 = 0,56
|0,1574000000 +0,0006705000 x 827 - 0,0000002744 x 8272 = 0,524233
|}

'''Table 4. Calculation of daily yield (DY, kg) and daily components (DY, %).'''
{| class="wikitable"
|Trait
|DY
|Milking
|DY (kg)
|DY (%)
|-
|Milk
|DMY
|a.m.
|12,00 / 0,531831 = 22,56356
|
|-
|
|
|p.m.
|14,00 / 0,531831 = 25,07145
|
|-
|Protein
|DPY
|a.m.
|0,41 / 0,529663 = 0,781629
|(0,781629 / 22,56356) x 100 = 3,46
|-
|
|
|p.m.
|0,48 / 0,559181 = 0,851245
|(0,851245 / 25,07145) x 100 = 3,40
|-
|Fat
|DFY
|a.m.
|0,49 / 0,516941 = 0,956395
|(0,956395 / 22,56356) x 100 = 4,24
|-
|
|
|p.m.
|0,56 / 0,524233 = 1,068227
|(1,068227 / 25,07145) x 100 = 4,26
|}

==== References ====

* Jenko, J., Perpar, T., Logar, B., Sadar, M., Ivanovič, B., Jeretina, J., Verbič, J., Podgoršek, P. 2008. Comparison of different models for estimating daily yields from a.m./p.m. milkings in Slovenian dairy scheme. Presented at the 36th ICAR Session, Niagara Falls, New York, United States, June 16-20, 2008.
* Jenko, J., Perpar, T., Gorjanc G., Babnik, D. 2010. Evaluation of different approaches for the estimation of daily yield from single milk testing scheme in cattle, J. Dairy Res., 77 (2010), pp. 137-143; DOI: 10.1017/S0022029909990586

== Procedure 2 – Computing of Accumulated Lactation Yield ==
<div class="mw-collapsible mw-collapsed">
<div>
=== The Test Interval Method (TIM) (Sargent, 1968<ref>Sargent, F. D., V. H. Lyton, and 0. G. Wall, J r . 1968. Test interval method of calculating Dairy Herd Improvement Association records. J. Dairy Sci. 51:170.</ref>) ===
Test Interval Method is the reference method for calculating accumulated yields. Another adaptation of the method is the Centering Date Method where the yields from the preceding recording are used until the mid point of the recording interval and then substituted by the yields from the following recording.

The following equations are used to compute the lactation record for milk yield (MY), for fat (and protein) yield (FY), and for fat (and protein) percent (FP).
[[File:Equation1111.png|none|thumb|653x653px]]
Where:
M1, M2, Mn are the weights in kilograms, given to one decimal place, of the milk yielded in the 24 hours of the recording day.

F1, F2, Fn are the fat yields estimated by multiplying the milk yield and the fat percent (given to at least two decimal places) collected on the recording day.

I1, I2, In-1 are the intervals, in days, between recording dates.

I0 is the interval, in days, between the lactation period start date and the first recording date.

In is the interval, in days, between the last recording date and the end of the lactation period.

The equation applied for fat yield and percentage must be applied for any other milk components such as protein and lactose.

Details of how to apply the formulae are shown in Table 3 using the example data in Table 1, below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" align = "left" |'''''Table 1. Raw data used in example (TIM).'''''
|- style="background-color:#efefef;"
| colspan="6" align = "left"|'''Data:'''

'''Calving March 25'''
|- style="background-color:#efefef;"
|
|'''Date of'''

'''recording'''
|'''Number'''

'''of days'''
|'''Quantity of milk'''

'''weighed in kg'''
|'''Fat'''

'''percentage'''
|'''Fat'''

'''in grams'''
|-
|April
|8
|14
|28.2
|3.65
|1 029
|-
|May
|6
|28
|24.8
|3.45
|856
|-
|June
|5
|30
|26.6
|3.40
|904
|-
|July
|7
|32
|23.2
|3.55
|824
|-
|August
|2
|26
|20.2
|3.85
|778
|-
|August
|30
|28
|17.8
|4.05
|721
|-
|September
|25
|26
|13.2
|4.45
|587
|-
|October
|27
|32
|9.6
|4.65
|446
|-
|November
|22
|26
|5.8
|4.95
|287
|-
|December
|20
|28
|4.4
|5.25
|231
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left"|'''''Table 2. Lactation period summary (TIM).'''''
|-
|Beginning of lactation:
|March 26
|-
|End of lactation:
|January 3
|-
|Duration of lactation period:
|284 days
|-
|Number of testings (weighings):
|10
|}
</center>
<center>
{| class="wikitable"
| colspan="8" |'''''Table 3. Computations using Test Interval Method.'''''
|- style="background-color:#efefef;"
| colspan="3" rowspan="2" |'''Interval'''

'''both days included'''
|
| colspan="2" |'''Daily production'''
| colspan="2" |'''Sum'''
|- style="background-color:#efefef;"
|'''Days'''
|'''Kg milk'''
|'''Grams of fat'''
|'''Kg milk'''
|'''Kg fat'''
|-
|Mar 26
|<nowiki>-</nowiki>
|Apr 8
|14
|28.2
|1 029
|395
|14.410
|-
|Apr 9
|<nowiki>-</nowiki>
|May 6
|28
|(28.2+24.8)/2
|(1 029+856) /2
|742
|26.389
|-
|May 7
|<nowiki>-</nowiki>
|June 5
|30
|(24.8+26.6) /2
|(856+904) /2
|771
|26.400
|-
|June 6
|<nowiki>-</nowiki>
|July 7
|32
|(26.6+23.2) /2
|(904+824) /2
|797
|27.648
|-
|July 8
|<nowiki>-</nowiki>
|Aug. 2
|26
|(23.2+20.2) /2
|(824+778) /2
|564
|20.817
|-
|Aug. 3
|<nowiki>-</nowiki>
|Aug 30
|28
|(20.2+17.8) /2
|(778+721) /2
|532
|20.980
|-
|Aug 31
|<nowiki>-</nowiki>
|Sept. 25
|26
|(17.8+13.2) /2
|(721+587) /2
|403
|17.008
|-
|Sept. 26
|<nowiki>-</nowiki>
|Oct. 27
|32
|(13.2+9.6) /2
|(587+446) /2
|365
|16.541
|-
|Oct. 28
|<nowiki>-</nowiki>
|Nov. 22
|26
|(9.6+5.8) /2
|(446+287) /2
|200
|9.536
|-
|Nov. 23
|<nowiki>-</nowiki>
|Dec. 20
|28
|(5.8+4.4) /2
|(287+231) /2
|143
|7.253
|-
|Dec. 21
|<nowiki>-</nowiki>
|Jan. 3
|14
|4.4
|231
|62
|3.234
|-
|
|
|
|284
|
|
|4973
|190.216
|-
| colspan="8" |
|-
| colspan="8" |Total quantity of milk: 4 973. kg
|-
| colspan="8" |Total quantity of fat: 190 kg
|-
| colspan="8" |Average fat percentage (190.216 / 4973) x 100 = 3.82%
|}
</center>

=== Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. Livest. Prod. Sci. 17:l.</ref>) ===
With the method 'Interpolation using Standard Lactation Curves' missing test day yields and 305 day projections are predicted. The method makes use of separate standard lactation curves representing the expected course of the lactation, for a certain herd production level, age at calving and season of calving and yield trait. By interpolation using standard lactation curves, the fact that after calving milk yield generally increases and subsequently decreases is taken into account. The daily yields are predicted for fixed days of the lactation: day 0, 10, 30, 50 etc.

The cumulative yield is calculated as follows in :
[[File:Equation2222222.png|none|thumb|474x474px]]
where:

yi = the i-th daily yield;

INTi = the interval in days between the daily yields yi and yi+1;

''n'' = total number of daily yields (measured daily yields and predicted daily yields).

The next example illustrates the calculation of a record in progress. The cow was tested at day 35 and day 65 of the lactation. To determine the lactation yield, daily milk yields are determined for day 0, 10, 30 and 50 of the lactation, by means of the standard lactation curves. The daily yields are in Table 4.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Measured and derived daily yields, used to calculate the record in progress in the example (ISLC).'''''
|- style="background-color:#efefef;"
|'''Day of lactation'''
|'''Milk (kg)'''
|'''Note'''
|-
|0
|25.9
|Predicted
|-
|10
|27.8
|Predicted
|-
|30
|31.7
|Predicted
|-
|35
|31.8
|Measured
|-
|50
|32.9
|Interpolated using standard lactation curve
|-
|65
|33.0
|Measured
|}
</center>

Next, the record in progress can be calculated by means of the formula for a cumulative yield as follows:

[(10 - 1) * 25.9 + (10+1) * 27.8] / 2 +

[(20 - 1) * 27.8 + (20+1) * 31.7] / 2 +

[(5 - 1) * 31.7 + (5+1) * 31.8] / 2 +

[(15 - 1) * 31.8 + (15+1) * 32.9] / 2 +

[(15 - 1) * 32.9 + (15+1) * 33.0] / 2 = 2005.3 kg.

This corresponds to the surface below the line through the predicted and measured daily yields (see Figure 1).
[[File:Figure1.png|center|thumb|621x621px|''Figure 1. Example of calculation of record in progress.'']]

=== Best prediction (BP) (VanRaden, 1997<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. J. Dairy Sci. 80:3015-3022.</ref>) ===
Recorded milk weights are combined into a lactation record using standard selection index methods. Let vector y contain M1, M2, to Mn and let E('''y''') contain corresponding the expected values for each recorded day. The E(y) are obtained from standard lactation curves for the population or for the herd and should account for the cow's age and other environmental factors such as season, milking frequency, etc. The yields in '''y''' covary as a function of the recording interval between them (I). Diagonal elements in Var(y) are the population or herd variance for that recording day and off diagonals are obtained from autoregressive or similar functions such as Corr(M1, M2)=0.995I for first lactations or 0.992I for later lactations. Covariances of one observation with the lactation yield, for example Cov(M1, MY), are the sum of 305 individual covariances. E(MY) is the sum of 305 daily expected values. Lactation milk yield is then predicted as Equation 3:
[[File:Equation333333.png|none|thumb|640x640px]]
With best prediction, predicted milk yields have less variance than true milk yields. With TIM, estimated yields have more variance than true yields. The reason is that predicted yields are regressed toward the mean unless all 305 daily yields are observed. With best prediction, the predicted MY for a lactation without any observed yields is E(MY) which is the population or herd mean for a cow of that age and season. With TIM, the estimated MY is undefined if no daily yields are recorded.

Milk, fat, and protein yields can be processed separately using single-trait best prediction or jointly using multi-trait best prediction. Replacement of M1, M2, to Mn with F1, F2, to Fn or P1, P2, to Pn gives the single-trait predictions for fat or for protein. Multi-trait predictions require larger vectors and matrices but similar algebra. Products of trait correlations and autoregressive correlations, for example, may provide the needed covariances.

=== Multiple-Trait Procedure (MTP) (Schaeffer & Jamrozik, 1996<ref>Schaeffer, L.R., and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. J. Dairy Sci. 79:2044-2055.</ref>) ===
The Multiple-Trait Procedure predicts 305-d lactation yields for milk, fat, protein and SCS, incorporating information about standard lactation curves and covariances between milk, fat, and protein yields and SCS. Test day yields are weighted by their relative variances, and standard lactation curves of cows of similar breed, region, lactation number, age, and season of calving are used in the estimation of lactation curve parameters for each cow. The multiple-trait procedure can handle long intervals between test days, test days with milk only recorded, and can make 305-d predictions on the basis of just one test day record per cow. The procedure also lends itself to the calculation of peak yield, day of peak yield, yield persistency, and expected test-day yields, which could be useful management tools for a producer on a milk recording program.

The MTP method is based upon Wilmink's model in conjunction with an approach incorporating standard curve parameters for cows with the same production characteristics. Wilmink's function for one trait is given by Equation 4.

Equation 4. Wilmink function for one trait (MTP).

y = A + B''t'' ± C''exp'' (-0.05''t'') + ''e''

where y is yield on day t of lactation, A, B, and C are related to the shape of the lactation curve.

The parameters A, B, and C need to be estimated for each yield trait. The yield traits have high phenotypic correlations, and MTP would incorporate these correlations. Use of MTP would allow for the prediction of yields even if data were not available on each test day for a cow.

The vector of parameters to be estimated for one cow are designated:
[[File:Vectro.png|center|thumb]]
where M, F, and P represent milk, fat, and protein, respectively, and S represents somatic cell score. The vector c is to be estimated from the available test-day records. Let c0 represent the corresponding parameters estimated across all cows with the same production characteristics as the cow in question.

Let
[[File:Vector2.png|center|thumb]]

be the vector of yield traits and somatic cell scores on test ''k'' at day ''t'' of the lactation.

The incidence matrix, ''Xk'', is constructed as follows:
[[File:Vector3.png|center|thumb|558x558px]]

The MTP equations are:
[[File:Equation55555.png|none|thumb|560x560px]]
and ''n'' is the number of tests for that cow. ''Rk'' is a matrix of order 4 that contains the variances and covariances among the yields on ''kth'' test at day ''t'' of lactation. The elements of this matrix were derived from regression formulas based on fitting phenotypic variances and covariances of yields to models with ''t'' and ''t2'' as covariables. Thus, element ''ij'' of ''Rk'' would be determined by

rij(t) = ß0ij + ß1ij (t) + ß2ij (t2)

G is a 12 x 12 matrix containing variances and covariances among the parameters in '''ĉ''' and represents the cow to cow variation in these parameters, which includes genetic and permanent environmental effects, but ignores genetic covariances between cows. The parameters for '''''G''''' and '''''Rk''''' vary depending on the breed, but must be known. Initially, these matrices were allowed to vary by region of Canada in addition to breed, but this meant that there could exist two cows with identical production records on the same days in milk, but because one cow was in one region and the other cow was in another region, then the accuracy of their predictions would be different. This was considered to be too confusing for dairy producers, so that regional differences in variance-covariance matrices were ignored and one set of parameters would be used for all regions for a particular breed. Estimation of G is described later.

If a cow has a test, but only milk yield is reported, then

y’k(Mk 0 0 0)

and
[[File:And.png|center|thumb|540x540px]]

The inverse of '''''Rk''''' is the regular inverse of the nonzero submatrix within '''''Rk''''', ignoring the zero rows and columns. Thus, missing yields can be accommodated in MTP.

Accuracy of predicted 305-d lactation totals depends on the number of test-day records during the lactation and DIM associated with each test. Thus, any prediction procedure will require reliability figures to be reported with all predictions, especially if fewer tests at very irregular intervals are going to be frequent in milk recording. At the moment, an approximate procedure is applied that uses the inverse elements of '''(X’R-1X + G-1) -1.'''

==== 1.1 Example calculations ====
Four test day records on a 25 month old, Holstein cow calving in June from Ontario are given in the Table 5 below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 5. Example test day data for a cow (MTP).'''''
|- style="background-color:#efefef;"
|'''Test no.'''
|'''DIM=''t'''''
|'''Exp(-0.05''t'')'''
|'''Milk (kg)'''
|'''Fat (kg)'''
|'''Protein (kg)'''
|'''SCS'''
|-
|1
|15
|0.47237
|28.8
|
|
|3.130
|-
|2
|54
|0.06721
|29.2
|1.12
|0.87
|2.463
|-
|3
|188
|0.000083
|23.7
|0.97
|0.78
|2.157
|-
|4
|250
|0.0000037
|20.8
|
|
|2.619
|}
</center>

Notice that two tests do not have fat and protein yields, and that intervals between tests are irregular and large. The vector of standard curve parameters based on all available comparable cow, is
[[File:Vector4.png|center|thumb]]
The R^(-1)_k matrices for each test day need to be constructed. These matrices are derived from regression equations. The equations for Holsteins were:
<center>
{| class="wikitable" style="text-align: center;"
|''rMM(t) =''
|71.0752 - 0.281201''t'' + 0.0004977''t2''
|-
|''rMF(t) =''
|2.4365 - 0.013274''t'' + 0.0000302''t2''
|-
|''rMP(t) =''
|2.0504 - 0.008286''t'' + 0.0000163''t2''
|-
|''rMS(t) =''
|<nowiki>-1.7993 + 0.013209</nowiki>''t'' - 0.000056''t2''
|-
|''rFF(t) =''
|0.1312 - 0.000725''t'' + 0.000001586''t2''
|-
|''rFP(t) =''
|0.0739 - 0.000386''t'' + 0.000000926''t2''
|-
|''rFS(t) =''
|<nowiki>- 0.0386 + 0.000292</nowiki>''t'' - 0.000001796''t2''
|-
|''rPP(t) =''
|0.066 - 0.000267''t'' + 0.0000005636''t2''
|-
|''rPS(t) =''
|<nowiki>- 0.0404 + 0.000369</nowiki>''t'' - 0.000001743''t2''
|-
|''rSS(t) =''
|3.0404 - 0.000083''t'' - 0.000006105''t2''
|}
</center>

The inverses of the residual variance-covariance matrices for yields for the four test days are as follows:
<center>
{| class="wikitable" style="text-align: center;"
|
|0.0151259
|0
|0
|0.0080354
|-
|'''R^(-1)_1''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0080354
|0
|0
|0.3334553
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.1685584
|0.345947
|<nowiki>-4.851935</nowiki>
|0.0254775
|-
|'''R^(-1)_2''' = =
|<nowiki>-0.345947</nowiki>
|26.830915
|<nowiki>-17.40281</nowiki>
|<nowiki>-0.041445</nowiki>
|-
|
|<nowiki>-4.851935</nowiki>
|<nowiki>-17.40281</nowiki>
|187.18579
|<nowiki>-0.584885</nowiki>
|-
|
|0.0254775
|<nowiki>-0.041445</nowiki>
|<nowiki>-0.584885</nowiki>
|0.3365425
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.2620161
|0.1479068
|<nowiki>-7.943903</nowiki>
|0.0316069
|-
|'''R^(-1)_3''' = =
|0.1479068
|54.446977
|<nowiki>-56.01333</nowiki>
|0.3306741
|-
|
|<nowiki>-7.943903</nowiki>
|<nowiki>-56.01333</nowiki>
|317.9609
|<nowiki>-0.92601</nowiki>
|-
|
|0.0316069
|0.3306741
|<nowiki>-0.92601</nowiki>
|0.3654369
|}
{| class="wikitable" style="text-align: center;"
|

|0.0329465
|0
|0
|0.0251039
|-
|'''R^(-1)_4''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0251039
|0
|0
|0.3981981
|}

Inverse matrix G^(-1) of order 12 is the same for all cows of the same breed:

[[File:Left 6x6.jpg|center|thumb|600x600px|Inverse matrix G^(-1) of order 12]]

</center>
Note that many covariances between different parameters of the lactation curves have been set to zero. When all covariances were included, the prediction errors for individual cows were very large, possibly because the covariances were highly correlated to each other within and between traits. Including only covariances between the same parameter among traits gave much smaller prediction errors.

The elements of the MTP equations of order 12 for this cow are shown in partitioned format also:

'''X’R-1X ='''
<center>[[File:Elements of the MTP equations of order 12.jpg|center|thumb|600x600px|Elements of the MTP equations of order 12]]
</center>
[[File:Equation7.png|center|thumb|632x632px]]

The solution vector for this cow is
[[File:Equation6666.png|center|thumb]]

To predict 305-day yields, Y305
[[File:Equation7777.png|none|thumb|551x551px]]
Equation 6 is used separately for each trait (milk, fat, protein, and SCS). The results for this cow were 7456 kg milk, 301 kg fat, and 239 kg protein. The result for SCS is divided by 305 to give an average daily SCS of 2.477.
</div>
</div>

= Appendices =
== Appendix 1 - Adjustment factors to calculate 24-hour yields using the Liu method ==
<div class="mw-collapsible mw-collapsed">
<div>
In Table 6 the adjustment factors to calculate 24-hour yields, using the Liu method, can be found. The description of the Liu method can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2.]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" |'''''Table 1. Adjustment factors to calculate 24-hour yields using the Liu method. Milking time (MT) is either 1 (PM) or 2 (AM), i = parity class, j= milking interval class and k = stage of lactation class.'''''
|- style="background-color:#efefef;"
|'''MT'''
|'''i'''
|'''j'''
|'''k'''
| colspan="2" |'''Milk yield (DMY)'''
| colspan="2" |'''Fat yield (DFY)'''
| colspan="2" |'''Protein yield (DPY)'''
|-
| colspan="4" |
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|-
|1
|1
|1
|1
|5.29333
|1.83283
|0.30911
|1.43518
|0.18984
|1.77461
|-
|1
|1
|1
|2
|4.17676
|1.97447
|0.2803
|1.56914
|0.12246
|2.00568
|-
|1
|1
|1
|3
|4.26476
|1.95945
|0.18826
|1.82468
|0.12624
|2.0137
|-
|1
|1
|1
|4
|3.41282
|2.01814
|0.25025
|1.64707
|0.12519
|1.99629
|-
|1
|1
|1
|5
|1.79548
|2.22665
|0.06578
|2.09515
|0.05249
|2.24065
|-
|1
|1
|1
|6
|3.7751
|1.95508
|0.12854
|1.93892
|0.11936
|2.00979
|-
|1
|1
|1
|7
|1.544
|2.1478
|0.06425
|2.06779
|0.0569
|2.13851
|-
|1
|1
|2
|1
|5.8584
|1.79409
|0.33193
|1.42953
|0.20756
|1.7288
|-
|1
|1
|2
|2
|5.45524
|1.84258
|0.32877
|1.43235
|0.21332
|1.74001
|-
|1
|1
|2
|3
|4.64052
|1.86706
|0.27155
|1.57017
|0.16439
|1.84539
|-
|1
|1
|2
|4
|2.86835
|2.06209
|0.18647
|1.79403
|0.10803
|2.0193
|-
|1
|1
|2
|5
|2.11336
|2.12055
|0.10435
|1.97206
|0.07193
|2.10651
|-
|1
|1
|2
|6
|2.00673
|2.0636
|0.1386
|1.83336
|0.06892
|2.06532
|-
|1
|1
|2
|7
|1.71752
|2.11269
|0.06501
|2.0379
|0.05569
|2.12881
|-
|1
|1
|3
|1
|2.80244
|2.02183
|0.17663
|1.72438
|0.11078
|1.96422
|-
|1
|1
|3
|2
|3.47396
|1.98268
|0.2135
|1.6805
|0.10471
|1.99092
|-
|1
|1
|3
|3
|2.81702
|2.04348
|0.20754
|1.71868
|0.1127
|1.98403
|-
|1
|1
|3
|4
|3.1989
|1.998
|0.21578
|1.6991
|0.10802
|1.99517
|-
|1
|1
|3
|5
|2.47055
|2.04826
|0.15418
|1.83151
|0.07492
|2.07547
|-
|1
|1
|3
|6
|1.923
|2.07728
|0.11783
|1.89678
|0.06457
|2.08391
|-
|1
|1
|3
|7
|1.85264
|2.0873
|0.13047
|1.86711
|0.071
|2.06917
|-
|1
|1
|4
|1
|2.75042
|1.96631
|0.24794
|1.61741
|0.09248
|1.95376
|-
|1
|1
|4
|2
|2.97505
|1.96711
|0.20029
|1.71842
|0.09381
|1.97081
|-
|1
|1
|4
|3
|2.33365
|2.02986
|0.17021
|1.79996
|0.07631
|2.03167
|-
|1
|1
|4
|4
|3.41505
|1.94107
|0.1845
|1.76799
|0.10989
|1.95456
|-
|1
|1
|4
|5
|2.67488
|1.97797
|0.13433
|1.85893
|0.09432
|1.97755
|-
|1
|1
|4
|6
|1.89907
|2.04841
|0.08715
|1.96251
|0.07132
|2.04225
|-
|1
|1
|4
|7
|1.80326
|2.03554
|0.1251
|1.86477
|0.06072
|2.04747
|-
|1
|1
|5
|1
|2.76763
|1.92863
|0.15754
|1.72474
|0.10187
|1.88749
|-
|1
|1
|5
|2
|3.36896
|1.92048
|0.2236
|1.64149
|0.12369
|1.8823
|-
|1
|1
|5
|3
|2.22763
|2.00452
|0.17614
|1.7474
|0.08019
|1.9782
|-
|1
|1
|5
|4
|2.44625
|1.97049
|0.17217
|1.74753
|0.0889
|1.94647
|-
|1
|1
|5
|5
|2.379
|1.97307
|0.15965
|1.76134
|0.0896
|1.94575
|-
|1
|1
|5
|6
|1.62948
|2.02491
|0.11021
|1.85546
|0.0852
|1.94593
|-
|1
|1
|5
|7
|1.45651
|2.0254
|0.07479
|1.92789
|0.05846
|2.00196
|-
|1
|1
|6
|1
|2.01088
|1.9497
|0.16548
|1.68143
|0.101
|1.85846
|-
|1
|1
|6
|2
|2.96605
|1.93064
|0.25841
|1.52566
|0.12097
|1.86061
|-
|1
|1
|6
|3
|2.2281
|1.96085
|0.19036
|1.69013
|0.08032
|1.9375
|-
|1
|1
|6
|4
|2.39473
|1.952
|0.17854
|1.72423
|0.06863
|1.97582
|-
|1
|1
|6
|5
|2.37955
|1.94127
|0.19579
|1.66419
|0.08447
|1.93156
|-
|1
|1
|6
|6
|0.36203
|2.12393
|0.14291
|1.75822
|0.03845
|2.04562
|-
|1
|1
|6
|7
|1.5702
|1.96794
|0.1336
|1.76796
|0.06449
|1.94829
|-
|1
|1
|7
|1
|3.93654
|1.82772
|0.2359
|1.61894
|0.15032
|1.76054
|-
|1
|1
|7
|2
|4.39662
|1.81581
|0.24969
|1.5881
|0.16909
|1.74794
|-
|1
|1
|7
|3
|3.78325
|1.82778
|0.19228
|1.71802
|0.12368
|1.8268
|-
|1
|1
|7
|4
|3.39116
|1.86302
|0.1969
|1.71838
|0.12282
|1.848
|-
|1
|1
|7
|5
|3.20111
|1.83255
|0.09893
|1.86309
|0.1044
|1.84257
|-
|1
|1
|7
|6
|3.75639
|1.78665
|0.25205
|1.56174
|0.14105
|1.76802
|-
|1
|1
|7
|7
|1.42153
|1.95649
|0.09226
|1.85882
|0.04636
|1.96245
|-
|1
|1
|8
|1
|2.3454
|1.90436
|0.14321
|1.77423
|0.10703
|1.82306
|-
|1
|1
|8
|2
|3.97557
|1.82746
|0.26651
|1.58374
|0.15298
|1.76385
|-
|1
|1
|8
|3
|4.26939
|1.80503
|0.22918
|1.64925
|0.12924
|1.81061
|-
|1
|1
|8
|4
|2.90779
|1.89861
|0.18578
|1.73968
|0.13948
|1.79679
|-
|1
|1
|8
|5
|2.8265
|1.87632
|0.19374
|1.67929
|0.12377
|1.80944
|-
|1
|1
|8
|6
|2.26312
|1.87397
|0.09917
|1.82528
|0.08819
|1.84453
|-
|1
|1
|8
|7
|0.31382
|2.04402
|0.05049
|1.95773
|0.02612
|1.99012
|-
|1
|2
|1
|1
|4.63752
|1.99615
|0.31102
|1.58962
|0.16637
|1.96686
|-
|1
|2
|1
|2
|5.56226
|1.91521
|0.26761
|1.64342
|0.16973
|1.94145
|-
|1
|2
|1
|3
|4.51983
|1.96962
|0.26221
|1.65088
|0.12245
|2.03857
|-
|1
|2
|1
|4
|4.51563
|1.93033
|0.18468
|1.80715
|0.15252
|1.94807
|-
|1
|2
|1
|5
|2.60334
|2.07338
|0.16011
|1.81257
|0.09892
|2.05493
|-
|1
|2
|1
|6
|2.86068
|1.98457
|0.15381
|1.79197
|0.08619
|2.04046
|-
|1
|2
|1
|7
|1.6596
|2.11753
|0.13089
|1.83687
|0.09908
|1.96479
|-
|1
|2
|2
|1
|3.94656
|2.03607
|0.23716
|1.6988
|0.19559
|1.88765
|-
|1
|2
|2
|2
|4.20525
|1.98621
|0.3553
|1.46663
|0.1657
|1.92175
|-
|1
|2
|2
|3
|3.31729
|2.04589
|0.29682
|1.57761
|0.12491
|2.00945
|-
|1
|2
|2
|4
|1.95977
|2.13926
|0.16059
|1.79846
|0.06713
|2.12835
|-
|1
|2
|2
|5
|1.49014
|2.14889
|0.10057
|1.90772
|0.05279
|2.14047
|-
|1
|2
|2
|6
|0.82235
|2.22517
|0.07573
|1.94963
|0.04014
|2.17549
|-
|1
|2
|2
|7
|1.53608
|2.08972
|0.11472
|1.81148
|0.0676
|2.03957
|-
|1
|2
|3
|1
|3.85525
|2.00429
|0.27991
|1.62403
|0.12863
|1.98973
|-
|1
|2
|3
|2
|4.1508
|1.9852
|0.3635
|1.47515
|0.13952
|1.97074
|-
|1
|2
|3
|3
|3.31493
|2.02332
|0.31131
|1.55183
|0.11703
|2.00696
|-
|1
|2
|3
|4
|2.47354
|2.0652
|0.20828
|1.71637
|0.09402
|2.04147
|-
|1
|2
|3
|5
|1.68517
|2.08809
|0.14418
|1.80246
|0.06917
|2.05808
|-
|1
|2
|3
|6
|1.316
|2.12714
|0.11206
|1.87179
|0.04723
|2.12486
|-
|1
|2
|3
|7
|0.4841
|2.20538
|0.04633
|2.02915
|0.02369
|2.18113
|-
|1
|2
|4
|1
|2.82623
|2.01819
|0.25826
|1.69268
|0.11251
|1.97665
|-
|1
|2
|4
|2
|3.24039
|1.9811
|0.36283
|1.50648
|0.11719
|1.96246
|-
|1
|2
|4
|3
|2.4545
|2.03386
|0.19627
|1.75339
|0.09698
|2.00807
|-
|1
|2
|4
|4
|2.46446
|2.01626
|0.17827
|1.76414
|0.08026
|2.02912
|-
|1
|2
|4
|5
|2.11339
|2.00724
|0.14884
|1.77964
|0.07749
|2.00585
|-
|1
|2
|4
|6
|1.51141
|2.04563
|0.11559
|1.82474
|0.06194
|2.02586
|-
|1
|2
|4
|7
|0.95936
|2.09963
|0.07044
|1.95281
|0.03645
|2.0993
|-
|1
|2
|5
|1
|3.36561
|1.97323
|0.2649
|1.65361
|0.13019
|1.92402
|-
|1
|2
|5
|2
|3.66222
|1.95479
|0.35065
|1.51028
|0.14652
|1.89882
|-
|1
|2
|5
|3
|3.20442
|1.96165
|0.28676
|1.58823
|0.12031
|1.93028
|-
|1
|2
|5
|4
|1.78673
|2.0426
|0.17183
|1.75198
|0.0678
|2.02025
|-
|1
|2
|5
|5
|1.61868
|2.01988
|0.11914
|1.80878
|0.06624
|1.99283
|-
|1
|2
|5
|6
|1.30123
|2.02218
|0.10515
|1.80653
|0.05345
|2.00292
|-
|1
|2
|5
|7
|0.65695
|2.08269
|0.06835
|1.89102
|0.0332
|2.0525
|-
|1
|2
|6
|1
|2.3773
|1.9669
|0.24867
|1.6336
|0.08319
|1.94741
|-
|1
|2
|6
|2
|2.82556
|1.95506
|0.31731
|1.51798
|0.12008
|1.89324
|-
|1
|2
|6
|3
|2.7235
|1.94883
|0.30621
|1.5177
|0.09365
|1.93764
|-
|1
|2
|6
|4
|1.77727
|1.98273
|0.17989
|1.69341
|0.07314
|1.95161
|-
|1
|2
|6
|5
|0.81041
|2.05295
|0.13961
|1.74391
|0.04468
|2.01091
|-
|1
|2
|6
|6
|0.72188
|2.0465
|0.09874
|1.79927
|0.03137
|2.03309
|-
|1
|2
|6
|7
|1.21598
|1.97942
|0.07065
|1.87211
|0.04484
|1.98491
|-
|1
|2
|7
|1
|3.55054
|1.89128
|0.27402
|1.61031
|0.10827
|1.89085
|-
|1
|2
|7
|2
|5.0062
|1.81574
|0.3119
|1.54857
|0.18009
|1.76865
|-
|1
|2
|7
|3
|3.95204
|1.84947
|0.30465
|1.53907
|0.16048
|1.789
|-
|1
|2
|7
|4
|2.36233
|1.9168
|0.18751
|1.70412
|0.09531
|1.88355
|-
|1
|2
|7
|5
|1.48851
|1.94443
|0.09973
|1.81041
|0.05904
|1.92497
|-
|1
|2
|7
|6
|1.22525
|1.94454
|0.06617
|1.87082
|0.05516
|1.91259
|-
|1
|2
|7
|7
|1.13847
|1.93756
|0.08109
|1.83388
|0.04706
|1.93165
|-
|1
|2
|8
|1
|4.09874
|1.87708
|0.20312
|1.73434
|0.15506
|1.83083
|-
|1
|2
|8
|2
|4.66403
|1.84302
|0.31808
|1.56093
|0.18049
|1.78288
|-
|1
|2
|8
|3
|3.24375
|1.89351
|0.2827
|1.59546
|0.13583
|1.83427
|-
|1
|2
|8
|4
|2.24175
|1.92084
|0.17795
|1.72611
|0.09636
|1.87438
|-
|1
|2
|8
|5
|1.63783
|1.93625
|0.1225
|1.78642
|0.0659
|1.90934
|-
|1
|2
|8
|6
|2.01753
|1.89095
|0.13742
|1.74752
|0.08289
|1.86553
|-
|1
|2
|8
|7
|0.97568
|1.97215
|0.05926
|1.88807
|0.04057
|1.95672
|-
|2
|1
|1
|1
|3.44076
|1.73133
|0.27759
|1.55037
|0.13323
|1.68913
|-
|2
|1
|1
|2
|4.99596
|1.64527
|0.2322
|1.58033
|0.17533
|1.62422
|-
|2
|1
|1
|3
|3.83372
|1.68144
|0.25087
|1.52033
|0.14525
|1.66706
|-
|2
|1
|1
|4
|3.87034
|1.68102
|0.20979
|1.60153
|0.13627
|1.68885
|-
|2
|1
|1
|5
|1.76134
|1.80424
|0.15241
|1.70485
|0.06231
|1.81524
|-
|2
|1
|1
|6
|0.79304
|1.89072
|0.09906
|1.80312
|0.03277
|1.89435
|-
|2
|1
|1
|7
|1.43535
|1.80614
|0.0593
|1.81589
|0.0407
|1.85002
|-
|2
|1
|2
|1
|3.72284
|1.68499
|0.19226
|1.66567
|0.1237
|1.66453
|-
|2
|1
|2
|2
|4.42667
|1.66508
|0.24314
|1.55652
|0.14361
|1.66251
|-
|2
|1
|2
|3
|2.7019
|1.75871
|0.32717
|1.38452
|0.11056
|1.72312
|-
|2
|1
|2
|4
|2.41538
|1.75937
|0.14575
|1.68355
|0.09038
|1.74138
|-
|2
|1
|2
|5
|1.65412
|1.81649
|0.13926
|1.70623
|0.0597
|1.81378
|-
|2
|1
|2
|6
|2.0843
|1.7735
|0.21052
|1.57508
|0.07244
|1.78566
|-
|2
|1
|2
|7
|1.43238
|1.80651
|0.08031
|1.78712
|0.05269
|1.81727
|-
|2
|1
|3
|1
|2.45314
|1.77068
|0.18152
|1.73443
|0.07657
|1.78025
|-
|2
|1
|3
|2
|3.01217
|1.70966
|0.19388
|1.66175
|0.05624
|1.80606
|-
|2
|1
|3
|3
|2.09997
|1.74945
|0.14493
|1.68277
|0.05446
|1.7922
|-
|2
|1
|3
|4
|2.36683
|1.71741
|0.12244
|1.71407
|0.06775
|1.75721
|-
|2
|1
|3
|5
|1.56776
|1.75755
|0.08776
|1.76946
|0.04244
|1.79675
|-
|2
|1
|3
|6
|1.63824
|1.75452
|0.09422
|1.76794
|0.04181
|1.80604
|-
|2
|1
|3
|7
|0.74114
|1.83421
|0.08039
|1.78306
|0.02347
|1.85596
|-
|2
|1
|4
|1
|1.47047
|1.78588
|0.17271
|1.69379
|0.06511
|1.74985
|-
|2
|1
|4
|2
|2.22168
|1.72985
|0.20701
|1.59429
|0.08178
|1.71455
|-
|2
|1
|4
|3
|2.50108
|1.69618
|0.16828
|1.61962
|0.08598
|1.70516
|-
|2
|1
|4
|4
|1.97141
|1.7202
|0.1446
|1.66357
|0.06856
|1.73201
|-
|2
|1
|4
|5
|1.17054
|1.75879
|0.1172
|1.69234
|0.04624
|1.75806
|-
|2
|1
|4
|6
|1.74755
|1.70968
|0.12562
|1.67603
|0.0629
|1.72333
|-
|2
|1
|4
|7
|0.52482
|1.80155
|0.07345
|1.75615
|0.02671
|1.79288
|-
|2
|1
|5
|1
|1.76464
|1.76219
|0.24301
|1.59094
|0.07156
|1.73136
|-
|2
|1
|5
|2
|1.99594
|1.73438
|0.1984
|1.5954
|0.06489
|1.73449
|-
|2
|1
|5
|3
|1.8804
|1.72362
|0.13019
|1.67977
|0.06783
|1.71916
|-
|2
|1
|5
|4
|1.83337
|1.71477
|0.11197
|1.70244
|0.05764
|1.73194
|-
|2
|1
|5
|5
|1.49752
|1.72615
|0.13128
|1.65461
|0.04656
|1.7433
|-
|2
|1
|5
|6
|1.3042
|1.7305
|0.07173
|1.75315
|0.04482
|1.7399
|-
|2
|1
|5
|7
|2.00868
|1.67669
|0.12298
|1.64761
|0.09175
|1.64669
|-
|2
|1
|6
|1
|0.84993
|1.75972
|0.12918
|1.74026
|0.0328
|1.74802
|-
|2
|1
|6
|2
|1.93666
|1.67406
|0.16606
|1.59943
|0.04535
|1.7106
|-
|2
|1
|6
|3
|2.12115
|1.64964
|0.19988
|1.50821
|0.05229
|1.68986
|-
|2
|1
|6
|4
|0.68831
|1.73901
|0.09674
|1.6838
|0.01696
|1.75787
|-
|2
|1
|6
|5
|1.13081
|1.69479
|0.06413
|1.72559
|0.04936
|1.67757
|-
|2
|1
|6
|6
|0.5893
|1.72537
|0.02598
|1.80138
|0.01591
|1.74082
|-
|2
|1
|6
|7
|0.72519
|1.71955
|0.03157
|1.78405
|0.02889
|1.71972
|-
|2
|1
|7
|1
|1.85937
|1.66064
|0.2416
|1.49676
|0.06807
|1.63599
|-
|2
|1
|7
|2
|1.8527
|1.64892
|0.2374
|1.43845
|0.06336
|1.6431
|-
|2
|1
|7
|3
|1.56905
|1.66084
|0.15434
|1.55598
|0.04336
|1.68109
|-
|2
|1
|7
|4
|0.74968
|1.69857
|0.13496
|1.56636
|0.02871
|1.6933
|-
|2
|1
|7
|5
|1.08222
|1.65925
|0.10847
|1.613
|0.03305
|1.67829
|-
|2
|1
|7
|6
|1.1124
|1.68059
|0.14267
|1.57525
|0.04416
|1.6776
|-
|2
|1
|7
|7
|0.88031
|1.6751
|0.10534
|1.60483
|0.04216
|1.66444
|-
|2
|1
|8
|1
|0.62802
|1.72402
|0.19225
|1.54631
|0.03247
|1.69368
|-
|2
|1
|8
|2
|0.83902
|1.68303
|0.15492
|1.53421
|0.05922
|1.61411
|-
|2
|1
|8
|3
|1.33727
|1.63407
|0.19835
|1.43309
|0.05874
|1.61141
|-
|2
|1
|8
|4
|1.06381
|1.64762
|0.11026
|1.58762
|0.04019
|1.64574
|-
|2
|1
|8
|5
|1.13714
|1.61716
|0.13322
|1.53166
|0.05648
|1.59149
|-
|2
|1
|8
|6
|1.19134
|1.60463
|0.11089
|1.54864
|0.06258
|1.56912
|-
|2
|1
|8
|7
|1.58872
|1.60204
|0.066
|1.64659
|0.04748
|1.63282
|-
|2
|2
|1
|1
|3.46775
|1.78609
|0.28956
|1.68515
|0.15003
|1.72171
|-
|2
|2
|1
|2
|5.69879
|1.67614
|0.3725
|1.5045
|0.19774
|1.64659
|-
|2
|2
|1
|3
|5.18985
|1.66571
|0.40124
|1.40574
|0.17828
|1.65793
|-
|2
|2
|1
|4
|3.43435
|1.74182
|0.20332
|1.66994
|0.11075
|1.76221
|-
|2
|2
|1
|5
|2.48643
|1.76219
|0.13714
|1.7396
|0.09636
|1.75624
|-
|2
|2
|1
|6
|1.41151
|1.82292
|0.15415
|1.6725
|0.06549
|1.80013
|-
|2
|2
|1
|7
|0.9096
|1.8409
|0.08811
|1.7823
|0.03467
|1.85275
|-
|2
|2
|2
|1
|1.85358
|1.83615
|0.28355
|1.64765
|0.06055
|1.83138
|-
|2
|2
|2
|2
|3.81188
|1.74978
|0.25972
|1.62799
|0.11238
|1.7646
|-
|2
|2
|2
|3
|3.16717
|1.76679
|0.29832
|1.53409
|0.09407
|1.78959
|-
|2
|2
|2
|4
|2.33664
|1.78934
|0.22694
|1.60101
|0.07273
|1.80371
|-
|2
|2
|2
|5
|2.01675
|1.79303
|0.10664
|1.79792
|0.06062
|1.8184
|-
|2
|2
|2
|6
|1.80809
|1.80081
|0.13659
|1.70935
|0.07335
|1.79213
|-
|2
|2
|2
|7
|1.01661
|1.8295
|0.0548
|1.84688
|0.03414
|1.84213
|-
|2
|2
|3
|1
|2.01474
|1.8142
|0.21867
|1.74325
|0.05359
|1.83088
|-
|2
|2
|3
|2
|3.53989
|1.71985
|0.28196
|1.60868
|0.10823
|1.73763
|-
|2
|2
|3
|3
|3.38412
|1.69907
|0.27409
|1.56164
|0.11042
|1.71397
|-
|2
|2
|3
|4
|2.2171
|1.74622
|0.16076
|1.70107
|0.07372
|1.75906
|-
|2
|2
|3
|5
|1.11799
|1.80944
|0.11087
|1.75678
|0.03792
|1.81891
|-
|2
|2
|3
|6
|1.40464
|1.76033
|0.10048
|1.72933
|0.05342
|1.75745
|-
|2
|2
|3
|7
|0.11328
|1.8972
|0.04052
|1.87101
|0.00787
|1.88753
|-
|2
|2
|4
|1
|2.59777
|1.74476
|0.28154
|1.66509
|0.10763
|1.71072
|-
|2
|2
|4
|2
|3.53853
|1.69511
|0.38311
|1.46839
|0.13243
|1.66523
|-
|2
|2
|4
|3
|2.80538
|1.70587
|0.26686
|1.55787
|0.1126
|1.68024
|-
|2
|2
|4
|4
|2.18191
|1.72068
|0.18333
|1.65612
|0.085
|1.71029
|-
|2
|2
|4
|5
|1.23383
|1.7716
|0.12824
|1.71179
|0.04845
|1.76628
|-
|2
|2
|4
|6
|0.85652
|1.79279
|0.0763
|1.79314
|0.03563
|1.78528
|-
|2
|2
|4
|7
|0.97995
|1.77178
|0.0797
|1.7577
|0.03846
|1.77043
|-
|2
|2
|5
|1
|2.47016
|1.74985
|0.32061
|1.60073
|0.10455
|1.71058
|-
|2
|2
|5
|2
|3.76194
|1.68979
|0.32787
|1.54675
|0.11781
|1.69109
|-
|2
|2
|5
|3
|2.61421
|1.70766
|0.20307
|1.64866
|0.08315
|1.71378
|-
|2
|2
|5
|4
|1.6809
|1.74028
|0.16795
|1.66491
|0.06202
|1.73305
|-
|2
|2
|5
|5
|1.31241
|1.75722
|0.14383
|1.68302
|0.05338
|1.74562
|-
|2
|2
|5
|6
|1.66563
|1.71781
|0.12721
|1.69231
|0.06147
|1.72101
|-
|2
|2
|5
|7
|0.87471
|1.74991
|0.07882
|1.71706
|0.04173
|1.73246
|-
|2
|2
|6
|1
|1.70055
|1.72832
|0.20839
|1.67759
|0.06001
|1.71779
|-
|2
|2
|6
|2
|3.20558
|1.65143
|0.33676
|1.47797
|0.09642
|1.6546
|-
|2
|2
|6
|3
|1.5827
|1.71538
|0.19719
|1.62038
|0.05324
|1.71254
|-
|2
|2
|6
|4
|1.7692
|1.69473
|0.14854
|1.66225
|0.05758
|1.69946
|-
|2
|2
|6
|5
|1.33003
|1.70542
|0.10726
|1.69398
|0.04565
|1.7096
|-
|2
|2
|6
|6
|1.01266
|1.71155
|0.09376
|1.70285
|0.04005
|1.70822
|-
|2
|2
|6
|7
|0.9856
|1.70091
|0.06454
|1.73063
|0.0394
|1.69796
|-
|2
|2
|7
|1
|2.02441
|1.67788
|0.30435
|1.5407
|0.08673
|1.63673
|-
|2
|2
|7
|2
|1.43949
|1.71143
|0.30098
|1.47963
|0.06527
|1.67295
|-
|2
|2
|7
|3
|1.68946
|1.66442
|0.24777
|1.47116
|0.06594
|1.64834
|-
|2
|2
|7
|4
|1.10967
|1.68591
|0.15663
|1.60109
|0.04949
|1.67069
|-
|2
|2
|7
|5
|0.77866
|1.70882
|0.11248
|1.64389
|0.03402
|1.70215
|-
|2
|2
|7
|6
|0.67502
|1.69719
|0.10289
|1.62419
|0.03507
|1.67744
|-
|2
|2
|7
|7
|0.65216
|1.70336
|0.05545
|1.73388
|0.02233
|1.72102
|-
|2
|2
|8
|1
|1.33877
|1.67358
|0.18369
|1.64385
|0.06055
|1.63818
|-
|2
|2
|8
|2
|0.71697
|1.71038
|0.25461
|1.49037
|0.04798
|1.66397
|-
|2
|2
|8
|3
|2.13197
|1.62429
|0.2393
|1.47673
|0.08136
|1.6065
|-
|2
|2
|8
|4
|1.16932
|1.66188
|0.13759
|1.60108
|0.0463
|1.64856
|-
|2
|2
|8
|5
|1.48369
|1.62387
|0.12547
|1.58988
|0.06919
|1.5925
|-
|2
|2
|8
|6
|1.18879
|1.65442
|0.10031
|1.62813
|0.07392
|1.58846
|-
|2
|2
|8
|7
|0.58052
|1.68546
|0.02696
|1.7382
|0.01982
|1.70519
|}
</center>
</div>
</div>

== Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme ==
<div class="mw-collapsible mw-collapsed">
<div>
=== Abstract ===
Based on comments on imprecision of the estimation method for 24-hour fat % in AM/PM milk recording schemes the regression formula was extended and re-estimated. Non-linearity for the existing effects of protein % of the milk sample, interval before sampling, milk amount of sample, milk amount of previous milking and interval before the previous milking was incorporated by using polynomials. Extensions were made by adding the effects of time of sampling, parity and month of sampling as class variables and lactation stage as polynomial. In total a reduction of the standard deviation of the difference between true and estimated 24-hour fat % of 2.4% was reached (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

'''''Keywords''''': estimation, fat %, AM/PM.

=== Introduction ===
The AM/PM milk recording routine is based on only one morning (a.m.) or evening (p.m.) milk sample which are collected in an alternating way. A condition to take part in this AM/PM milk recording in The Netherlands is that on farm electronic milk measurements (EMM) are available. EMM-data consists of time of milking and milk quantity of every milking. Based on one milk sample and the EMM-data the 24-hour fat % is estimated (Peeters & Galesloot, 2002<ref name=":2">Peeters, R. and P. Galesloot, 2002.Estimating daily fat yield from a single milking on test day for herds with a robotic milking system. J. Dairy Sci. 85, 682-688.</ref>). Also for farms with an automatic milking system (AMS) this estimation is used when only one milk sample is available for analysis on milk composition.

Based on comments from farmers on fluctuations in 24-hour fat % preliminary research was conducted. This showed that the current estimation caused an underestimation of 24-hour fat % based on an a.m.-sample of 0.09% while the estimate based on a p.m.-sample was overestimated by 0.05%. Possible causes for this fluctuation are differences in milk-fat synthesis between day- and night-time as was shown by Gilbert et al. (1972) <ref>Gilbert, G.R., G.L. Hargrove and M. Kroger, 1972. Diurnal variations in milk yield, fat yield, milk fat % and milk protein % by the test interval method. J. Dairy Sci. 56, 409-410.</ref>and Lee & Wardorp (1984)<ref>Lee, A.J. and Wardorp, 1984. Predicting daily milk yield, fat percent, and protein percent from morning or afternoon tests. J. Dairy Sci. 67, 351-360.</ref>. Other factors of imprecision in the current estimation can be caused by lactation stage and parity, two factors that are accounted for in the method of Liu et al. (2000)<ref>Liu, Z., R. Reents, F. Reinhardt and K Kuwan, 2000. Approaches to estimating daily yield from single milk testing schemes and use of a.m.-p.m. records in test-day model genetic evaluation in dairy cattle. J. Dairy Sci. 83, 2672-2682.</ref>.

The objective of this research is to re-estimate the regression formula which is used to estimate the 24-hour fat %s in AM/PM milk recording and AMS recordings with only one sample. By testing for non-linearity of current effects and introducing new explanatory variables the aim is to increase the accuracy of the estimated 24-hour fat %.

=== Material and Methods ===
The data needed for the objective had to meet a number of criteria. The most important criteria were that the data comprised:

* differences in interval between milking times;
* different milking times;
* multiple samples per cow per herd test date;
* milking time and quantity of all milkings;

Only data of farms that use an AMS met all of these criteria. Therefore the research was conducted on data of all farms that used an AMS from January 20th 2001 until July 1st 2004. Records with only one sample per herd test date were excluded from the analysis.

In order to estimate as well as validate the new regression formula the each herd test date was assigned at random into two separate datasets. Dataset 1 was used for estimation and contained 371.528 samplings on 50.591 cows on 537 farms. Dataset 2 was used for validation and contained 371.885 milkings on 50.643 cows on 538 farms. Some characteristics of variables of both datasets are presented in Table 1.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" |'''''Table 1. Characteristics of variables in dataset 1 (estimation) and dataset 2 (validation).'''''
|-
| rowspan="2" |'''Variable'''
| colspan="2" |'''Dataset 1 (estimation)'''
| colspan="2" |'''Dataset 2 (validation)'''
|-
|'''Mean'''
|'''Std'''
|'''Mean'''
|'''Std'''
|-
|Sample milk amount (kg)
|10.1
|3.1
|10.1
|3.1
|-
|Sample fat (%)
|4.40
|0.76
|4.41
|0.76
|-
|Sample protein (%)
|3.49
|0.35
|3.49
|0.35
|-
|Time at sampling
|12.29
|7.24
|12.31
|7.24
|-
|Interval before sample (min)
|520
|154
|521
|155
|-
|Interval before prev. milking (min)
|526
|158
|527
|159
|}
</center>

=== Methods ===
The analysis started with the currently used regression formula which uses the effects: fat %, protein %, milk amount of sampling, interval before sampling, milk amount of the previous milking and interval before the previous milking (Peeters & Galesloot, 2002<ref name=":2" />). All these effects are considered to be linear. As an extra check of the data this regression formula was re-estimated and compared to the currently used regression formula. In order to estimate the regression formula first of all the 24-hour fat % was determined by using a weighted average of all milk samples for that cow on that herd test date.

Subsequently, a number of changes to the regression formula were tested for their effect on the accuracy of the 24-hour fat %. The changes that are tested are:

# non-linearity of the current effects;
# effect of time at sampling;
# effect of lactation stage;
# effect of parity;
# month of milk recording;

The effects were all tested in a similar way by plotting the residuals of the regression formula without the effect that is tested to the tested effect. Based on this plot a possible relation between residual and effect becomes clear and the best way of incorporating the effect is shown. The conclusion if an effect had a positive effect on the accuracy of the regression formula was based on the standard deviation of the difference between estimated and true 24-hour fat %. Also the correlation between the two fat %s and the b-factor (regression coefficient) of the linear regression between the two fat %s were considered.

=== Results ===
The regression coefficients of the re-estimated regression formula differed slightly from the estimates by Peeters & Galesloot (2002)<ref name=":1" />, probably due to the different dataset.

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %.
[[File:Imagefig1.png|center|thumb|''Figure 1a: Average residual per class for the variables sample fat %'']]
[[File:Imagefig1b.png|center|thumb|''Figure 1b: Sample protein %'' ]]
[[File:Imagefig1c.png|center|thumb|''Figure 1c : Interval before sampling'']]
[[File:Imagefig1d.png|center|thumb|''Figure 1d : Interval before previous milking'']]
[[File:Imagefig1e.png|center|thumb|''Figure 1e : Sample milk amount'']]
[[File:Imagefig1f.png|center|thumb|''Figure 1f: Milk amount before sampling'']]

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %. Of all variables, only fat % of the milk sample (Figure 1a) seemed to be linear. A 2nd order polynomial fitted the interval before the previous milking. The other variables, i.e. protein % of the milk sample, interval before sampling, milk amount of sample and milk amount of the previous milking were described by a 3rd order polynomial. For all variables except fat % of the sample higher order polynomials were found significant. This however was caused by the large amount of data and no longer a possible biological effect since it also had no effect on the accuracy of the estimation.

The effect of time of sampling showed a large amount of variability over time. Using a polynomial to fit the data was therefore difficult. Estimation of the effect by hourly intervals was a good alternative as is shown in Figure 2. Lactation stage had mainly an effect in the first 50 days of lactation as is shown by Figure 3. A 3rd order polynomial fitted the data properly.
[[File:Imagefig2.png|center|thumb|''Figure 2. Average residual per class for time of sampling (minutes after midnight).'']]
[[File:Imagefig33.png|center|thumb|''Figure 3. Average residual per class for lactation stage (days).'']]

The effects of parity and month of milk sampling were both considered as class variables. For parity the effects of parity 1 to 6 and 7 or higher were considered. Table 2 shows that mainly for the lower parities the estimated 24-hour fat % was overestimated. Also the months May to October, usually the pasture period, showed an overestimation of 24-hour fat %.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" |'''''Table 2. Effect of parity and month of sampling on estimated 24-hour fat % (*100).'''''
|-
|'''Parity'''
|'''Estimate'''
|'''Month of sampling'''
|'''Estimate'''
|-
|1
|<nowiki>-6.58</nowiki>
|January
|<nowiki>-0.24</nowiki>
|-
|2
|<nowiki>-3.56</nowiki>
|February
|<nowiki>-0.28</nowiki>
|-
|3
|<nowiki>-1.42</nowiki>
|June
|<nowiki>-0.54</nowiki>
|-
|4
|<nowiki>-0.48</nowiki>
|April
|<nowiki>-0.27</nowiki>
|-
|5
|<nowiki>-0.35</nowiki>
|May
|<nowiki>-2.07</nowiki>
|-
|6
|<nowiki>-0.35</nowiki>
|June
|<nowiki>-3.36</nowiki>
|-
|7+
|<nowiki>-0.00</nowiki>
|July
|<nowiki>-4.32</nowiki>
|-
|
|
|August
|<nowiki>-5.52</nowiki>
|-
|
|
|September
|<nowiki>-4.74</nowiki>
|-
|
|
|October
|<nowiki>-2.24</nowiki>
|-
|
|
|November
|<nowiki>-0.97</nowiki>
|-
|
|
|December
|<nowiki>-0.00</nowiki>
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" |'''''Table 3. Statistics of the difference between true and estimated 24-hour fat % for six regression formulas (current, re-estimated + five steps), each also including preceding steps.'''''
|-
|style="text-align: left;"|'''Regression'''
|'''Std.'''
|'''Min'''
|'''Max'''
|'''Cor'''
|'''b-factor'''
|-
|style="text-align: left;"|Current, re-estimated
|0.2856
|<nowiki>-1.840</nowiki>
|2.224
|0.898
|0.807
|-
|style="text-align: left;"|Non-linearity
|0.2820
|<nowiki>-1.890 </nowiki>
|2.198
|0.901
|0.812
|-
|style="text-align: left;"|Time of sampling
|0.2817
|<nowiki>-1.877 </nowiki>
|2.211
|0.901
|0.813
|-
|style="text-align: left;"|Lactation stage
|0.2803
|<nowiki>-1.883 </nowiki>
|2.196
|0.902
|0.814
|-
|style="text-align: left;"|Parity
|0.2794
|<nowiki>-1.887 </nowiki>
|2.179
|0.903
|0.816
|-
|style="text-align: left;"|Month of sampling
|0.2788
|<nowiki>-1.868 </nowiki>
|2.175
|0.903
|0.817
|}
</center>

Table 3 shows some statistics of the difference between the true and estimated 24-hour fat % based on dataset 2 (validation) of the different regression formulas. Each of the five changes to the regression formula had a (minor) positive effect on either the standard deviation of the difference between the true and estimated 24-hour fat % (Std.), the correlation (Cor) between the two fat %s, the b-factor of the linear regression between the two fat %s or a combination of the these. All changes together reduced the standard deviation with 2.4% from 0.2856 to 0.2788, increased the correlation from 0.898 to 0.903 and increased the b-factor from 0.807 to 0.817.

=== Conclusions ===
The regression formula to estimate the 24-hour fat % based on one milk sample was improved. Improvements were first of all considering non-linearity of the variables by using polynomials for protein % of the milk sample (3rd order), interval before sampling (3rd order), milk amount of sample (3rd order), milk amount of previous milking (3rd order) and interval before the previous milking (2nd order). Secondly, adding the effects of time of sampling (class variable), lactation stage (3rd order polynomial), parity (class variable) and month of sampling (class variable) gave a further reduction of the difference between true and estimated 24-hour fat %. The total reduction in standard deviation of the difference between true and estimated 24-hour fat % is 2.4% (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

== Appendix 3 - A unified Python implementation of standardized 305 day yield calculation methods ==
The ICAR guideline is translated into an open-source Python package that can serve as a reference implementation for 305-day yield calculation. In addition to implementing the methods described in the original guideline (with the exception of the multi-trait method, which will be added in future work), the package incorporates 14 lactation-curve models, including traditional parametric models, Bayesian fitting approaches, and an AI-based model. The package also provides tools to derive biologically relevant lactation characteristics such as time to peak, peak yield, cumulative yield, and persistency. The package is publicly available through PyPI and can be installed directly using pip install lactationcurve (van Leerdam et al., 2026). Extensive documentation was developed alongside the package to improve transparency and reproducibility [https://bovi-analytics.github.io/bovi/lactationcurve.html https://bovi-analytics.github.io/bovi/lactationcurve.html.]

Through a companioning website (https://tools.bovi-analytics.org<nowiki/>/), users can upload milk-recording data in CSV format, fit and visualize the implemented lactation-curve models, and compare different cumulative milk-yield methodologies on both test-day and fully daily-recorded lactations using metrics such as RMSE, Pearson correlation, MAPE, and MAE. Reference datasets are provided to allow organizations to benchmark their own calculations against alternative methodologies. In addition, downloadable PDF reports summarize the results through detailed statistics and scatterplots, both overall and stratified by parity.
</div>
</div>

Section 02 – Cattle Milk Recording

2026-07-22T17:30:46Z

Cmosconi:

= Overview =
<div class="mw-collapsible mw-collapsed">
<div>
== Introduction ==
Information about milk production traits is very important for managing and breeding dairy herds. The milk recording process starts with the collection of animal identification, a calving date of milking cows, the amount of milk given and the date with time or time frame of a day. A milk sample may be taken. The obtained milk sample is analysed for milk constituents. The results of the analysis plus the data about milk yield and time of milking are stored in a database. Subsequently a number of parameters, cumulative yields and indices are calculated and stored in the database and, finally, reported to the farmer

This Section 2 of the ICAR Guidelines focuses on the milk recording process for dairy cattle.

== Scope ==
Figure 1 gives a pictorial summary of the main elements of this guideline.

In summary, this section of the ICAR Guidelines covers the milk recording process from the enrolment of a herd for milk recording, through to the delivery of information which a herd owner can use to assist in a range of decisions.
[[File:Scope of Section 2 - Dairy cattle milk recording..png|thumb|Figure 1. Scope of Section 2 -Dairy cattle milk recording.|center|524x524px]]

Not covered in this section are:
# Standards and guidelines for ICAR approval of milk recording devices. Please consult [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices|Section 11]] for this subject.
# Standards and guidelines for ICAR approval of ID devices. Please consult [[Section 10 – Identification Device Certification|Section 10]] for this subject.
# Standards and guidelines for preparation of milk samples and for quality assurance of milk analysis. Please consult [[Section 12 – Milk Analysis|Section 12]] for this subject.
# Standards and guidelines for in-line milk analysis on the farm. Please consult [[Section 13 – On-farm Milk Analysis|Section 13]] for this subject.

== Enrolment ==

Enrolment of new herds in the recording process should involve an agreement between the farmer and the recording organisation regarding technical and financial questions such as:

# General information about the recording programme itself, i.e.
#* Herd and cow identification.
#* Scope of recorded data, including database setup as required by the user.
#* Scheduling recording.
#* Data capture and processing.
#* Recording methods and intervals.
#* Milk measuring and meters.
#* Sampling and sample transport.
#* Reports (outcomes) and supporting decisions.
# Definition of supervision scheme and other quality assurance and plausibility checking steps.
# Fee structure and invoicing.
# Approval of technicians by milk recording organisations (MROs) so as to give them free access to farms for all recording and supervision actions.

In cases where the owner of the recorded cows or his employees carry out the recording itself, it is up to the organisation to decide upon, and provide for, any necessary training.

== Standard and Guidelines for Milk Recording ==
These standards and guidelines for milk recording are valid for all milking systems, including AMS where applicable.
====General Standards and Guidelines for milk recording====
#ICAR-approved (electronic) milk meters and sampling devices must be used on the recording day (see [https://wiki.icar.org/index.php/Section_11_%E2%80%93_Testing,_Approval_and_Checking_of_Measuring,_Recording_and_Sampling_Devices#Procedure_1:_Procedure_for_Application_for_Testing_of_Measuring,_Recording_and_Sampling_Devices_or_Sensor_Systems Procedure 1 of Section 11 - Guidelines for Testing, Approval and Checking of Milk Recording Devices]). The list of approved milk meters, jars and AMS and automatic milk sampler/tray combinations sampling devices can be found on the [https://www.icar.org/index.php/certifications/icar-certifications-for-milk-meters-for-cow-sheep-goats/ ICAR web page].
#Milk weights are recorded for each milking of the recording period. The measurement may be done using any of the ICAR approved recording devices, or by weighing. The minimum accuracy of the measurement is 0.2 kg.
#Where milk constituents are analysed, the equipment used must meet ICAR standards for accuracy. Please consult [[Section 12 – Milk Analysis|Sections 12]] and [[Section 13 – On-farm Milk Analysis|Section 13]] of the Guidelines for details.
#The accuracy of the equipment used for milk recording and sampling must be checked by an agency approved by the member organisations, on a regular and systematic basis using methods approved by ICAR. The list of methods is given in [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices#Procedure 6: Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices|Procedure 6 of Section 11]] - Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices.
#All analyses of the constituents of a milk sample must be carried out on the same milk sample.
#These samples should ideally represent the 24-hour milking period.
#If milk samples do not represent a 24-hour period, the results of milk analyses must be corrected to a 24-hour period by a method approved by ICAR (see [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]).
#In cases where the duration of recording deviates from 24 hours, the results must be converted into 24-hour yields. Only approved 24-hour yield calculation methods can be used. The appropriate methodology is described in [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]
#As date of recording, we recommend to use the date on which the last sample was taken. As alternative, the date of the first sample can be used.
#Calculation methods
##The quantities of milk and milk constituents shall be calculated according to one of the methods outlined in this section of the ICAR Guidelines (see [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Standard methods for calculating 24 hour yields]).
##Member organisations should keep the ICAR Secretariat informed about the calculation methods being used by the records processing operations in their organisation or country and shall be responsible for ensuring that the records are corrected and calculated as specified in this section of the ICAR Guidelines.
====Standards and Guidelines for milk recording using AMS====
This subsection covers systems where milk weights, milk quality or other traits of the cows are monitored constantly and automatically. This can be done in both automatic and manually operated milking systems.

Requirements:
*Animal identification is automatic and reliable. Farm transponders can also be used for automatic identification if they are linked to the cow’s official identification in farm software.
*All individual milkings must be recorded from all AMSs in the farm and transmitted to the recording database for calculation, interrupted milkings included.
*For official milk recording purposes, the data file obtained from electronic milk meters must contain the following: 1) Cow ID, 2) Milking time stamp, 3) Milk weight and 4) Sampling stamp to mark the milking where the sample comes from.
*All milkings within the recording period may be sampled, and in this case the samples should be analysed separately. Alternatively, a one-milking sample can be taken for each cow, followed by fat correction calculation.
*All cows in milk on the recording day have to be sampled. The sampling device must remain in operation until all cows are sampled. When the number of available sampling devices is smaller than the number of AMS units, sampling may need to be prolonged beyond one day to allow complete sampling of all cows. In that case, the sampling device has to be moved between AMS units.
*During sampling, the automatic sampler must be monitored to make sure there are vials left for the next cows.
*24-hour yield calculations must be carried out by a MRO, independently of the AMS manufacturer. This is done in order to guarantee harmonisation of calculation methods between the different brands of equipment and software.
*Data of all milkings over a given time period must be collected for the 24-hour milk yield calculation. A 96-hour data collection period is recommended.
Recommendations:
#Ideally, data of all milkings should be collected and used to compute lactation yield.
#Description of formats to exchange data recorded by an AMS can be requested from the manufacturer or the ICAR ADE data exchange standard for milking data can be used.
#In the case of milk recording method B (see [[Section 02 – Cattle Milk Recording#Recording|chapter 1.4 "Recording]]") with AMS, the milk recording organization should make sure that the farmer knows how to load or transfer data.
#Data can be extracted by: 1) manual operation by MRO Technician’s or Farmer (file extraction), 2) automated system and data transfer through an Application Programming Interface (API), 3) another data transfer and exchange system.
#Raw milk recording data from the AMS must be easily accessible for MRO data processing.
#For official milk recording purposes, the data file obtained from electronic milk meters may also contain the following: 1) Vial ID (this is obligatory with M sampling scheme), 2) Milking duration, 3) Milking speed, 4) Incomplete milking in automatic milking systems and 5) Other relevant data measured or reported by the equipment.
#Individual milkings should be tested for milk secretion rate in order to detect interrupted and unrecorded milkings, which in turn have an effect on the calculated 24-hour yields. If there is an interrupted milking or a milking that follows an interrupted milking at the beginning of the recording period, these two milkings must be excluded from the calculations. During the recording period they can be excluded but do not need to be.
#It is recommended to individually sample all milkings within the 24-hour recording period for 24-hour fat content calculation due to the high variability of milking frequency and milk fat content. In cases where sampling all milkings is not possible, please consult Chapter 2 of [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 - Computing 24-hour Yields] (for approved correction calculation methods).
#It is recommended to sample only milkings with a preceding interval longer than 4 hours.
====Authorisation to record====
It is recommended that professional milk recording technicians are trained and certified before they carry out recordings on their own. Ideally, such training includes a period of supervised work with a certified technician. Where such a certification system is in place, it is not allowed to record without an authorisation.

It is also recommended that frequent training is given to milk recording technicians on new technologies and equipment, safety instructions and data quality issues.

In B and C recording, farmers or their employees doing the practical recording need to be capable of operating the recording equipment correctly (e.g. milk meters, data capture tools) and are familiar with recording techniques.

It is recommended to have a conformation test from a certified recording agency and that frequent training take place.
====Cows to be recorded====
In a recorded herd, all milk-producing cows must be recorded. If a herd is divided into groups, all animals in the group have to be recorded on the same recording scheme. If different recording schemes are practiced on the farm all cows must be recorded according to the standards for recording and sampling intervals in table 3.

Acceptable reasons for missing data are discussed below, in 5.5. Missing results and/or abnormal intervals are reported [[Section 02 – Cattle Milk Recording#Missing results|here]].

===Identification (ID)===
====Herd ID====
Each herd in milk recording must be allocated a unique permanent identification number.
====Animal ID====
An official milk recording system must be based on a clearly identifiable and unique animal ID. It is recommended that one identification scheme for the whole country is used. Animal identification must also be in accordance with national and international regulation (e.g. EU member countries with EU legislation - 1760/2000 for cattle), and with relevant parts of currently valid ICAR Guidelines. The animal must be marked with an ICAR approved identification device or system. If the ID of imported animals is changed, the connection to the original ID must be maintained. Management numbers for cows can be used aside the official ID.
====Identification of the sample vial====
The sample, the milk weight and the cow ID must be linked at the milking.

Vials can be identified according to:
#Vial placement in the sampling unit.
#Cow or sample ID written on the vials.
#Barcoded vial with printed cow ID.
#Barcoded vial with cow ID registered at the milking.
#RFID vial with cow ID registered at the milking.
=====Sample identification without electronic equipment=====
Samples are identified according to their placement in the sampling unit. Additionally, sample or cow numbers can be written on the vials with a waterproof marker. If this marking is not done, there must be a sure and efficient way to identify sample No. 1 (e.g. different colour) and the sequence of other samples.

Each sampling unit must be connected to a list of samples where cow ID is given for each sample. Each transportation box also has to carry the relevant herd ID’s and, preferably, the sampling dates.
=====Barcoded vials=====
Samples are identified according to the barcode on the vial label.

If the label contains cow and/or herd ID, no electronic equipment is needed at the recording. The samples can be sent to the laboratory without accompanying sample lists or herd ID markings on the box.

If the label contains a random sample ID number, the cow ID must be connected with it on the farm. This is done with a barcode reader and computer programmes making the connection possible.
=====Vials with RFID=====
Samples are identified according to the RFID chip in the vial. This system requires the use of RFID readers and specific computer programmes creating a file where the cow and vial ID’s are connected.
=====Automatic sampling systems=====
In automatic milking systems (AMS), ICAR approved automatic samplers have to be used. Sample identification in these systems can be based on vial placement, barcode or RFID. The file with corresponding cow ID is in the management programme of the milking system. Data transfer is carried out with specific software and via a specific interface from the AMS to the MRO.
=====Sample ID in the laboratory=====
For impartiality and better quality, it is recommended that the samples are identified without cow ID and sent to the laboratory anonymously and the analysis results are merged afterwards in the data processing centre.
====Connection of the sample to milking and 24 h yield====
=====Sample and milk weight from the same milking=====
The ideal situation is that the sample and milk weight represent the same milking.
=====Sample from one milking, milk weight from two=====
A corrected analysis is routinely attached to the 24-hour yield.
=====Sample from one milking, milk weight from two or more, corrected by intervals=====
In this case, a 24-hour-yield is also combined with a one-milking sample, but the 24‑hour yield is obtained by correcting the recorded milkings according to the length of the preceding milking intervals. For example, if a cow has produced 20 kg milk in two milkings and the preceding intervals total 20 hours, her 24-hour yield is calculated as 20 kg * (24 h/20 h) = 24 kg. A corrected analysis is attached to this 24‑hour yield.
=====Sample from one milking or day, milk weight from several days=====
With electronic milk meters, it is possible to use the milk production from several days. This gives better accuracy of milk yield estimation; the highest accuracy with uncorrected milk weights is reached using a 4-day average. The problem is that the sample results become disconnected from the milk yield and a loss in fat and protein yield accuracy will occur. Ideally, fat and protein production should be connected to the recording day even in AMS.

In this case, there are three options to connect samples to the 24-hour yield:
#Milk weight is estimated from a longer measurement period but for fat and protein yield estimation only the milk yield on sampling day is used.
#Information only from the recording day for constituents in milk and milk yield estimation.
#Combination of multiple day milk yield with constituents from sampling. See ICAR procedures for using data from more than one day (Lazenby ''et al''., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>, estimation of fat and protein yield (Galesloot and Peeters , 2000)<ref name=":1">Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>.
The analysis data are merged with milk weights in the laboratory or data processing centre and the date of the analysis must be known.

=== Traits to be recorded ===

==== Definition of milking speed and box time ====

===== Introduction =====
Automated Milking Systems (AMS) do measure many traits. The definition of these traits might be different per brand of AMS. Data of these traits is often used by e.g. milk recording organisations, herdbooks or management software providers. When organisations store these data in their databases and use for certain services, it is important to know how these traits are defined.

These definitions could be used by milk recording organisations etc. to take into account differences between traits measured by different brands of AMS. These definitions could also be used by manufacturers of AMS to take into account for product development, to get more alignment in trait definitions between different brands of AMS.

Aim of this document is to propose a harmonized definition of some traits measured by AMS.

At this stage, the traits milking speed and box time are taken into account. Traits related to teat coordinates are described in Section 5 (Conformatoin Recording) of the ICAR guidelines.

==== Average milking speed ====
Definition = AverageMilkingSpeed (gr/min) = {TotalMilkYield / TotalMilkingTime}

* Total milk yield (kg) = Sum of all quarter level milk yields (kg)
* Total milking time = Last Take-off time (of any teat) - Begin of milk flow (of any teat)

Recommendations for manufacturers:

* Exclude any pre-treatment time from milking time.
* Provide take-off settings (threshold in gr/min at take-off, user-defined or default) and settings for the beginning of the measurement period, as milking time will be influenced by take-off settings and by the definition of the beginning of the milk flow.

Recommendations for data users:

* Don't report milking sessions with kick-off´s, interrupted and re-attached milkings because milking time will vary for these milkings.

==== Box time ====
Different types of box time:

* Milking
* Feed-only
* Pass-through
* Selection
* Training

Definition = {End box time - Begin box time} (HH:MM:SS)

* Begin box time = datetime of recognition of animal
* End box time = datetime when cow has exited the box (which might be different from opening of the gate), best to detect when cow has actually left the box

Additional data is needed to understand the status and completeness of the milking visit (Wethal and Heringstad, 2019). Registered issues during the milking are e.g.

* ff: at least 1 teat cup kicked off
* TeatNotFound: unable to find at least 1 of the teats for milking
* IncompleteMilking/FailedMilking: Minimum of 1 teat was registered as incompletely milked.
* The expected milk yield for a milking session depends on previous milkings. Settings like yield less than 80% of expectation for a teat, the milking session would be recorded as having an incompletely milked teat.
* Manual interaction like teat manually attached or milking finished manually.

Recommendations for manufacturers:

* Make the codes available that express if a milking was successful and the cause if the milking was not successful.
* Uniform names and definitions for interrupted, incomplete or failed milkings as well.

Recommendations for data users:

* Check the availability of a code that expresses if a milking was successful and the cause if the milking was not successful. The meaning of the code can be used to consider if the box time record has to be used for the intended purpose or not.
* To check if there is any extra box time due to feeding concentrates, e.g. through user specific settings such as 'PriorityFeeding'.

=== Traits to be recorded ===
In official milk recording, the following data have to be recorded, wherever available:

# Identification of each cow in the herd, even if they remain in the herd for a very short time.
# Birth date, sex, breed and parents of each animal when known.
# All services and embryo flushings and transfers: date, recipient, sire, dam of the embryo.
# All animal deaths and movements between farms and owners.
# Recording dates and locations.
# Milk yields for each cow and recording date.
# Fat content in milk for each cow and sampling date.

It is recommended to record also the following:

# Protein content in milk for each cow and sampling date.
# Milk somatic cell count for each cow and sampling date.
# Other results obtained from milk analysis.
# Milking duration and milking speed where possible.
# Milking times during recording.
# Recording methods and respective symbols used in records.
# Information about cow during the rearing period.

=== Recording method ===
The recording method for the herd consists of using five different symbols for:

# Responsibility for the practical recording.
# Sampling scheme.
# Recording interval.
# Sampling interval (if different from the above).
# Number of milkings per day (especially any deviation from 2x milking).

The symbols in Table 2 should be used:<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Symbols for milk recording schemes.''
|- style="background-color:#efefef; text-align:center;"

|'''Responsibility for recording'''
|'''Sampling scheme'''
|'''Recording interval (weeks)'''
|'''Sampling interval (weeks)'''
|'''Number of milkings per day'''
|-
| style="text-align:center;" | A
| style="text-align:center;" | P
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | B
| style="text-align:center;" | E
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | C
| style="text-align:center;" | Z
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" |
| style="text-align:center;" | T
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" |
| style="text-align:center;" | M
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:center;" | R x
|-
| style="text-align:center;" |
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | S x
|}
</center>

As an example: Recording method is CP36, 2x means that this is a recording where records/ samples are taken partly by the owner (farmer), and partly by a technician from the MRO, where the recording frequency is every 3 weeks, where the sampling frequency is every 6 weeks, and where the number of milkings per day is 2. If a national nomenclature system is used, it should be possible to transfer this system into ICAR nomenclature.

The reference milk recording method is by a representative of the recording organisation, measuring and sampling every four weeks, with proportional sampling and two milkings per day (AP44, 2x).

Recording other than by the reference method must be indicated using the appropriate symbols.

It is recommended that a limit is set for changing the recording method e.g. so that normally it is only possible to change the method twice per year.

It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

In the next sections the symbols are explained:
====Responsibility for the recording====
This symbol indicates who is responsible for measuring the milk yields and taking samples in the herd.
#Representative of the MRO (Method A; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Farmer or his/her representative (Method B; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Mixed responsibility (Method C; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
====ICAR Standards for sampling schemes====
=====Proportional sampling (P)=====
Samples and milk weights are taken at each milking during the recording day. The sampled amount corresponds to the milk yield of each milking. This is achieved by the use of a pipette in equal number of pipetting at each milking or of a specially designed tool which ensures proportional sampling to create one mixed sample. This is the default sampling scheme with no necessary correction to the analysis results, all other schemes must be reported.
=====Equal measure sampling (E)=====
Samples and milk weights are taken at each milking during the recording day. The amount of the sample is measured to be equal at each milking and mixed into one sample. The analysis results for fat should be corrected if one of the milking intervals is shorter than 10 or longer than 14 hours.
=====Multiple sampling (M)=====
Samples are taken at more than one milking during the recording day while milk weights are taken at each milking or over several days. Samples from different milkings are not mixed but they are kept in distinct vials so that each cow has at least two samples. The analysis results must be corrected to correspond to the 24-hour fat and protein yields. For example: a cow is milked 3x during 24 hours and 2 or 3 separate samples are taken, kept and analysed in different vials. This is the gold standard for AMS. It produces the most accurate results but is more expensive.
=====One-milking sampling with milk weights from more than one milking (Z)=====
Samples are taken from one milking during the recording day while milk weights are taken at each milking or over several days. The analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Alternated one-milking recording (T)=====
Samples and milk weights are taken during one milking, alternating between morning and evening milkings. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Constant one-milking recording (C)=====
Samples and milk weights are taken during one milking, constantly during morning or evening milking. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====In-line analysis recording (I)=====
Milk is not sampled but its constituents are continuously analysed by a stationary analyser.
====ICAR Standards for recording and sampling intervals====

<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Standards for recording and sampling intervals.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| rowspan="2" style="text-align:center;" |'''Recording or sampling interval (weeks)'''
| rowspan="2" style="text-align:center;" |'''Minimum number of recordings or samplings per year'''
| colspan="2" style="text-align:center;" |'''Interval between recordings or samplings (days)'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| rowspan="10" style="text-align:center;" |Reference method
| style="text-align:center;" |1
| style="text-align:center;" |44
| style="text-align:center;" |4
| style="text-align:center;" |10
|-
| style="text-align:center;" |2
| style="text-align:center;" |22
| style="text-align:center;" |10
| style="text-align:center;" |18
|-
| style="text-align:center;" |3
| style="text-align:center;" |15
| style="text-align:center;" |16
| style="text-align:center;" |26
|-
| style="text-align:center;" |4
| style="text-align:center;" |11
| style="text-align:center;" |22
| style="text-align:center;" |37
|-
| style="text-align:center;" |5
| style="text-align:center;" |9
| style="text-align:center;" |32
| style="text-align:center;" |46
|-
| style="text-align:center;" |6
| style="text-align:center;" |8
| style="text-align:center;" |38
| style="text-align:center;" |53
|-
| style="text-align:center;" |7
| style="text-align:center;" |7
| style="text-align:center;" |44
| style="text-align:center;" |60
|-
| style="text-align:center;" |8
| style="text-align:center;" |6
| style="text-align:center;" |50
| style="text-align:center;" |70
|-
| style="text-align:center;" |9
| style="text-align:center;" |5
| style="text-align:center;" |55
| style="text-align:center;" |75
|-
| style="text-align:center;" |Daily
| style="text-align:center;" |310
| style="text-align:center;" |1
| style="text-align:center;" |3
|}
</center>

====ICAR standards for number of milkings per day====

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 3. Symbols for number of milkings per day.''
|- style="background-color:#efefef; text-align:center;"
|'''Number of milkings per day'''
|'''Symbol'''
|-
| style="text-align:center;" | Once per day milking
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | Two milkings
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | Three milkings
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" | Four milkings
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" | Continuous milking (e.g. AMS)
| style="text-align:center;" | R x
|-
| style="text-align:center;" | Regular milkings not at the same times on each day (e.g. 10 milkings per week)
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" | Shown as the average number of milkings per day.
| style="text-align:center;" |
|-
| style="text-align:center;" | Animals that are both milked and suckled. (Number of times milked to prefix the S)
| style="text-align:center;" | S x
|}
</center>

Where a herd is dry for a period of the year, the minimum number of recordings should be adjusted proportionately to the production period.

Minimum number of herd recordings should be at least 85% of the normal number of recordings.

=== Missing results and/or abnormal intervals ===
{{anchor|Missing_results}}A recorded 24-hour yield is the best estimate of the yield and the constituents of the milk, weighed, sampled and recorded within 24 hours on the day of recording.
#When herds are normally milked at intervals such that the recording day is other than 24 hours, the yields shall be adjusted to a 24-hour interval using the following procedure (or other procedures approved by the ICAR):
#*Divide 24 by the interval, then multiply by the yield. For example:
#**For a 25 hour interval (24/25) x 35 kg = 33.6 kg
#**For a 20 hour interval (24/20) x 35 kg = 42.0 kg
#A recording is a set of daily test values for a given animal on a given day of recording, one or some or all of them can be missed (missing values)
#Missing values can be due to:
#*Out of range.
#*Sickness.
#*Disaster.
#*No sample analysis results.
#The number of the official and complete (milk, fat and protein) recordings in the lactation or other accumulated yield should be reported.
#Permitted range of the daily recorded values is given in Table 5. Outside of these ranges, the daily recorded<ref>'''Note:''' High fat breeds have breed average higher than 5.0 for fat %.</ref> value will be considered as a missing value.

<center>
{| class="wikitable"
! colspan="7" style="text-align:left;" | ''Table 5. Permitted range of the daily recorded values.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| colspan="2" style="text-align:center;" |'''Milk (kg)'''
| colspan="2" style="text-align:center;" |'''Fat %'''
| colspan="2" style="text-align:center;" |'''Protein %'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| style="text-align:center;" | Main Dairy Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 1.5
| style="text-align:center;" | 9.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 7.0
|-
| style="text-align:center;" | High Fat1 Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 2.0
| style="text-align:center;" | 12.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 9.0
|}
</center>1Note: High fat breeds have breed average higher than 5.0 for fat %The true daily recorded values collected from animals labelled by the farmer as sick, injured or under treatment must be used in the computation of the lactation record unless the milk yield is less than 50% of the previous milk yield or less than 60% of the predicted yield. In such a case, the whole set of daily recorded values may be considered as missing.

Estimates of the missing values of a daily recording can be computed by using interpolation procedures or by more sophisticated procedures approved by ICAR

== Samples ==

=== Representative sample ===
The milk sample has to represent the complete milking linked to it. This is achieved by mixing the milk thoroughly or pouring it into another vessel right before sampling.

Sampling scheme P requires using a pipette for making the sample proportional between different milkings.

With sampling scheme E, it is advisable to use a measuring cup to make sure the sample parts actually are equal.

Immediately after sampling, the vials have to be preserved, capped, shaken and marked. Samples should be stored cool and dark.

=== Transport ===
Samples should be transported for analysis to a laboratory as soon as possible after sampling.

The samples need to be packed for transport and handled during transport in a manner that guarantees that sample IDs are not compromised or mixed. It is also recommended to protect the packages from external interference.

The packing material must be clean and disposable or easy to clean.

During transportation, it is recommended that the temperature of the samples stays below +10°C.

== Database ==
Storing the recorded data in a milk recording database is an indispensable part of the recording. It is recommended to use the quickest possible means to store the data in the database in order to ensure up-to-date breeding values and management applications. Where computerised data capture is possible, it should not take more than five days after the recording to have the complete recording data set in the database.

The application of the Guidelines in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield], together with other parts of the Guidelines, ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

The guidelines on storage of data collected by the milk recording process are:

# For every recording, cow identification (ID), 24-hour milk yield or individual milk yields with a minimum of 0.2 kg (or the equivalent thereof) milk accuracy and recording date have to be stored.
# Where possible, it is advisable to store each milking separately. The data stored can include milk yield, time and date of milking, and milking scheme.
# Analysed results of the milk sample are stored, namely: sample ID, fat content (or percentage), sample status, sample type. Optional data can be stored on protein and/or lactose content, somatic cell count and additional analyses.
# Analysis results can be linked to one or more milkings of the cow.
# In case of storage or performance problems it might be necessary to remove old data of individual cow milkings from the database.
# Recording day information is the yield over 24 hours and should at least be kept in the database for the current lactation and the previous lactation.
# If recording day information is changed after batch processing it should be marked with a user-ID and time stamp.
# Yields are stored in kg or lbs or, in the case of fat and protein contents, in percent units.

The necessary additional information about how the results have been obtained include:

# Who did the recording (certified technician, farmer etc.).
# Herd and/or cow milking frequency.
# How many milkings were measured.
# How many milkings were sampled.
# Sampling scheme when sampling.
# Daily yield calculation method used.
# Recording and sampling intervals.
# It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

Basic checks for recording data:

# Farm (herd) ID: identified by a unique key.
# Animal ID: has to be unique in database.
# Format of animal ID: compliant to international standards of identification and registration.
# Recording date: less than or equal to today, greater than last recording date.
# Milk yield: stored with one decimal.
# 24 hour milk yield within range ( Table 5).
# Fat and protein content: e.g. within a range of +/- 3 standard deviation of population average (Table 5).
# Calving date: greater than birthday of cow (e.g. greater than birthday of cow + 20 months).
# Calving date: less than or equal to today.
# Sample analysis

This section of the ICAR Guidelines examines how observations are performed on farms and how data are collected, analysed and reported back to farmers. It forms an integral part with other sections of the ICAR Guidelines. It ensures that samples are analysed to the relevant degree of accuracy for the purposes of milk recording, breeding value prediction and other areas of usage. ICAR members operate in a range of situations, ranging from places with almost fully automated recording systems to areas with no roads and electricity. Therefore, the guidelines only demand standards that can be followed, irrespective of production situations and recommend more advanced options, where possible or required. Under the guidelines some practices might not be permitted while other practices are tolerated but not recommended.

== Yield calculations ==
This section covers 24-hour yields and accumulated yields for milk, fat, protein and somatic cells. It also describes the procedure for acceptance of new methods not previously mentioned in the guidelines.

The basic requirements for all calculation methods are that rounding shall only take place at the last step of the computation.

=== Lactation period ===

==== Commencement of the lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, is considered to commence is:

# The day that the cow calves (calving date), or
# In the absence of a calving date, the best estimate of the day that the cow commenced milk production.

A (valid) calving is defined as a parturition taking place:

# After the mid-point of the gestation period if a service has been recorded, or,
# After at least 75% of the normal gestation period has elapsed since the previous calving recorded if no service event has been recorded.

Any parturition falling outside the above definition shall be recorded as an abortion and shall not start a new lactation period.

For cows of dairy breeds the normal gestation length shall be deemed to be 280 days unless more specific breed information is available for use.

If the first recording is done on the calving date or within the first 4 days after calving, the milk yield and constituents at the first recording should not form part of the official lactation record, especially for automated milking systems (AMS) with multiple recorded days.

==== Completion of lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, has been completed is or:

# The day that the cow ceases to give milk (goes dry) or
# The day the cow gives less than 3.0 kg/day or 1.0 kg/milking in a recording (unless recorded sick) or
# When it is common practice not to record the dry-off date, the day of the midpoint between the last recording with the cow in milk and the first recording day with the animal dry may be assumed to be the dry-off date.

The lactation period ends on whichever date above occurs first.

Cows may be recorded as absent or sick on the recording day, without the lactation period being defined as terminated.

=== Production period ===
In the case where yield records are calculated on the basis of a period of production, usually a year, the record should be expressed as a ‘production period record‘ (symbol PP).

The production period begins the day after the end of the previous production period and ends as defined by the length (in days) of the production period.

=== Additional notes ===
For any ICAR method the interval between two consecutive recordings must routinely fulfil the value for the acceptable range on the herd level.

If the first recording occurs within 14 days from calving, then no adjustment is required to the first recorded value when computing the accumulated record. If the first recording occurs 15 to 95 days from calving, then an adjustment procedure may be applied.

If the 305th day of a lactation falls before the last recording, the interpolation method should be used also for the last period to compute the yields.

=== Standard methods for calculating 24 hour yields ===
The ICAR approved methods are presented in '''[https://www.icar.org/Guidelines/02-Procedure-1-Computing-24-Hour-Yield.pdf Procedure 1 of Section 2]'''. They include:

1. Methods for calculating daily yields from AM/PM milkings:

# Method of Delorenzo and Wiggans (1986)<ref>Delorenzo, M.A., and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. [https://www.journalofdairyscience.org/article/S0022-0302(86)80678-6/pdf J Dairy Sci 69; 2386]</ref>
# Method of Liu et al. (2019). Please note that in 2022 the method of Liu et al. (2000)<ref name=":0">Liu, Z., R. Reents, F. Reinhardt and K. Kuwan. 2000. Approaches to Estimating Daily Yield from Single Milk Testing Schemes and Use of a.m.-p.m. Records in Test-Day Model Genetic Evaluation in Dairy Cattle. [https://www.journalofdairyscience.org/article/S0022-0302(00)75161-7/pdf J. Dairy Sci. 83:2672-2682].</ref> has been updated to the method of Liu et al. (2019). We recommend to organisations that currently have implemented the method of Liu et al. (2000)<ref name=":0" /> to update to method of Liu et al. (2019).
# Method of Kyntäjä et al. (2021)<ref name=":3">1. Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. [https://www.icar.org/Documents/technical_series/ICAR-Technical-Series-no-25-Virtual-Meeting/Kyntaja.pdf ICAR Technical Series no. 25: 171-175.]</ref>

2. Methods to estimate 24h yield from Automatic Milking Systems:

# Using data on more than one day (Lazenby et al., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Using data on 1 day (Bouloc et al., 2002)<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Estimation of fat and protein yield (Galesloot and Peeters, 2000)<ref>Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>
# Sampling period (Hand et al., 2004<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D.F. 2004. Comparison of Protocols to Estimate 24 Hour Percent Fat and Protein. Presented at 34th ICAR session, Sousse, Tunisia, June, 2004. Proceedings of the 34th ICAR Meeting EAAP Publication No. 113:219-224</ref>; Bouloc et al., 2004)

3. Standard methods to estimate 24h yield from electronic milk meters:

# Estimation of 24-hour milk yield
# Using data on more than one day (Hand et al., 2006)<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. [https://doi.org/10.3168/jds.S0022-0302(06)72240-8 J. Dairy Sci. 89:1723-1726]</ref>
# Estimation of 24-hour fat and protein yield

=== Standard methods for calculating accumulated yields ===
The ICAR approved methods are presented in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_2_%E2%80%93_Computing_of_Accumulated_Lactation_Yield Procedure 2 of Section 2]. They include:

# Test Interval Method (TIM) (Sargent, 1968)<ref>Sargent, F.D., V.H. Lyton, and O.G. Wall, Jr . 1968. Test interval method of calculating Dairy Herd Improvement Association records. [https://doi.org/10.3168/jds.S0022-0302(68)86943-7 J. Dairy Sci. 51:170].</ref>
# Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987)<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. [https://doi.org/10.1016/0301-6226(87)90049-2 Livest. Prod. Sci. 17:l].</ref>
# Best prediction (VanRaden, 1997)<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. [https://doi.org/10.3168/jds.S0022-0302(97)76268-4 J. Dairy Sci. 80:3015-3022].</ref>
# Multiple-Trait Procedure (MTP) (Schaeffer and Jamrozik, 1996)<ref>Schaeffer, L.R. and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. [https://doi.org/10.3168/jds.S0022-0302(96)76578-5 J. Dairy Sci. 79:2044-2055.]</ref>

=== Procedure to approve new methods ===

# All parties interested in seeking approval for any new accumulated yield calculation method will notify the ICAR Secretariat and provide a description of the proposed method.
# These parties will provide a detailed report including statistical details, scientific references and other relevant data to the ICAR Dairy Cattle Milk Recording Working Group.
# The ICAR Dairy Cattle Milk Recording Working Group will then consider the proposal and recommend that it be conditionally approved, approved or rejected.
# The final steps will consist of approval by the General Assembly and publication in the guidelines. .

== Reporting ==
This subsection covers reports, data files, statistics and calculated key figures provided to farmers for breeding and management purposes.

It is recommended that farmers are given reports after each recording and at the end of the recording year or another longer recording period. These reports should contain data on both cow and herd level. In bigger herds, it is also advisable to present results by management groups or otherwise chosen cow groups within the herd. The reporting may be done on paper, through web pages and/or in the form of data files or electronic reports.

Where data files are distributed or direct access given to the results in the database, care must be taken that data ownership is clearly defined. This also includes defining who has access to data and how this access can be authorised.

ICAR members are advised to prepare annual statistics in a reasonable timeframe after closing the recording year. The minimum data requirements are what is needed for the ICAR [https://my.icar.org/stats/list Dairy Cattle Yearly Enquiry on-line database].

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 5. Examples of key figures for herd to be used by farmers and other users.''
|- style="background-color:#efefef; text-align:center;"
|style="text-align:left |'''Key figure'''
|style="text-align:left |'''Explanation'''
|-
| style="text-align:left;" | 12-month rolling average yield
| style="text-align:center;" | Total milk, fat and protein produced during the 365 (366) days preceding the recording divided by the average number of cows for the same period.
|-
| style="text-align:left;" | Average 305-day yield
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations finished during the reporting period divided with the number of finished 305-day lactations.
|-
| style="text-align:left;" | Average 305-day yield within a period
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations during the reporting period divided with the average number of cows on a 305-day lactation within the reporting period.
|-
| style="text-align:left;" | Average annual yield
| style="text-align:center;" | Total milk, fat and protein produced during the recording year divided by the average number of cows for the same recording year.
|-
| style="text-align:left;" | Average calving interval
| style="text-align:center;" | The average preceding intervals of all calvings second and more during the reporting period.
|-
| style="text-align:left;" | Average fat, protein or lactose contents in milk
| style="text-align:center;" | Total fat, protein and lactose yields divided by the total milk yield, usually expressed with two decimals.
|-
| style="text-align:left;" | Average lactation yield
| style="text-align:center;" | Total milk, fat and protein produced within lactations of any length finished during the reporting period divided with the number of finished lactations.
|-
| style="text-align:left;" | Average lactation yield within a period
| style="text-align:center;" | Total milk, fat and protein produced during the reporting period divided with the average number of cows in milk within the reporting period.
|-
| style="text-align:left;" | Average number of cows
| style="text-align:center;" | Average number of cows in the herd (or group) on a given day during the reporting period. Usually expressed with one decimal.
|-
| style="text-align:left;" | Average somatic cell count
| style="text-align:center;" | The average of all individual cow somatic cell counts weighted for individual milk yields.
|-
| style="text-align:left;" | Daily milk, fat and protein yields
| style="text-align:center;" | 1) Total daily milk, fat and protein yields divided by number of cows, or 2) Total daily milk, fat and protein yields divided by number of cows in milk.
|-
| style="text-align:left;" | Energy Corrected Milk (ECM)
| style="text-align:center;" | Calculated according to a national standard.
Example from the Nordic countries:

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + milk yield, kg * 0.7832)/3.14

or, if lactose has been analysed

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + lactose yield * 16.54 + milk yield, kg * 0.0207)/3.14.

From solids expressed as %:

ECM = [(fat content, % * 383 + protein content, % * 242 + 783.2)/3140]* milk yield, kg

or, if lactose has been analysed

ECM = [(fat content, % * 383 + protein content, % * 242 + lactose content, % * 165.4 + 20.7)/3140]* milk yield, kg.
|-
| style="text-align:left;" | Number of lactations
| style="text-align:center;" | Total number of finished lactations in the herd (or group) during the reporting period.
|-
| style="text-align:left;" | Reporting period
| style="text-align:center;" | The period presented in the given report. The most usual options are: one day, one recording interval, lactation, rolling 365 days, recording or calendar year, and the cow’s lifetime.
|}
</center>

== Decisions ==

As a result of the recording process and reports prepared on the basis of its results, decisions can be made on one or more of the following:

=== Short term impact: day-to-day management decisions taken on farms ===

# Decisions about bulk milk quality.
# Feeding decisions - daily diet based on group or individual performance.
# Pasture management decisions.
# Grouping decisions - placing cows in different management or feeding groups.
# Culling decisions - decisions on the sale or slaughter of cattle.
# Mating decisions.
# Decisions regarding programmes of certification for milk and milk products.
# Decisions based on data flow from MRO’s to farms and vice versa.

=== Medium-term impact ===

# Farmers’ decisions based on advisory services, veterinarians, independent experts and other services.
# Decisions about production planning on farms (herd development).

=== Long-term impact ===
# Breeding programme and selection decisions - breeding partners informed by genetic evaluation ([[Section 09 – Dairy Cattle Genetic Evaluation|Section 9)]] based on milk recording results.
# Decisions based on herd book and breeder association activities and deciding on business actions related to breeding animals, i.e. in some countries animal recording data are required for international trade with breeding animals.

=== Strategic decisions ===
# Research programmes concerning management, recording and breeding.
# Political decisions about possible subsidies in dairy cattle breeding at the governmental level and implementing measurements according to agriculture policy.

== Quality control ==
This Section together with other parts of the Guidelines ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

=== Bulk tank data comparison ===
It is a recommended practice to compare milk recording data with dairy deliveries and bulk tank milk contents. This can be done on the recording day or over a longer period of time. The calculation is done as follows:

# Comparison ratio = Total recorded milk yield, kg /Total milk produced, kg. This comparison is used where there is a reliable estimate of the farm use of milk.
# Quick comparison ratio = Total recorded milk yield, kg/ Total milk delivered, kg. This comparison is used where farm use of milk is not estimated.
# Content comparison = Recorded average fat / Bulk tank average fat
# Comparison ratio for fat = Total recorded fat yield, kg/ Total fat produced, kg
# Total recorded milk yield, kg = Ʃ (Individual milk yield, kg)
# Total milk delivered, kg = Total milk delivered, litres * milk density kg/litre
# Total milk produced, kg = (Total milk delivered, litres + Milk used or discarded on the farm, litres) * milk density kg/litre
# Total fat produced, kg = Total milk produced, kg x (Bulk tank fat percent/100)
# Recorded average fat = Ʃ [Individual milk yield kg x (Individual fat percent/100)]/Ʃ (Individual milk yield, kg)

The recommended acceptable range for comparison ratios is 0.95 - 1.05, and for quick comparison ratios 0.90 - 1.00, with due regard to herd size.

=== One day bulk tank data comparison ===
Milk yields and fat yields or contents are compared on the recording day. Comparing the contents is routinely possible where every delivery is sampled or by taking a bulk tank sample (see point [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Bulk_tank_data_comparison 1.10] above for how the comparison is done.)

=== Bulk tank data comparison over a longer period ===
Milk yields and fat yields or contents are compared over a longer period of time, e.g. 4 months or 12 months. This option requires a routine to obtain the applicable data from the dairies or milk buyers. Farm use of milk may be taken into account where applicable.

=== Bulk tank sample ===
Bulk tank samples can be used to verify the milk contents analysis obtained in milk recording. A sample is taken from a well-mixed bulk tank on the recording day. It must represent the milk of the whole 24-hour period. Bulk tank fat and protein contents are then compared to the weighted averages of the fat and protein percent obtained from milk recording. Normally, the difference between the values should not be more than 5%.

=== Supervised or repeated recording ===
Supervised recording is a tool designed to verify that individual cow records are reliable. It is based on repeating the herd recording as soon as possible after the original recording, and the obtained results are compared with the original recording. It is obligatory for ICAR Certificate of Quality (CoQ) holders to practice regular supervision, irrespective of recording methods used.

It is recommended that the supervised recording will follow immediately after the original recording, but for a good reason it can be postponed for up to 7 days.

The farmer and any other staff doing the original recording must not know that a supervised recording will follow. The technician who performs the supervised recording should not be the same person who did the original recording.

Usually supervised recording is done by recording the whole herd again, using the same sampling scheme and recording method (or a reference method) as in the previous recording. When herd size exceeds 200 cows, it is also allowed to do a supervised recording to selected, or randomised groups of animals in the herd.

Choosing the herds for supervised recording may be random or based on preselection. Traits for this preselection may include high yield, great increase in yield, presence of bull dams in the herd, and general suspicions about the correctness of herd results.

The traits compared in supervised recording must include milk and fat. Comparing protein is also recommended.

=== Supervision - example of comparison calculations ===

# Milk, fat and protein yields per cow are calculated for both the original and the supervised milking.
# Individual cow records where results between supervised recording and the original recording differ outside the norms might be excused where a good explanation can be given for exclusion (illness, heat, missed milking)
# Deviations (%) are calculated for each cow and yield constituent according to the formula: deviation = (supervised yield/unsupervised yield)*100-100
# Herd averages of the absolute values for each yield constituent are calculated.
# If the supervised recording occurs within 2 days of the original recording, the acceptable difference in herd averages are 7% for milk and protein and 9% for fat.
# If the supervised recording occurs between 3 and 7 days after the original recording, the acceptable difference of the aforementioned herd averages are 9% for milk and protein and 12% for fat.

The limits mentioned in these examples are typically applied by some of the member organisations, and are not meant to be understood as exact norms. Such norms should be laid down by each member organisation.

=== Evaluation of recording data ===
It is recommended that data quality is evaluated for each herd recording day. When such an evaluation is applied, the following features of the data have to be included:

# Person responsible for the recording.
# ICAR approval and calibration status of the recording equipment if owned by the farmer.
# Number of herd recordings per time period and/or recording interval.
# Number of herd samplings per time period and/or sampling interval.

The following features are also recommended to be included if possible:

# Deviation of milk and fat yields from dairy deliveries.
# Deviation of milk and fat yields from previous or predicted yields.
# Standard deviation of individual cow records.
# Number of recorded and/or sampled milkings within the recording day.
# Number of cows missed or not recorded in the recording.
</div>
</div>
= Procedures =
== Procedure 1: Computing 24-hour Yields ==
<div class="mw-collapsible mw-collapsed">
<div>
=== Methods to calculate 24-hour yield for milk yield and fat percentage from a single milking ===

==== Method of Delorenzo & Wiggans (1986)<ref>Delorenzo, M.A. and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. J. Dairy Sci. 69: 2386-2394.</ref> ====
Daily milk (DMY) and fat yield (DFY) estimates are based on measured yield and milking frequency. An adjustment factor accounts for differences in the average milking interval (expressed in decimal hours) between the preceding milking and the measured milking, and the time of day of the measured milking (started in a.m. or p.m.). For 2X milking, an additional adjustment is applied to milk yield for the interaction between milking interval and stage of lactation, with mid lactation (158 DIM) set to zero. Milking interval does not affect protein and solids non fat (SNF) percentages and so the percentages for the sampled milking are used for test-day estimates. Protein yield is calculated from the measured percentage and the adjusted milk yield.

The prediction of DMY and DFY from single milking on morning or evening in herds milked twice a day requires factors, that are the reciprocal of the proportion of total yield expected from single milkings in relation to the milking interval.

We propose to derive these coefficients (intercept, slope, etc.) for each country separately.

===== Adjustment of milking interval =====
The milking interval is the interval between milking time for the observed milking and the milking time preceding the observed milking. The milking interval is divided into 15-minutes classes. Factors for milk and fat yields may be calculated to each class using Equation 1:

''Equation 1. Factors for milk and fat yields.''
[[File:Equation 1.png|none|thumb|397x397px]]

===== Adjustment of lactation stage =====
Because the lactation stage of the cow has an influence on the effect of different milking intervals on milk production a second adjustment is made for every interval class through a covariate of days in milk as addition:

Covariate x (days in milk - 158)

===== Estimating sample day yields =====
Formulas for prediction sample day yields and percentages in herds with two milkings are:

''Equation 2. Equation for predicting 24-hour milk yield.''
[[File:Equation2.png|none|thumb|428x428px]]

''Equation 3. Equation for predicting 24-hour fat percentage.''
[[File:Equation3.png|none|thumb|431x431px]]

''Equation 4. Equation for predicting 24-hour fat yield.''
[[File:Equation4.png|none|thumb]]

''Equation 5. Equation for predicting 24-hour protein yield.''
[[File:Equation5.png|none|thumb|316x316px]]

===== Calculation examples =====

====== Practical Application ======
Two sets of factors are available for estimating DMY from a single milking, each for morning or evening milking sampling. The factors are calculated from the formula as described above and given in Table 1.
<center>
{| class="wikitable"
| colspan="5" align="left" |'''''Table 1. Factor of milk yield and covariate for herds milked twice a day.'''''
|- style="background-color:#efefef;"
| rowspan="2" align="center" |'''Length of milking interval in hours (minutes in decimal)'''
| colspan="2" align="center" |'''Morning milking'''
| colspan="2" align="center" |'''Evening milking'''
|- style="background-color:#efefef;"
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
|-
| align="center" |< 9.00
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.594
| align="center" |0.00378
|-
| align="center" |9.00-9.24
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.534
| align="center" |0.00485
|-
| align="center" |9.25-9.49
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.477
| align="center" |0.00486
|-
| align="center" |9.50-9.74
| align="center" |2.411
| align="center" |0.00716
| align="center" |2.423
| align="center" |0.00511
|-
| align="center" |9.75-9.99
| align="center" |2.359
| align="center" |0.00726
| align="center" |2.370
| align="center" |0.00473
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |10.00-10.24
| align="center" |2.310
| align="center" |0.00458
| align="center" |2.321
| align="center" |0.00337
|-
| align="center" |10.25-10.49
| align="center" |2.262
| align="center" |0.00399
| align="center" |2.273
| align="center" |0.00214
|-
| align="center" |10.50-10.74
| align="center" |2.217
| align="center" |0.00294
| align="center" |2.227
| align="center" |0.00000
|-
| align="center" |10.75-10.99
| align="center" |2.173
| align="center" |0.00223
| align="center" |2.183
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |11.00-11.24
| align="center" |2.131
| align="center" |0.00000
| align="center" |2.140
| align="center" |0.00000
|-
| align="center" |11.25-11.49
| align="center" |2.091
| align="center" |0.00000
| align="center" |2.099
| align="center" |0.00000
|-
| align="center" |11.50-11.74
| align="center" |2.052
| align="center" |0.00000
| align="center" |2.060
| align="center" |0.00000
|-
| align="center" |11.75-11.99
| align="center" |2.014
| align="center" |0.00000
| align="center" |2.022
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |12.00
| align="center" |2.000
| align="center" |0.00000
| align="center" |2.000
| align="center" |0.00000
|-
| align="center" |12.01-12.24
| align="center" |1.978
| align="center" |0.00000
| align="center" |1.986
| align="center" |0.00000
|-
| align="center" |12.25-12.49
| align="center" |1.943
| align="center" |0.00000
| align="center" |1.951
| align="center" |0.00000
|-
| align="center" |12.50-12.74
| align="center" |1.910
| align="center" |0.00000
| align="center" |1.917
| align="center" |0.00000
|-
| align="center" |12.75-12.99
| align="center" |1.877
| align="center" |0.00000
| align="center" |1.884
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |13.00-13.24
| align="center" |1.846
| align="center" |0.00000
| align="center" |1.852
| align="center" |-0.00190
|-
| align="center" |13.25-13.49
| align="center" |1.815
| align="center" |0.00000
| align="center" |1.822
| align="center" |-0.00231
|-
| align="center" |13.50-13.74
| align="center" |1.786
| align="center" |-0.00167
| align="center" |1.792
| align="center" |-0.00308
|-
| align="center" |13.75-13.99
| align="center" |1.757
| align="center" |-0.00258
| align="center" |1.763
| align="center" |-0.00339
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |14.00-14.24
| align="center" |1.730
| align="center" |-0.00347
| align="center" |1.736
| align="center" |-0.00509
|-
| align="center" |14.25-14.49
| align="center" |1.703
| align="center" |-0.00363
| align="center" |1.709
| align="center" |-0.00471
|-
| align="center" |14.50-14.74
| align="center" |1.677
| align="center" |-0.00332
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |14.75-14.99
| align="center" |1.652
| align="center" |-0.00316
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |≥ 15.00
| align="center" |1.628
| align="center" |-0.00235
| align="center" |1.683
| align="center" |-0.00454
|}
</center>

For estimating daily fat percentage there is only one table independent of morning or evening sampling – refer to Table 2.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" |'''''Table 2. Factor of fat percentage for herds milked twice a day.'''''
|- style="background-color:#efefef;"
|'''Length of milking'''

'''interval in hours'''
|'''Fat (percentage'''

'''factor)'''
|-
|< 9.00
|0.919
|-
|9.00-9.24
|0.927
|-
|9.25-9.49
|0.934
|-
|9.50-9.74
|0.941
|-
|9.75-9.99
|0.948
|-
|
|
|-
|10.00-10.24
|0.955
|-
|10.25-10.49
|0.961
|-
|10.50-10.74
|0.968
|-
|10.75-10.99
|0.974
|-
|
|
|-
|11.00-11.24
|0.980
|-
|11.25-11.49
|0.986
|-
|11.50-11.74
|0.992
|-
|11.75-11.99
|0.997
|-
|
|
|-
|12.00
|1.000
|-
|12.01-12.24
|1.003
|-
|12.25-12.49
|1.008
|-
|12.50-12.74
|1.013
|-
|12.75-12.99
|1.018
|-
|
|
|-
|13.00-13.24
|1.023
|-
|13.25-13.49
|1.028
|-
|13.50-13.74
|1.033
|-
|13.75-13.99
|1.037
|-
|
|
|-
|14.00-14.24
|1.042
|-
|14.25-14.49
|1.046
|-
|14.50-14.74
|1.050
|-
|14.75-14.99
|1.054
|-
|≥ 15.00
|1.058
|}
</center>

Milking-interval factors are calculated using Equation 1, where the intercept and slope are as in Table 3.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 3. Slope and intercept for milk yield and fat yield.'''''
|- style="background-color:#efefef;"
| rowspan="2" |'''Trait'''
| colspan="2" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started in a.m.'''
|'''For measured milking started in p.m.'''
|-
|Milk yield
|0.0654
|0.0634
|0.0363
|-
|Fat yield
|0.1965
|0.1939
|0.0254
|}
</center>
The milking interval has no significant influence on protein percentage. Therefore, the protein percentage of the sampled milking is used as the daily protein percentage.

====== Calculation of daily yields from morning milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Data for a cow from morning milking.'''''
|-
|Begin of recording:
|6:15
|(Morning milking)
|-
|Start of preceding milking:
|17:25
|
|-
|Length of milking interval:
|12 hours 50 minutes
|(Expressed as decimal 12.83)
|-
|Milk results at morning:
|12,0
|Milk-kg
|-
|
|4,12
|Fat-percentage
|-
|
|3,45
|Protein-percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 5. Factors for morning milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.877
|-
|The covariate is
|0
|-
|The factor for fat percentage from Table 2 is
|1.018
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 6. Example calculations for morning milking.'''''
|-
|The sample-day milk yield:
|1.877 x 12,0 kg + 0 x (120 - 158) = 22,5 kg
|-
|The sample-day fat percentage:
|1.018 x 4,12 = 4,19
|-
|The sample-day fat yield:
|22,5 kg x 0,0419 = 0,94 kg
|-
|The sample-day protein yield:
|22,5 kg x 0,0345 = 0,78 kg
|}
</center>

====== Calculation of daily yields from evening milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 7. Data for a cow from evening milking.'''''
|-
|Begin of recording:
|16:48
|Evening milking
|-
|Start of preceding milking:
|6:35
|
|-
|Length of milking interval:
|13 hours 47 minutes
|Expressed as decimal 13.78
|-
|Milk results at evening:
|14,0
|Milk kg
|-
|
|4,00
|Fat percentage
|-
|
|3,40
|Protein percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 8. Factors for evening milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.763
|-
|The covariate is
|<nowiki>-0,00339</nowiki>
|-
|The factor for fat percentage from Table 2 is
|1.037
|}
{| class="wikitable"
| colspan="2" |'''''Table 9. Example calculations for evening milking.'''''
|-
|The sample-day milk yield:
|1.763 x 14,0 kg - 0,00339 x (120 - 158) = 24,8 kg
|-
|The sample-day fat percentage:
|1.037 x 4,00 = 4,15
|-
|The sample-day fat yield:
|24,8 kg x 0,0415 = 1,03 kg
|-
|The sample-day protein yield:
|24,8 kg x 0,0340 = 0,84 kg
|}
</center>

====== Alternate recording of components and milk yield at both milkings ======
For this plan only the sample-day fat yield has to be calculated with regard to milking interval. The milk yield is the sum of evening and morning milk results.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 10. Example data for a cow from both milkings.'''''
|-
|Begin of recording evening:
|17:25
|
|-
|Milk results at evening:
|10:00
|Milk kg (only milking-yield)
|-
|Begin of recording morning:
|6:15
|
|-
|Milk results at morning:
|12:00
|Milk kg
|-
|
|4:20
|Fat percentage
|-
|
|3:50
|Protein percentage
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 11. Factor for fat percentage.'''''
|-
|Length of milking interval:
|12 hours 50 minutes (expressed

as decimal 12.83)
|-
|The factor for fat percentage from Table 2 is
|1.018.
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 12. Example calculation of daily yields.'''''
|-
|The sample-day milk yield:
|10,0 kg + 12,0 kg = 22,0 kg
|-
|The sample-day fat percentage:
|1.018 x 4,20 = 4,28
|-
|The sample-day fat yield:
|22,0 kg x 0,0428 = 0,94 kg
|-
|The sample-day protein yield:
|22,0 kg x 0,0350 = 0,77 kg
|}
</center>

====== Calculation for 3X Milking ======
For 3X herds, a single milking or two consecutive milkings may be weighed. The sample may be collected at one or both of these milkings. Stage of lactation × milking interval adjustments are not used for greater than 2× milking. These AM/PM factors for estimating daily yields in 3X herds should not be confused with factors that adjust 3X records to a 2X basis. Milking-interval factors are calculated using the same formula with the intercept and slope as in Table 13.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" align = "left" |'''''Table 13. Slope and intercept factors for 3X milking.'''''
|- style="background-color:#efefef;"
| rowspan="2" | '''Trait'''
| colspan="3" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started between 2 a.m. and 9:59 a.m.'''
|'''For measured milking started between 10 a.m. and 5:59 p.m.'''
|'''For measured milking started between 6:00 p.m. and 1:59 a.m.'''
|-
|Milk yield
|0.077
|0.068
|0.066
|0.0329
|-
|Fat yield
|0.186
|0.186
|0.182
|0.0186
|}
</center>
When two milkings are included for sampling, the intercepts and intervals for both milkings are included in determining a factor for calculated estimated milk yield that is applied to the total yield from both milkings as in Equation 6.

''Equation 6. Milking interval factor for 3X milking.''
[[File:Equation6.png|none|thumb|536x536px]]
Milk and fat percent factors are calculated separately based on the number of milkings weighed or sampled.

====== Calculation for 4X - 6X Milking ======
The intercept terms for calculating 3X factors (0.077, 0.068, and 0.066) are multiplied by the factor [3 / (milkings per day)] for use in calculating factors for milking frequencies greater than 3X.

==== Method of Liu et al. (2019) ====
A multiple regression method (MRM) is used for estimating 24-hour daily milk yield (DMY), daily fat yield (DFY) and daily protein yield (DPY) based on partial yields from either morning (AM) or evening (PM) milking. Fat percentage (DFP) or protein percentage (DPP) on a 24-hour daily basis are then derived using the estimated 24-hour daily yields. The MRM can be used as a reference method for estimating daily yields and component percentages.

The method of Liu et al. (2019) is an updated version of the method of Liu et al. (2000). The model is only used for farms with 2 time milkings during 24 hours.

The following formula is used to estimate DMY, DFY, DPY based on partial yields (PMY, PFY,PPY) from either morning (AM) or evening (PM) milking:

''Equation 7. Model for predicting 24-hour yield.''

''yijk = a + bijk * xijk''

where:

yijk is the estimated 24-hour daily yield (DMY, DFY or DPY);

xijk is AM or PM partial daily yield on a test day (PMY, PFY, or PPY).

Subscript '''''i''''' represents class of parity effect with 2 levels: first and higher parities.

Subscript '''''j''''' represents class of length of preceding milking interval with 8 levels for AM milking: < 720 minutes, < 740 minutes, < 760 minutes, < 780 minutes, < 800 minutes, < 820 minutes, < 840 minutes, >= 840 minutes and 8 levels for PM milking: < 600 minutes, < 620 minutes, < 640 minutes, < 660 minutes, < 680 minutes, < 700 minutes, < 720 minutes, >= 720 minutes.

Subscript '''''k''''' represents class of lactation stage with 7 classes: < 60 days, < 120 days, < 180 days, < 240 days, < 300 days, < 360 days, >= 360 days.

'''''a''''' is the estimated intercept for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

'''''b'''''ijk is the estimated slope for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

The factors for '''''a''''' and '''''b'''''ijk can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Appendix_1_-_Adjustment_factors_to_calculate_24-hour_yields_using_the_Liu_method Appendix 1].

For a given yield trait a total number of 112 formulae are to be estimated for calculating 24-hour daily yield based on partial yield from either AM or PM milking. Component percentage for fat (DFP) and protein (DPP), on a 24-hour basis is calculated by dividing estimated fat or protein yield by estimated daily milk yield:[[File:Imagefinal.png|center|thumb|339x339px]]

===== Calculation example with method of Liu et al. (2019) =====
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" align = "left" |'''''Table 14. Data from an evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="6" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="6" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="6" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow'''

'''ID'''
|'''Calving date'''
|'''Lactation number'''
| colspan="2" |'''Milk yield (kg)'''
|'''Fat content (%)'''
|'''Protein content (%)'''
|'''Fat yield (kg)'''
|'''Protein yield (kg)'''
|'''Index1'''
|-
|A
|01.01.2020
|1
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1132
|-
|B
|01.01.2020
|2
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1232
|-
|C
|27.03.2020
|1
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1131
|-
|D
|27.03.2020
|2
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1231
|-
|
|
|
|
|
|
|
|
|
|
|}
'''1''' Index is marked in the Appendix table.
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 15. Calculation of 24-hour daily yield and components for evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="3" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="3" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="3" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow ID'''
|'''DMY (kg)'''
|'''DFY (kg)'''
| colspan="2" |'''DPY (kg)'''
|'''DFP (%)'''
|'''DPP (%)'''
|-
|A
|3,47396+25,0

<nowiki>*</nowiki> 1,98268 = 53,0401 ≈ '''53,0'''
|0,2135+0,995

<nowiki>*</nowiki> 1,68050 = 1,8855975
| colspan="2" |0,10471+0,8325* 1,99092 = 1,7621509
|1,8855975 / 53,04096*100

≈ '''3,55'''
|1,7621509 / 53,04096*100

≈ '''3,32'''
|-
|B
|4,15080+25,0* 1,98520 = 53,7808 ≈ '''53,8'''
|0,3635+0,995

<nowiki>*</nowiki> 1,47515 = 1,8312743
| colspan="2" |0,13952+0,8325* 1,97074 = 1,7801611
|1,8312743 / 53,7808*100

≈ '''3,41'''
|1,7801611 / 53,7808*100

≈ '''3,31'''
|-
|C
|2,80244+33,1

<nowiki>*</nowiki> 2,02183 = 69,72501 ≈ '''69,7'''
|0,17663+1,3339 * 1,72438 = 2,4767805
| colspan="2" |0,11078+1,1122 * 1,96422 = 2,2953855
|2,4767805 / 69,725013*100

≈ '''3,55'''
|2,2953855 / 69,725013*100

≈ '''3,29'''
|-
|D
|3,85525+33,1 * 2,00429 = 70,19725 ≈ '''70,2'''
|0,27991+1,3339 * 1,62403 = 2,4462036
| colspan="2" |0,12863+1,1122* 1,98973 = 2,3416077
|2,4462036 / 70,7197249*100 ≈ '''3,48'''
|2,3416077 / 70,7197249*100 ≈ '''''3,34'''''
|-
|
|
|
|
|
|
|
|}
</center>
'''Note''' that intercepts and slopes of the applied regression formulae are underscored.

===== Fat correction for equal measure sampling =====
With Equal measure sampling, it is advisable to use Equation 8 (or the like) to correct fat contents:

Equation 8. Fat correction for equal measure sampling.

Fat, % = Analysed fat, % + 0.69 – 1.3 x (morning milk/ 24-hour milk)

The relation of morning milk to 24-hour milk is to be calculated to at least four decimals.

==== 1.1 Method of Kyntäjä & Nokka (2021)<ref name=":3" />: 24-hour correction factors for fat percentage ====
This method can be applied to calculate 24-hour correction factors for fat percentage, in case the milk recording is based on two milkings, with at least one known milk yield and one sample. A 24-hour recording day is assumed.

The conventional way to calculate correction factors is based on a data set where all milkings have been recorded and analysed separately. This approach requires a lot of effort and extra analysis, and is not cheap to organise. Organisations that have access to a large number of records may be able to use those data to calculate correction factors even if they have no extra analysis.

Requirements for the data set:

# The data set has to be large enough. Every single factor needs to be based on at least 10,000 or, even better, 100,000 observations.
# Each individual data set must contain at least one preceding milking interval, milk weight, and analysed sample. If it contains more milk weights, intervals etc. that is even better. It is also good to include breed, lactation number, days in milk and other data that may have an effect on the factors.

===== Calculation example of the method of Kyntäjä & Nokka (2021)<ref>Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. ICAR Technical Series no. 25: 171-175.</ref> =====

====== The accumulated data set ======
Since 2003, Finland had accumulated a data set of 7.5 million recordings with data on the time of the sampled and preceding milking as reported by the farmer, the lab analysis results, and the 24-hour milk yield. Grouped according to the preceding interval, the analysed fat content gives a nice sigmoid curve with the highest fat content found after a 540 to 630 minutes’ interval (9 to 10.5 hours) and the lowest at 810 to 930 minutes (13.5 to 15.5 hours).
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 16. Average analysed milk fat percentage by preceding interval class, 2003 – 2020.'''''
|- style="background-color:#efefef;"
|'''Interval before'''

'''Sampling (minutes)'''
|'''Number of samples'''
|'''Median interval in the class'''
|'''Average fat content analysed (%)'''
|-
|<510
|93,577
|495
|4.20
|-
|510-539
|19,523
|525
|4.70
|-
|540-569
|111,268
|555
|4.79
|-
|570-599
|253,807
|585
|4.83
|-
|600-629
|1,461,587
|615
|4.75
|-
|630-659
|919,968
|645
|4.66
|-
|660-689
|1,168,683
|675
|4.56
|-
|690-719
|223,877
|705
|4.42
|-
|720-749
|517,447
|735
|4.28
|-
|750-779
|212,428
|765
|4.16
|-
|780-809
|924,014
|795
|4.12
|-
|810-839
|698,463
|825
|4.09
|-
|840-869
|1,104,778
|855
|4.07
|-
|870-899
|154,561
|885
|4.05
|-
|900-929
|77,024
|915
|4.07
|-
|>929
|26,977
|945
|4.13
|}
</center>

The results were also divided into subgroups according to lactation number, phase of lactation, and breed. The effect of the preceding milk interval on milk fat seems to be bigger with older cows and in the beginning of lactation. It was also bigger with Ayrshire cows as compared with Holsteins. At this point, however, the decision was made not to take these factors into account when calculating new correction factors.

====== Calculation of new factors ======
The results above were turned into a simple set of correction factors, dependent solely on the preceding interval. In order to do this, two assumptions were made:

# A 24-hour recording day was assumed. This way, we can deduce the second milking interval from the one we know and mirror the fat percent for that milking.
# Milk secretion rate was assumed to be constant around the 24-hour period. This allows us to deduce the share of the 24-hour yield produced at each milking.

These assumptions allow us to create the new correction factors by mirroring the milk yield and milk fat content in the milking whose actual data we have not got. This way, we get the following formula:

Equation 9. Correction factor.
[[File:Equation9.png|none|thumb|545x545px]]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left" |'''''Table 17. Calculation of the mirrored milking and the correction factors'''''
|- style="background-color:#efefef;"
|'''Interval before sampling (minutes)'''
|'''Average fat in the sampled milking (%)'''
|'''Share of 24-hour milk in the sampled milking'''
|'''Mirrored interval (minutes)'''
|'''Average fat in the mirrored milking (%)'''
|'''Calculated 24-hour average fat(%)'''
|'''Correction factor'''
|-
|<510
|4.21
|0.34
|>929
|4.14
|4.16
|0.989
|-
|510-539
|4.77
|0.36
|900-929
|4.08
|4.33
|0.907
|-
|540-569
|4.82
|0.39
|870-899
|4.05
|4.35
|0.903
|-
|570-599
|4.84
|0.41
|840-869
|4.07
|4.38
|0.906
|-
|600-629
|4.76
|0.43
|810-839
|4.09
|4.37
|0.919
|-
|630-659
|4.66
|0.45
|780-809
|4.12
|4.36
|0.936
|-
|660-689
|4.56
|0.47
|750-779
|4.16
|4.35
|0.953
|-
|690-719
|4.43
|0.49
|720-749
|4.29
|4.36
|0.984
|-
|720-749
|4.29
|0.51
|690-719
|4.43
|4.36
|1.016
|-
|750-779
|4.16
|0.53
|660-689
|4.56
|4.35
|1.046
|-
|780-809
|4.12
|0.55
|630-659
|4.66
|4.36
|1.059
|-
|810-839
|4.09
|0.57
|600-629
|4.76
|4.37
|1.070
|-
|840-869
|4.07
|0.59
|570-599
|4.84
|4.38
|1.076
|-
|870-899
|4.05
|0.61
|540-569
|4.82
|4.35
|1.073
|-
|900-929
|4.08
|0.64
|510-539
|4.77
|4.33
|1.062
|-
|>929
|4.14
|0.66
|<510
|4.21
|4.16
|1.006
|}
</center>

=== Methods to calculate 24-hour yields in Automatic Milking Systems ===

==== General remarks about calculation of 24-hour milk yield ====
It is characteristic for AMS systems that individual cows set their own milking rhythm, thus making it largely irrelevant to use the traditional model of measuring milk yields and sampling at all milkings in the herd during the recording day. In order to determine how much an individual cow’s real 24-hour milk, fat and protein yield is, more complex calculations are required, especially with milk fat that varies considerably from milking to milking. For protein content and cell counts, no correction is needed for a one-milking sample.

The basic idea with calculating a 24-hour milk yield from AMS data is that milk yields per milking are converted into milk yield per time unit (minute or hour) during the preceding interval. This milk yield per time unit is then converted into milk yield in 24 hours. In order to do this, the data set must also contain time stamps for each milking.

How many milkings or how long a measurement period is used for creating 24-hour yields depends on the milk recording organisation. The fewer milkings are used the more random variance there will be in the individual cow milk yields. The absolute minimum is two milkings with preceding intervals, while a measuring period of 96 hours is recommended.

The sampled milking must always be inside the milk yield measurement period. For the calculation of fat and protein yields, it is recommended to use only those milk yields that are from the same period or day. With Z sampling, the 24-hour fat and protein yields may be calculated based on a shorter measurement period than what is used for calculating the 24-hour milk yields.

==== Calculation of milk yield using data of several days (Lazenby ''et al''., 2002<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Automatic Milking Systems (AMS). The average of most recent milk weights can be calculated using a number of preceding milkings or a number of preceding days. If number of milkings is used, the optimal estimate of the milking rate is obtained using an average of current milking together with the 12 most recent milkings back in time. The optimal estimate is the maximum value of the difference curve at which the correlation with the ‘true’ 24-hour milk yield is greatest and the variance across milkings is minimized. If number of days is used, the optimal estimate of the milking rate is obtained using an average of all milkings occurred in the last 96 hours (4 most recent days). In Table 18 the percent of maximum difference for various number of milkings and days is reported. The optimal estimate is independent from stage of lactation and parity.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 18. Percent maximum for different number of days and milkings.'''''
|- style="background-color:#efefef;"
|'''Days'''
|'''Percent Max.'''
|'''Current milking'''

'''+ most recent milkings'''
|'''Percent max.'''
|-
|1
|49.38
|10
|97.85
|-
|2
|77.26
|11
|99.08
|-
|3
|92.34
|12
|99.70
|-
|4
|98.91
|13
|99.81
|-
|5
|98.50
|14
|99.40
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table19.png|center|thumb|911x911px]]
Therefore, 24-hour yield estimation using most recent milkings (1+12) is computed using Equation 10.

''Equation 10. 24-hour yield estimation using 12 previous milkings from AMS.''
[[File:Equation10.png|none|thumb|527x527px]]
and, 24-hour yield estimation using all milkings occurred in the last 96 hours (most recent 4 days), all milking in the last 4 days are included is computed using Equation 11.

''Equation 11. 24 hours yield estimation using milkings from the last 96 hours from AMS''
[[File:Equation11.png|none|thumb|534x534px]]

===== Advantages and disadvantages of this method =====
In terms of Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between milk weights and contents may arise if contents are recorded on one day only. Moreover, some cows may begin or finish their lactation during the period of recording. In this case the computation of milk yield must be adapted. The number of data that need to be validated is higher (for instance, contents have short interval between two milkings).

==== Calculation of milk yield using data on 1 day (Bouloc ''et al''., 2002<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
When the number of milkings is reduced to milkings obtained during one day only, the accuracy of the estimation of the true performance is the same as classical milk recording methods with the same interval between two test days. For instance, Milk Yield estimated from all the milkings recorded during 24 hours, and with an interval between two test days of four weeks has the same accuracy as A4.

==== Calculation of fat and protein yield (Galesloot & Peeters, 2000<ref name=":1" />) ====
Calculation of fat and protein percent must be based on milk weights at time of sampling. The 24-hour protein percentage can be predicted by the protein percentage of the sample without adjustment. However, the 24-hour fat percentage is more difficult to predict, as levels of fat percent are inversely proportional to the amount of milk yield. It is important then to have a close connection between time of samples and actual milk yields.

The Peeters and Galesloot method is a multiple linear regression model for estimating 24-hour fat percent and yields from one-sampled milking during the AMS sampling period. Six different statistical models were tested. This method takes into account fat percent, protein percent, milk weight and milking interval of the sampled milking, milking interval and milk weight of the previous milking (simple model). Another model, based on six different classification of variables (Ca - Cf) such as, time of sampled milking, interval preceding the sampled milking, ratio of fat to protein percent, parity, lactation stage, can be applied (complex model).

===== Simple model =====
24-hour Fat% = b0 + b1* Fat%(n) + b2* Prot%(n) + b3* Int(n) + b4* Int(n-1) + b5* Milk(n) + b6* Milk (n-1) + e

b0= Intercept, b1 to b6 = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, e = Residual effect.

===== Complex model =====
24-hour Fat%i = b0i + b1i* Fat%(n) + b2i* Prot%(n) + b3i* Int(n) + b4i* Int(n-1) + b5i* Milk(n) + b6i* Milk(n-1) + ei

b0i = Intercept, b1i to b6i = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, ei = Residual effect

i = subclass of classification for class variables Cx for x = a, b, c, d, e, f

Ca = Day Time of sampled milking (h) 0-5.59, 6.00-11.59, 12.00-17.59, 18.00-23.59

Cb = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440

Cc = Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

Cd = Parity 1, 2, ≥ 3

Ce = Lactation stage 1-99, 100-199, ≥200

Cf = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440 and Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

The best prediction of 24-hour fat percent and 24-hour fat yields from this method, includes fat percent, protein percent, milk weight and milking interval of the sampled milking, milk weight and milking interval of the preceding milking and the interaction between milking interval, the ratio of fat to protein percent of the sampled milking (complex model corresponding to Cf classification).

The Peeters and Galesloot method has been updated by Roelofs et al. (2006)<ref>Peeters, R. and P. J. B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. J Dairy Sci. 85:682-688.</ref>. The Roelofs method is described in [[Section 02 – Cattle Milk Recording#Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme|Appendix 2]] of this Section.

N.B. This method has been developed by CRV. CRV has available a set of parameters, estimated with this method. For more information about costs and advice on application of this method, please contact CRV. ICAR has no benefit from the application of this method or any other method described in these guidelines.

==== Calculation example of 24-hour fat and protein yields with sampling scheme M ====
With this method, all milkings in a 24-hour recording period must be sampled. The obtained separate analysis results are then used to compute a 24-hour yield of milk solids, and a weighted average of their content.

Individual milkings (last 96 hours) and recording day contents:
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left" |'''''Table 20. Calculation of 24-hour fat and protein contents with sampling scheme M.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY/MM/DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat%'''
|'''Protein%'''
|-
|1
|2021/09/09
|20:45
|525
|13.7
|26.1
|
|
|-
|2
|2021/09/10
|5:30
|617
|16.0
|25.9
|
|
|-
|3
|2021/09/10
|15:47
|720
|18.7
|26.0
|
|
|-
|4
|2021/09/11
|3:25
|645
|16.8
|26.0
|
|
|-
|5
|2021/09/11
|14:10
|899
|18.3
|20.3
|
|
|-
|6
|2021/09/11
|23:27
|557
|14.6
|26.2
|
|
|-
|7
|2021/09/12
|10:51
|684
|17.4
|25.4
|4.53
|3.17
|-
|8
|2021/09/12
|19:44
|533
|14.1
|26.5
|4.92
|3.18
|-
|9
|2021/09/13
|1:35
|351
|9.9
|28.2
|5.92
|3.07
|}
</center>

For example, calculation of fat% on recording day:

24-hour Fat% = (9.9 kg milk x 5.92% fat + 14.1 kg milk x 4.92 % fat + 17.4 kg milk x 4.53 % fat) / (9.9 + 14.1 + 17.4) kg milk = 5.00 %

To calculate the 24-hour fat yield, the calculated 24-hour milk yield is multiplied by the fat content thus obtained (5.00 %).

The same method is used for protein, somatic cell count, urea, lactose and other milk constituents.

Estimation of milk contents: It is recommended to set the robot not to take samples if the preceding milking of the individual cow is not more than 4 hours earlier. If such milkings occur the milk sampled from them is not suitable for 24-hour fat calculation.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left"|'''''Table 21. Calculation of 24-hour fat and protein contents with sampling scheme M where one milking interval was shorter than 4 hours.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY-MM-DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat %'''
|'''Protein%'''
|-
|1
|2021/11/12
|20:05
|590
|15.4
|26.4
|
|
|-
|2
|2021/11/13
|6:31
|626
|16.3
|26.0
|
|
|-
|3
|2021/11/13
|17:12
|641
|17.1
|26.7
|
|
|-
|4
|2021/11/14
|4:40
|688
|17.5
|25.4
|
|
|-
|5
|2021/11/14
|15:11
|631
|16.4
|26.0
|
|
|-
|6
|2021/11/15
|2:25
|674
|16.5
|24.5
|
|
|-
|7
|2021/11/15
|9:47
|452
|10.8
|23.9
|
|
|-
|8
|2021/11/15
|18:30
|523
|13.6
|26.0
|4.71
|3.36
|-
|9
|2021/11/15
|21:15
|165
|3.1
|18.8
|5.161
|3.481
|-
|10
|2021/11/16
|7:49
|634
|16.5
|26.0
|4.47
|3.21
|}
1 Time between two consecutive milkings shorter than 4 hours, data not taken into account for calculation of milk contents.
</center>

Calculation of the fat content of milk during the recording day:

24-hour Fat% = (16.5 kg milk x 4.47 % fat + 13.6 kg milk x 4.71 % fat) / (16.5 kg + 13.6 kg) = 4.57 %

The same method is used for protein, somatic cells, urea, lactose and other milk constituents.

=== Methods to calculate 24-hour yields from electronic milk meters ===

==== Using data on more than one day (Hand ''et al''., 2006<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. J. Dairy Sci. 89:1723–1726.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Electronic Milk Meters. The average of most recent milk weights can be calculated using a number of preceding days. Table 22 reports the concordance correlations for a range of multiple-day averages. As soon as at least the 3 preceding days are used in the calculation, the concordance correlation reaches a high value of at least 0.981. There are no significant differences between 3, 4, 5, 6 and 7-day averages. The correlations are independent from stage of lactation and parity. Thus, 24-hour yields can be the average of from 3 to 7 daily milkings previous to the test day when fat and protein samples were taken.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 22. Concordance correlations for different multiple-day averages.'''''
|- style="background-color:#efefef;"
|'''Multiple-day average'''
|'''Concordance correlation'''
|-
|1
|0.957
|-
|2
|0.975
|-
|3
|0.981
|-
|4
|0.981
|-
|5
|0.982
|-
|6
|0.981
|-
|7
|0.981
|-
|10
|0.979
|-
|14
|0.977
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table20.png|center|thumb|923x923px]]

Therefore, 24-hour yield estimation averaging over 5 days is given by Equation 12.

''Equation 12. 24-hour yield estimation averaging over 5 days.''
[[File:Equation12.png|center|thumb|601x601px]]

===== Advantages and disadvantages of this method =====
Concerning Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between Milk weights and contents have been shown. The estimation bias increases proportionally to the number of days use to compute the 24-hour average. Thus, this method is recommended only if milk weight is the only variable of interest. If milk contents are of interest then the milk weight should be calculated using the milkings from the same day of sampling.

==== Estimation of 24-hour fat and protein yield ====
Fat and protein yields should be determined from the 24-hour yield on the day of sampling, and not the averaged value.

=== Calculation of daily fat percentage from single samples by Gerke et al., 2025 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Gerke.xlsx here]

Constant access to the automatic milking system (AMS) leads to varying milking frequency of cows and subsequently varying milking interval lengths (MI) and milk yield (MY) of single milkings. This influences milk production and can result in variable milk composition in individual milkings during the day. Therefore, the fat percentage from one sampled milking must be adjusted before it can be used as a daily value. The method described specifies the data required and the calculation procedure for deriving a corrected 24 h milk fat percentage from a single sample on test day (TD) in AMS herds.

==== Model specification ====
The multiple linear regression includes transformation, interaction, and polynomial parameters to model non-linearity and thereby improve prediction accuracy. Beside F% of a single milking (''m'') on TD, the model focused on lactation characteristics and milk recording data of up to 4 preceding milkings. With milking intervals ranging between 4 and 20 hours, the method can be applied to milk recording samples from cows with 2 or 3 milkings whose milking intervals lengths (MI) before sampling accumulate to less than 24 h.

The functional form of the model described below specifies the data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample:[[File:Image A.png|center|thumb|636x636px|'''Data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample''']]
</div>where:

DF% = estimated 24 h fat percentage on TD

''m'' = sampled milking on TD

''m-x'' = x milkings before the milking where the sample was taken (x: 1-3)

F% = fat percentage of the sampled milking ''m''

MY(''m'') = milk yield (kg) of ''m''

MI(''m'') = length of time interval (min) preceding the sampled milking ''m''

MY(''m''-x) = milk yields of the 1-3 preceding milkings of ''m''

MI(''m''-x) = milking interval length corresponding to MY(''m''-x)

DIM = days in milk on TD ranging between 5 and 330 d

Parity = parity class (e.g primiparous = 1 and multiparous = 0)

Daytime = time-of-day group of ''m'' (e.g. morning/noon/evening)

e = residual error

The method and its implementation are described in detail by Gerke et al. (2025).

==== Calculation and examples ====
The mathematical notation, with the corresponding regression coefficients in Table 1 for calculating the daily fat percentage (DF%):[[File:Calculating the daily fat percentage (DF%).jpg|center|Calculating the daily fat percentage (DF%)|thumb|511x511px]][[File:Calculating the daily fat percentage (DF%) 2.jpg|center|frame|'''Table 1. Coefficients for regression formula.''']]
</div>
[[File:Example data required for estimating 24 h fat percentage (DF%).jpg|alt=Example data required for estimating 24 h fat percentage (DF%)|center|frame|'''Table 2.''' '''Example data required for estimating 24 h fat percentage (DF%)''']]
Based on the data assembled on TD (Table 2), the corrected 24 h fat percentage (DF%) can be calculated using the mathematical formula und its corresponding coefficients listed in Table 1 as shown in the following examples:
[[File:Corrected 24 h fat percentage.jpg|alt=Corrected 24 h fat percentage|center|thumb|661x661px|'''Corrected 24 h fat percentage''']]

=== Reference ===
Gerke, J. S., Kammer, M., Werner, A., Köstler, R., Piepenburg, J., Mayerhofer, M., … Duda, J. (2025). Estimating daily fat percentage from single samples in herds with automatic milking system using a regression model. ''Livestock Science'', ''293'', 105649. doi: 10.1016/j.livsci.2025.105649

=== Calculation of daily fat percentage from single samples by Jenko et al., 2008, 2010 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Jenko.xlsx here]

This method estimates daily milk yield (DMY), daily fat yield (DFY), and daily protein yield (DPY) in the alternate one-milking recording (T) scheme. Daily fat percentage (DFP) and daily protein percentage (DPP) are then derived from the daily yield (DY) estimates. Utilizing this method allows us to remove the risk of underestimating high and overestimating low DY and contents.

The following formula is used to estimate the DY from the partial yield (PY) and the estimated PY/DY ratio (y):

DY=PYi/yi

where the subscript i is either morning (a.m.) or evening (p.m.).

The value of y is calculated based on the milking interval in minutes (MI), estimated intercept (µ) and regression coefficients (b1 and b2) for yield traits in a.m. or p.m. milking using the following equations for DMY and DPY:

'''Equation 1. Model for milk yield and protein yield.'''

yi = µ + b1 × MI

and for DFY

'''Equation 2. Model for fat yield.'''

yi = µ + b1 × MI + b2 × MI2

The intercept and regression coefficients can be either estimated from the data with records from both a.m. and p.m. milking or the estimates from Table 1 can be applied.

'''Table 1. Intercept and regression coefficients for calculation of daily yield.'''
{| class="wikitable"
|'''Daily yield'''
|'''Milking'''
|'''µ'''
|'''b1'''
|'''b2'''
|-
|DMY
|a.m.
|0,1081000000
|0,0005503000
|
|-
|
|p.m.
|0,0884200000
|0,0005683000
|
|-
|DPY
|a.m.
|0,1124000000
|0,0005419000
|
|-
|
|p.m.
|0,0966400000
|0,0005593000
|
|-
|DFY .
|a.m.
|0,5903000000
|<nowiki>-0,0005093000</nowiki>
|0,0000005377
|-
|
|p.m.
|0,1574000000
|0,0006705000
|<nowiki>-0,0000002744</nowiki>
|}
Finally, daily fat percentage (DFP) and daily protein percentage (DPP) are calculated from the estimated DY:

DFP=DFY/DMY × 100

DPP=DPY/DMY × 100

==== Calulation example with method of Jenko et al. (2008, 2010) ====
Example of the calculations of daily yields from morning milking and evening milking is presented in tables 3 and 4. Data from the Delorenzo and Wiggans method is used in the calculations (Table 2).

'''Table 2. Data for morning and evening milking.'''
{| class="wikitable"
|'''Milking'''
|'''a.m.'''
|'''p.m.'''
|-
|Beginning of recording
|06:15
|20:22
|-
|Start of preceding milking
|17:25
|06:35
|-
|Milking interval (min)
|770
|827
|-
|'''Milking results'''
|
|
|-
|Milk (kg)
|12,00
|14,00
|-
|Protein (%)
|3,45
|3,40
|-
|Fat (%)
|4,12
|4,00
|}

'''Table 3. Calculation of partial yield (PY) and calculation of y value.'''
{| class="wikitable"
|Trait
|Milking
|PY (%)
|PY (kg)
|y
|-
|Milk
|a.m.
|
|12,00
|0,1081000000 + 0,0005503000 x 770 = 0,531831
|-
|
|p.m.
|
|14,00
|0,0884200000 + 0,0005683000 x 827 = 0,558404
|-
|Protein
|a.m.
|3,45
|12,00 / 3,45 = 0,41
|0,1124000000 + 0,0005419000 x 770 = 0,529663
|-
|
|p.m.
|3,40
|14,00 / 3,40 = 0,48
|0,0966400000 + 0,0005593000 x 827 = 0,559181
|-
|Fat
|a.m.
|

4,12
|12,00 / 4,12 = 0,49
|0,5903000000 -0,0005093000 x 770 + 0,0000005377 x 7702 = 0,516941
|-
|
|p.m.
|

4,00
|12,00 / 4,00 = 0,56
|0,1574000000 +0,0006705000 x 827 - 0,0000002744 x 8272 = 0,524233
|}

'''Table 4. Calculation of daily yield (DY, kg) and daily components (DY, %).'''
{| class="wikitable"
|Trait
|DY
|Milking
|DY (kg)
|DY (%)
|-
|Milk
|DMY
|a.m.
|12,00 / 0,531831 = 22,56356
|
|-
|
|
|p.m.
|14,00 / 0,531831 = 25,07145
|
|-
|Protein
|DPY
|a.m.
|0,41 / 0,529663 = 0,781629
|(0,781629 / 22,56356) x 100 = 3,46
|-
|
|
|p.m.
|0,48 / 0,559181 = 0,851245
|(0,851245 / 25,07145) x 100 = 3,40
|-
|Fat
|DFY
|a.m.
|0,49 / 0,516941 = 0,956395
|(0,956395 / 22,56356) x 100 = 4,24
|-
|
|
|p.m.
|0,56 / 0,524233 = 1,068227
|(1,068227 / 25,07145) x 100 = 4,26
|}

==== References ====

* Jenko, J., Perpar, T., Logar, B., Sadar, M., Ivanovič, B., Jeretina, J., Verbič, J., Podgoršek, P. 2008. Comparison of different models for estimating daily yields from a.m./p.m. milkings in Slovenian dairy scheme. Presented at the 36th ICAR Session, Niagara Falls, New York, United States, June 16-20, 2008.
* Jenko, J., Perpar, T., Gorjanc G., Babnik, D. 2010. Evaluation of different approaches for the estimation of daily yield from single milk testing scheme in cattle, J. Dairy Res., 77 (2010), pp. 137-143; DOI: 10.1017/S0022029909990586

</div>
</div>

== Procedure 2 – Computing of Accumulated Lactation Yield ==
<div class="mw-collapsible mw-collapsed">
<div>
=== The Test Interval Method (TIM) (Sargent, 1968<ref>Sargent, F. D., V. H. Lyton, and 0. G. Wall, J r . 1968. Test interval method of calculating Dairy Herd Improvement Association records. J. Dairy Sci. 51:170.</ref>) ===
Test Interval Method is the reference method for calculating accumulated yields. Another adaptation of the method is the Centering Date Method where the yields from the preceding recording are used until the mid point of the recording interval and then substituted by the yields from the following recording.

The following equations are used to compute the lactation record for milk yield (MY), for fat (and protein) yield (FY), and for fat (and protein) percent (FP).
[[File:Equation1111.png|none|thumb|653x653px]]
Where:
M1, M2, Mn are the weights in kilograms, given to one decimal place, of the milk yielded in the 24 hours of the recording day.

F1, F2, Fn are the fat yields estimated by multiplying the milk yield and the fat percent (given to at least two decimal places) collected on the recording day.

I1, I2, In-1 are the intervals, in days, between recording dates.

I0 is the interval, in days, between the lactation period start date and the first recording date.

In is the interval, in days, between the last recording date and the end of the lactation period.

The equation applied for fat yield and percentage must be applied for any other milk components such as protein and lactose.

Details of how to apply the formulae are shown in Table 3 using the example data in Table 1, below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" align = "left" |'''''Table 1. Raw data used in example (TIM).'''''
|- style="background-color:#efefef;"
| colspan="6" align = "left"|'''Data:'''

'''Calving March 25'''
|- style="background-color:#efefef;"
|
|'''Date of'''

'''recording'''
|'''Number'''

'''of days'''
|'''Quantity of milk'''

'''weighed in kg'''
|'''Fat'''

'''percentage'''
|'''Fat'''

'''in grams'''
|-
|April
|8
|14
|28.2
|3.65
|1 029
|-
|May
|6
|28
|24.8
|3.45
|856
|-
|June
|5
|30
|26.6
|3.40
|904
|-
|July
|7
|32
|23.2
|3.55
|824
|-
|August
|2
|26
|20.2
|3.85
|778
|-
|August
|30
|28
|17.8
|4.05
|721
|-
|September
|25
|26
|13.2
|4.45
|587
|-
|October
|27
|32
|9.6
|4.65
|446
|-
|November
|22
|26
|5.8
|4.95
|287
|-
|December
|20
|28
|4.4
|5.25
|231
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left"|'''''Table 2. Lactation period summary (TIM).'''''
|-
|Beginning of lactation:
|March 26
|-
|End of lactation:
|January 3
|-
|Duration of lactation period:
|284 days
|-
|Number of testings (weighings):
|10
|}
</center>
<center>
{| class="wikitable"
| colspan="8" |'''''Table 3. Computations using Test Interval Method.'''''
|- style="background-color:#efefef;"
| colspan="3" rowspan="2" |'''Interval'''

'''both days included'''
|
| colspan="2" |'''Daily production'''
| colspan="2" |'''Sum'''
|- style="background-color:#efefef;"
|'''Days'''
|'''Kg milk'''
|'''Grams of fat'''
|'''Kg milk'''
|'''Kg fat'''
|-
|Mar 26
|<nowiki>-</nowiki>
|Apr 8
|14
|28.2
|1 029
|395
|14.410
|-
|Apr 9
|<nowiki>-</nowiki>
|May 6
|28
|(28.2+24.8)/2
|(1 029+856) /2
|742
|26.389
|-
|May 7
|<nowiki>-</nowiki>
|June 5
|30
|(24.8+26.6) /2
|(856+904) /2
|771
|26.400
|-
|June 6
|<nowiki>-</nowiki>
|July 7
|32
|(26.6+23.2) /2
|(904+824) /2
|797
|27.648
|-
|July 8
|<nowiki>-</nowiki>
|Aug. 2
|26
|(23.2+20.2) /2
|(824+778) /2
|564
|20.817
|-
|Aug. 3
|<nowiki>-</nowiki>
|Aug 30
|28
|(20.2+17.8) /2
|(778+721) /2
|532
|20.980
|-
|Aug 31
|<nowiki>-</nowiki>
|Sept. 25
|26
|(17.8+13.2) /2
|(721+587) /2
|403
|17.008
|-
|Sept. 26
|<nowiki>-</nowiki>
|Oct. 27
|32
|(13.2+9.6) /2
|(587+446) /2
|365
|16.541
|-
|Oct. 28
|<nowiki>-</nowiki>
|Nov. 22
|26
|(9.6+5.8) /2
|(446+287) /2
|200
|9.536
|-
|Nov. 23
|<nowiki>-</nowiki>
|Dec. 20
|28
|(5.8+4.4) /2
|(287+231) /2
|143
|7.253
|-
|Dec. 21
|<nowiki>-</nowiki>
|Jan. 3
|14
|4.4
|231
|62
|3.234
|-
|
|
|
|284
|
|
|4973
|190.216
|-
| colspan="8" |
|-
| colspan="8" |Total quantity of milk: 4 973. kg
|-
| colspan="8" |Total quantity of fat: 190 kg
|-
| colspan="8" |Average fat percentage (190.216 / 4973) x 100 = 3.82%
|}
</center>

=== Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. Livest. Prod. Sci. 17:l.</ref>) ===
With the method 'Interpolation using Standard Lactation Curves' missing test day yields and 305 day projections are predicted. The method makes use of separate standard lactation curves representing the expected course of the lactation, for a certain herd production level, age at calving and season of calving and yield trait. By interpolation using standard lactation curves, the fact that after calving milk yield generally increases and subsequently decreases is taken into account. The daily yields are predicted for fixed days of the lactation: day 0, 10, 30, 50 etc.

The cumulative yield is calculated as follows in :
[[File:Equation2222222.png|none|thumb|474x474px]]
where:

yi = the i-th daily yield;

INTi = the interval in days between the daily yields yi and yi+1;

''n'' = total number of daily yields (measured daily yields and predicted daily yields).

The next example illustrates the calculation of a record in progress. The cow was tested at day 35 and day 65 of the lactation. To determine the lactation yield, daily milk yields are determined for day 0, 10, 30 and 50 of the lactation, by means of the standard lactation curves. The daily yields are in Table 4.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Measured and derived daily yields, used to calculate the record in progress in the example (ISLC).'''''
|- style="background-color:#efefef;"
|'''Day of lactation'''
|'''Milk (kg)'''
|'''Note'''
|-
|0
|25.9
|Predicted
|-
|10
|27.8
|Predicted
|-
|30
|31.7
|Predicted
|-
|35
|31.8
|Measured
|-
|50
|32.9
|Interpolated using standard lactation curve
|-
|65
|33.0
|Measured
|}
</center>

Next, the record in progress can be calculated by means of the formula for a cumulative yield as follows:

[(10 - 1) * 25.9 + (10+1) * 27.8] / 2 +

[(20 - 1) * 27.8 + (20+1) * 31.7] / 2 +

[(5 - 1) * 31.7 + (5+1) * 31.8] / 2 +

[(15 - 1) * 31.8 + (15+1) * 32.9] / 2 +

[(15 - 1) * 32.9 + (15+1) * 33.0] / 2 = 2005.3 kg.

This corresponds to the surface below the line through the predicted and measured daily yields (see Figure 1).
[[File:Figure1.png|center|thumb|621x621px|''Figure 1. Example of calculation of record in progress.'']]

=== Best prediction (BP) (VanRaden, 1997<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. J. Dairy Sci. 80:3015-3022.</ref>) ===
Recorded milk weights are combined into a lactation record using standard selection index methods. Let vector y contain M1, M2, to Mn and let E('''y''') contain corresponding the expected values for each recorded day. The E(y) are obtained from standard lactation curves for the population or for the herd and should account for the cow's age and other environmental factors such as season, milking frequency, etc. The yields in '''y''' covary as a function of the recording interval between them (I). Diagonal elements in Var(y) are the population or herd variance for that recording day and off diagonals are obtained from autoregressive or similar functions such as Corr(M1, M2)=0.995I for first lactations or 0.992I for later lactations. Covariances of one observation with the lactation yield, for example Cov(M1, MY), are the sum of 305 individual covariances. E(MY) is the sum of 305 daily expected values. Lactation milk yield is then predicted as Equation 3:
[[File:Equation333333.png|none|thumb|640x640px]]
With best prediction, predicted milk yields have less variance than true milk yields. With TIM, estimated yields have more variance than true yields. The reason is that predicted yields are regressed toward the mean unless all 305 daily yields are observed. With best prediction, the predicted MY for a lactation without any observed yields is E(MY) which is the population or herd mean for a cow of that age and season. With TIM, the estimated MY is undefined if no daily yields are recorded.

Milk, fat, and protein yields can be processed separately using single-trait best prediction or jointly using multi-trait best prediction. Replacement of M1, M2, to Mn with F1, F2, to Fn or P1, P2, to Pn gives the single-trait predictions for fat or for protein. Multi-trait predictions require larger vectors and matrices but similar algebra. Products of trait correlations and autoregressive correlations, for example, may provide the needed covariances.

=== Multiple-Trait Procedure (MTP) (Schaeffer & Jamrozik, 1996<ref>Schaeffer, L.R., and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. J. Dairy Sci. 79:2044-2055.</ref>) ===
The Multiple-Trait Procedure predicts 305-d lactation yields for milk, fat, protein and SCS, incorporating information about standard lactation curves and covariances between milk, fat, and protein yields and SCS. Test day yields are weighted by their relative variances, and standard lactation curves of cows of similar breed, region, lactation number, age, and season of calving are used in the estimation of lactation curve parameters for each cow. The multiple-trait procedure can handle long intervals between test days, test days with milk only recorded, and can make 305-d predictions on the basis of just one test day record per cow. The procedure also lends itself to the calculation of peak yield, day of peak yield, yield persistency, and expected test-day yields, which could be useful management tools for a producer on a milk recording program.

The MTP method is based upon Wilmink's model in conjunction with an approach incorporating standard curve parameters for cows with the same production characteristics. Wilmink's function for one trait is given by Equation 4.

Equation 4. Wilmink function for one trait (MTP).

y = A + B''t'' ± C''exp'' (-0.05''t'') + ''e''

where y is yield on day t of lactation, A, B, and C are related to the shape of the lactation curve.

The parameters A, B, and C need to be estimated for each yield trait. The yield traits have high phenotypic correlations, and MTP would incorporate these correlations. Use of MTP would allow for the prediction of yields even if data were not available on each test day for a cow.

The vector of parameters to be estimated for one cow are designated:
[[File:Vectro.png|center|thumb]]
where M, F, and P represent milk, fat, and protein, respectively, and S represents somatic cell score. The vector c is to be estimated from the available test-day records. Let c0 represent the corresponding parameters estimated across all cows with the same production characteristics as the cow in question.

Let
[[File:Vector2.png|center|thumb]]

be the vector of yield traits and somatic cell scores on test ''k'' at day ''t'' of the lactation.

The incidence matrix, ''Xk'', is constructed as follows:
[[File:Vector3.png|center|thumb|558x558px]]

The MTP equations are:
[[File:Equation55555.png|none|thumb|560x560px]]
and ''n'' is the number of tests for that cow. ''Rk'' is a matrix of order 4 that contains the variances and covariances among the yields on ''kth'' test at day ''t'' of lactation. The elements of this matrix were derived from regression formulas based on fitting phenotypic variances and covariances of yields to models with ''t'' and ''t2'' as covariables. Thus, element ''ij'' of ''Rk'' would be determined by

rij(t) = ß0ij + ß1ij (t) + ß2ij (t2)

G is a 12 x 12 matrix containing variances and covariances among the parameters in '''ĉ''' and represents the cow to cow variation in these parameters, which includes genetic and permanent environmental effects, but ignores genetic covariances between cows. The parameters for '''''G''''' and '''''Rk''''' vary depending on the breed, but must be known. Initially, these matrices were allowed to vary by region of Canada in addition to breed, but this meant that there could exist two cows with identical production records on the same days in milk, but because one cow was in one region and the other cow was in another region, then the accuracy of their predictions would be different. This was considered to be too confusing for dairy producers, so that regional differences in variance-covariance matrices were ignored and one set of parameters would be used for all regions for a particular breed. Estimation of G is described later.

If a cow has a test, but only milk yield is reported, then

y’k(Mk 0 0 0)

and
[[File:And.png|center|thumb|540x540px]]

The inverse of '''''Rk''''' is the regular inverse of the nonzero submatrix within '''''Rk''''', ignoring the zero rows and columns. Thus, missing yields can be accommodated in MTP.

Accuracy of predicted 305-d lactation totals depends on the number of test-day records during the lactation and DIM associated with each test. Thus, any prediction procedure will require reliability figures to be reported with all predictions, especially if fewer tests at very irregular intervals are going to be frequent in milk recording. At the moment, an approximate procedure is applied that uses the inverse elements of '''(X’R-1X + G-1) -1.'''

==== 1.1 Example calculations ====
Four test day records on a 25 month old, Holstein cow calving in June from Ontario are given in the Table 5 below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 5. Example test day data for a cow (MTP).'''''
|- style="background-color:#efefef;"
|'''Test no.'''
|'''DIM=''t'''''
|'''Exp(-0.05''t'')'''
|'''Milk (kg)'''
|'''Fat (kg)'''
|'''Protein (kg)'''
|'''SCS'''
|-
|1
|15
|0.47237
|28.8
|
|
|3.130
|-
|2
|54
|0.06721
|29.2
|1.12
|0.87
|2.463
|-
|3
|188
|0.000083
|23.7
|0.97
|0.78
|2.157
|-
|4
|250
|0.0000037
|20.8
|
|
|2.619
|}
</center>

Notice that two tests do not have fat and protein yields, and that intervals between tests are irregular and large. The vector of standard curve parameters based on all available comparable cow, is
[[File:Vector4.png|center|thumb]]
The R^(-1)_k matrices for each test day need to be constructed. These matrices are derived from regression equations. The equations for Holsteins were:
<center>
{| class="wikitable" style="text-align: center;"
|''rMM(t) =''
|71.0752 - 0.281201''t'' + 0.0004977''t2''
|-
|''rMF(t) =''
|2.4365 - 0.013274''t'' + 0.0000302''t2''
|-
|''rMP(t) =''
|2.0504 - 0.008286''t'' + 0.0000163''t2''
|-
|''rMS(t) =''
|<nowiki>-1.7993 + 0.013209</nowiki>''t'' - 0.000056''t2''
|-
|''rFF(t) =''
|0.1312 - 0.000725''t'' + 0.000001586''t2''
|-
|''rFP(t) =''
|0.0739 - 0.000386''t'' + 0.000000926''t2''
|-
|''rFS(t) =''
|<nowiki>- 0.0386 + 0.000292</nowiki>''t'' - 0.000001796''t2''
|-
|''rPP(t) =''
|0.066 - 0.000267''t'' + 0.0000005636''t2''
|-
|''rPS(t) =''
|<nowiki>- 0.0404 + 0.000369</nowiki>''t'' - 0.000001743''t2''
|-
|''rSS(t) =''
|3.0404 - 0.000083''t'' - 0.000006105''t2''
|}
</center>

The inverses of the residual variance-covariance matrices for yields for the four test days are as follows:
<center>
{| class="wikitable" style="text-align: center;"
|
|0.0151259
|0
|0
|0.0080354
|-
|'''R^(-1)_1''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0080354
|0
|0
|0.3334553
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.1685584
|0.345947
|<nowiki>-4.851935</nowiki>
|0.0254775
|-
|'''R^(-1)_2''' = =
|<nowiki>-0.345947</nowiki>
|26.830915
|<nowiki>-17.40281</nowiki>
|<nowiki>-0.041445</nowiki>
|-
|
|<nowiki>-4.851935</nowiki>
|<nowiki>-17.40281</nowiki>
|187.18579
|<nowiki>-0.584885</nowiki>
|-
|
|0.0254775
|<nowiki>-0.041445</nowiki>
|<nowiki>-0.584885</nowiki>
|0.3365425
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.2620161
|0.1479068
|<nowiki>-7.943903</nowiki>
|0.0316069
|-
|'''R^(-1)_3''' = =
|0.1479068
|54.446977
|<nowiki>-56.01333</nowiki>
|0.3306741
|-
|
|<nowiki>-7.943903</nowiki>
|<nowiki>-56.01333</nowiki>
|317.9609
|<nowiki>-0.92601</nowiki>
|-
|
|0.0316069
|0.3306741
|<nowiki>-0.92601</nowiki>
|0.3654369
|}
{| class="wikitable" style="text-align: center;"
|

|0.0329465
|0
|0
|0.0251039
|-
|'''R^(-1)_4''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0251039
|0
|0
|0.3981981
|}

Inverse matrix G^(-1) of order 12 is the same for all cows of the same breed:

[[File:Left 6x6.jpg|center|thumb|600x600px|Inverse matrix G^(-1) of order 12]]

</center>
Note that many covariances between different parameters of the lactation curves have been set to zero. When all covariances were included, the prediction errors for individual cows were very large, possibly because the covariances were highly correlated to each other within and between traits. Including only covariances between the same parameter among traits gave much smaller prediction errors.

The elements of the MTP equations of order 12 for this cow are shown in partitioned format also:

'''X’R-1X ='''
<center>[[File:Elements of the MTP equations of order 12.jpg|center|thumb|600x600px|Elements of the MTP equations of order 12]]
</center>
[[File:Equation7.png|center|thumb|632x632px]]

The solution vector for this cow is
[[File:Equation6666.png|center|thumb]]

To predict 305-day yields, Y305
[[File:Equation7777.png|none|thumb|551x551px]]
Equation 6 is used separately for each trait (milk, fat, protein, and SCS). The results for this cow were 7456 kg milk, 301 kg fat, and 239 kg protein. The result for SCS is divided by 305 to give an average daily SCS of 2.477.
</div>
</div>

= Appendices =
== Appendix 1 - Adjustment factors to calculate 24-hour yields using the Liu method ==
<div class="mw-collapsible mw-collapsed">
<div>
In Table 6 the adjustment factors to calculate 24-hour yields, using the Liu method, can be found. The description of the Liu method can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2.]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" |'''''Table 1. Adjustment factors to calculate 24-hour yields using the Liu method. Milking time (MT) is either 1 (PM) or 2 (AM), i = parity class, j= milking interval class and k = stage of lactation class.'''''
|- style="background-color:#efefef;"
|'''MT'''
|'''i'''
|'''j'''
|'''k'''
| colspan="2" |'''Milk yield (DMY)'''
| colspan="2" |'''Fat yield (DFY)'''
| colspan="2" |'''Protein yield (DPY)'''
|-
| colspan="4" |
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|-
|1
|1
|1
|1
|5.29333
|1.83283
|0.30911
|1.43518
|0.18984
|1.77461
|-
|1
|1
|1
|2
|4.17676
|1.97447
|0.2803
|1.56914
|0.12246
|2.00568
|-
|1
|1
|1
|3
|4.26476
|1.95945
|0.18826
|1.82468
|0.12624
|2.0137
|-
|1
|1
|1
|4
|3.41282
|2.01814
|0.25025
|1.64707
|0.12519
|1.99629
|-
|1
|1
|1
|5
|1.79548
|2.22665
|0.06578
|2.09515
|0.05249
|2.24065
|-
|1
|1
|1
|6
|3.7751
|1.95508
|0.12854
|1.93892
|0.11936
|2.00979
|-
|1
|1
|1
|7
|1.544
|2.1478
|0.06425
|2.06779
|0.0569
|2.13851
|-
|1
|1
|2
|1
|5.8584
|1.79409
|0.33193
|1.42953
|0.20756
|1.7288
|-
|1
|1
|2
|2
|5.45524
|1.84258
|0.32877
|1.43235
|0.21332
|1.74001
|-
|1
|1
|2
|3
|4.64052
|1.86706
|0.27155
|1.57017
|0.16439
|1.84539
|-
|1
|1
|2
|4
|2.86835
|2.06209
|0.18647
|1.79403
|0.10803
|2.0193
|-
|1
|1
|2
|5
|2.11336
|2.12055
|0.10435
|1.97206
|0.07193
|2.10651
|-
|1
|1
|2
|6
|2.00673
|2.0636
|0.1386
|1.83336
|0.06892
|2.06532
|-
|1
|1
|2
|7
|1.71752
|2.11269
|0.06501
|2.0379
|0.05569
|2.12881
|-
|1
|1
|3
|1
|2.80244
|2.02183
|0.17663
|1.72438
|0.11078
|1.96422
|-
|1
|1
|3
|2
|3.47396
|1.98268
|0.2135
|1.6805
|0.10471
|1.99092
|-
|1
|1
|3
|3
|2.81702
|2.04348
|0.20754
|1.71868
|0.1127
|1.98403
|-
|1
|1
|3
|4
|3.1989
|1.998
|0.21578
|1.6991
|0.10802
|1.99517
|-
|1
|1
|3
|5
|2.47055
|2.04826
|0.15418
|1.83151
|0.07492
|2.07547
|-
|1
|1
|3
|6
|1.923
|2.07728
|0.11783
|1.89678
|0.06457
|2.08391
|-
|1
|1
|3
|7
|1.85264
|2.0873
|0.13047
|1.86711
|0.071
|2.06917
|-
|1
|1
|4
|1
|2.75042
|1.96631
|0.24794
|1.61741
|0.09248
|1.95376
|-
|1
|1
|4
|2
|2.97505
|1.96711
|0.20029
|1.71842
|0.09381
|1.97081
|-
|1
|1
|4
|3
|2.33365
|2.02986
|0.17021
|1.79996
|0.07631
|2.03167
|-
|1
|1
|4
|4
|3.41505
|1.94107
|0.1845
|1.76799
|0.10989
|1.95456
|-
|1
|1
|4
|5
|2.67488
|1.97797
|0.13433
|1.85893
|0.09432
|1.97755
|-
|1
|1
|4
|6
|1.89907
|2.04841
|0.08715
|1.96251
|0.07132
|2.04225
|-
|1
|1
|4
|7
|1.80326
|2.03554
|0.1251
|1.86477
|0.06072
|2.04747
|-
|1
|1
|5
|1
|2.76763
|1.92863
|0.15754
|1.72474
|0.10187
|1.88749
|-
|1
|1
|5
|2
|3.36896
|1.92048
|0.2236
|1.64149
|0.12369
|1.8823
|-
|1
|1
|5
|3
|2.22763
|2.00452
|0.17614
|1.7474
|0.08019
|1.9782
|-
|1
|1
|5
|4
|2.44625
|1.97049
|0.17217
|1.74753
|0.0889
|1.94647
|-
|1
|1
|5
|5
|2.379
|1.97307
|0.15965
|1.76134
|0.0896
|1.94575
|-
|1
|1
|5
|6
|1.62948
|2.02491
|0.11021
|1.85546
|0.0852
|1.94593
|-
|1
|1
|5
|7
|1.45651
|2.0254
|0.07479
|1.92789
|0.05846
|2.00196
|-
|1
|1
|6
|1
|2.01088
|1.9497
|0.16548
|1.68143
|0.101
|1.85846
|-
|1
|1
|6
|2
|2.96605
|1.93064
|0.25841
|1.52566
|0.12097
|1.86061
|-
|1
|1
|6
|3
|2.2281
|1.96085
|0.19036
|1.69013
|0.08032
|1.9375
|-
|1
|1
|6
|4
|2.39473
|1.952
|0.17854
|1.72423
|0.06863
|1.97582
|-
|1
|1
|6
|5
|2.37955
|1.94127
|0.19579
|1.66419
|0.08447
|1.93156
|-
|1
|1
|6
|6
|0.36203
|2.12393
|0.14291
|1.75822
|0.03845
|2.04562
|-
|1
|1
|6
|7
|1.5702
|1.96794
|0.1336
|1.76796
|0.06449
|1.94829
|-
|1
|1
|7
|1
|3.93654
|1.82772
|0.2359
|1.61894
|0.15032
|1.76054
|-
|1
|1
|7
|2
|4.39662
|1.81581
|0.24969
|1.5881
|0.16909
|1.74794
|-
|1
|1
|7
|3
|3.78325
|1.82778
|0.19228
|1.71802
|0.12368
|1.8268
|-
|1
|1
|7
|4
|3.39116
|1.86302
|0.1969
|1.71838
|0.12282
|1.848
|-
|1
|1
|7
|5
|3.20111
|1.83255
|0.09893
|1.86309
|0.1044
|1.84257
|-
|1
|1
|7
|6
|3.75639
|1.78665
|0.25205
|1.56174
|0.14105
|1.76802
|-
|1
|1
|7
|7
|1.42153
|1.95649
|0.09226
|1.85882
|0.04636
|1.96245
|-
|1
|1
|8
|1
|2.3454
|1.90436
|0.14321
|1.77423
|0.10703
|1.82306
|-
|1
|1
|8
|2
|3.97557
|1.82746
|0.26651
|1.58374
|0.15298
|1.76385
|-
|1
|1
|8
|3
|4.26939
|1.80503
|0.22918
|1.64925
|0.12924
|1.81061
|-
|1
|1
|8
|4
|2.90779
|1.89861
|0.18578
|1.73968
|0.13948
|1.79679
|-
|1
|1
|8
|5
|2.8265
|1.87632
|0.19374
|1.67929
|0.12377
|1.80944
|-
|1
|1
|8
|6
|2.26312
|1.87397
|0.09917
|1.82528
|0.08819
|1.84453
|-
|1
|1
|8
|7
|0.31382
|2.04402
|0.05049
|1.95773
|0.02612
|1.99012
|-
|1
|2
|1
|1
|4.63752
|1.99615
|0.31102
|1.58962
|0.16637
|1.96686
|-
|1
|2
|1
|2
|5.56226
|1.91521
|0.26761
|1.64342
|0.16973
|1.94145
|-
|1
|2
|1
|3
|4.51983
|1.96962
|0.26221
|1.65088
|0.12245
|2.03857
|-
|1
|2
|1
|4
|4.51563
|1.93033
|0.18468
|1.80715
|0.15252
|1.94807
|-
|1
|2
|1
|5
|2.60334
|2.07338
|0.16011
|1.81257
|0.09892
|2.05493
|-
|1
|2
|1
|6
|2.86068
|1.98457
|0.15381
|1.79197
|0.08619
|2.04046
|-
|1
|2
|1
|7
|1.6596
|2.11753
|0.13089
|1.83687
|0.09908
|1.96479
|-
|1
|2
|2
|1
|3.94656
|2.03607
|0.23716
|1.6988
|0.19559
|1.88765
|-
|1
|2
|2
|2
|4.20525
|1.98621
|0.3553
|1.46663
|0.1657
|1.92175
|-
|1
|2
|2
|3
|3.31729
|2.04589
|0.29682
|1.57761
|0.12491
|2.00945
|-
|1
|2
|2
|4
|1.95977
|2.13926
|0.16059
|1.79846
|0.06713
|2.12835
|-
|1
|2
|2
|5
|1.49014
|2.14889
|0.10057
|1.90772
|0.05279
|2.14047
|-
|1
|2
|2
|6
|0.82235
|2.22517
|0.07573
|1.94963
|0.04014
|2.17549
|-
|1
|2
|2
|7
|1.53608
|2.08972
|0.11472
|1.81148
|0.0676
|2.03957
|-
|1
|2
|3
|1
|3.85525
|2.00429
|0.27991
|1.62403
|0.12863
|1.98973
|-
|1
|2
|3
|2
|4.1508
|1.9852
|0.3635
|1.47515
|0.13952
|1.97074
|-
|1
|2
|3
|3
|3.31493
|2.02332
|0.31131
|1.55183
|0.11703
|2.00696
|-
|1
|2
|3
|4
|2.47354
|2.0652
|0.20828
|1.71637
|0.09402
|2.04147
|-
|1
|2
|3
|5
|1.68517
|2.08809
|0.14418
|1.80246
|0.06917
|2.05808
|-
|1
|2
|3
|6
|1.316
|2.12714
|0.11206
|1.87179
|0.04723
|2.12486
|-
|1
|2
|3
|7
|0.4841
|2.20538
|0.04633
|2.02915
|0.02369
|2.18113
|-
|1
|2
|4
|1
|2.82623
|2.01819
|0.25826
|1.69268
|0.11251
|1.97665
|-
|1
|2
|4
|2
|3.24039
|1.9811
|0.36283
|1.50648
|0.11719
|1.96246
|-
|1
|2
|4
|3
|2.4545
|2.03386
|0.19627
|1.75339
|0.09698
|2.00807
|-
|1
|2
|4
|4
|2.46446
|2.01626
|0.17827
|1.76414
|0.08026
|2.02912
|-
|1
|2
|4
|5
|2.11339
|2.00724
|0.14884
|1.77964
|0.07749
|2.00585
|-
|1
|2
|4
|6
|1.51141
|2.04563
|0.11559
|1.82474
|0.06194
|2.02586
|-
|1
|2
|4
|7
|0.95936
|2.09963
|0.07044
|1.95281
|0.03645
|2.0993
|-
|1
|2
|5
|1
|3.36561
|1.97323
|0.2649
|1.65361
|0.13019
|1.92402
|-
|1
|2
|5
|2
|3.66222
|1.95479
|0.35065
|1.51028
|0.14652
|1.89882
|-
|1
|2
|5
|3
|3.20442
|1.96165
|0.28676
|1.58823
|0.12031
|1.93028
|-
|1
|2
|5
|4
|1.78673
|2.0426
|0.17183
|1.75198
|0.0678
|2.02025
|-
|1
|2
|5
|5
|1.61868
|2.01988
|0.11914
|1.80878
|0.06624
|1.99283
|-
|1
|2
|5
|6
|1.30123
|2.02218
|0.10515
|1.80653
|0.05345
|2.00292
|-
|1
|2
|5
|7
|0.65695
|2.08269
|0.06835
|1.89102
|0.0332
|2.0525
|-
|1
|2
|6
|1
|2.3773
|1.9669
|0.24867
|1.6336
|0.08319
|1.94741
|-
|1
|2
|6
|2
|2.82556
|1.95506
|0.31731
|1.51798
|0.12008
|1.89324
|-
|1
|2
|6
|3
|2.7235
|1.94883
|0.30621
|1.5177
|0.09365
|1.93764
|-
|1
|2
|6
|4
|1.77727
|1.98273
|0.17989
|1.69341
|0.07314
|1.95161
|-
|1
|2
|6
|5
|0.81041
|2.05295
|0.13961
|1.74391
|0.04468
|2.01091
|-
|1
|2
|6
|6
|0.72188
|2.0465
|0.09874
|1.79927
|0.03137
|2.03309
|-
|1
|2
|6
|7
|1.21598
|1.97942
|0.07065
|1.87211
|0.04484
|1.98491
|-
|1
|2
|7
|1
|3.55054
|1.89128
|0.27402
|1.61031
|0.10827
|1.89085
|-
|1
|2
|7
|2
|5.0062
|1.81574
|0.3119
|1.54857
|0.18009
|1.76865
|-
|1
|2
|7
|3
|3.95204
|1.84947
|0.30465
|1.53907
|0.16048
|1.789
|-
|1
|2
|7
|4
|2.36233
|1.9168
|0.18751
|1.70412
|0.09531
|1.88355
|-
|1
|2
|7
|5
|1.48851
|1.94443
|0.09973
|1.81041
|0.05904
|1.92497
|-
|1
|2
|7
|6
|1.22525
|1.94454
|0.06617
|1.87082
|0.05516
|1.91259
|-
|1
|2
|7
|7
|1.13847
|1.93756
|0.08109
|1.83388
|0.04706
|1.93165
|-
|1
|2
|8
|1
|4.09874
|1.87708
|0.20312
|1.73434
|0.15506
|1.83083
|-
|1
|2
|8
|2
|4.66403
|1.84302
|0.31808
|1.56093
|0.18049
|1.78288
|-
|1
|2
|8
|3
|3.24375
|1.89351
|0.2827
|1.59546
|0.13583
|1.83427
|-
|1
|2
|8
|4
|2.24175
|1.92084
|0.17795
|1.72611
|0.09636
|1.87438
|-
|1
|2
|8
|5
|1.63783
|1.93625
|0.1225
|1.78642
|0.0659
|1.90934
|-
|1
|2
|8
|6
|2.01753
|1.89095
|0.13742
|1.74752
|0.08289
|1.86553
|-
|1
|2
|8
|7
|0.97568
|1.97215
|0.05926
|1.88807
|0.04057
|1.95672
|-
|2
|1
|1
|1
|3.44076
|1.73133
|0.27759
|1.55037
|0.13323
|1.68913
|-
|2
|1
|1
|2
|4.99596
|1.64527
|0.2322
|1.58033
|0.17533
|1.62422
|-
|2
|1
|1
|3
|3.83372
|1.68144
|0.25087
|1.52033
|0.14525
|1.66706
|-
|2
|1
|1
|4
|3.87034
|1.68102
|0.20979
|1.60153
|0.13627
|1.68885
|-
|2
|1
|1
|5
|1.76134
|1.80424
|0.15241
|1.70485
|0.06231
|1.81524
|-
|2
|1
|1
|6
|0.79304
|1.89072
|0.09906
|1.80312
|0.03277
|1.89435
|-
|2
|1
|1
|7
|1.43535
|1.80614
|0.0593
|1.81589
|0.0407
|1.85002
|-
|2
|1
|2
|1
|3.72284
|1.68499
|0.19226
|1.66567
|0.1237
|1.66453
|-
|2
|1
|2
|2
|4.42667
|1.66508
|0.24314
|1.55652
|0.14361
|1.66251
|-
|2
|1
|2
|3
|2.7019
|1.75871
|0.32717
|1.38452
|0.11056
|1.72312
|-
|2
|1
|2
|4
|2.41538
|1.75937
|0.14575
|1.68355
|0.09038
|1.74138
|-
|2
|1
|2
|5
|1.65412
|1.81649
|0.13926
|1.70623
|0.0597
|1.81378
|-
|2
|1
|2
|6
|2.0843
|1.7735
|0.21052
|1.57508
|0.07244
|1.78566
|-
|2
|1
|2
|7
|1.43238
|1.80651
|0.08031
|1.78712
|0.05269
|1.81727
|-
|2
|1
|3
|1
|2.45314
|1.77068
|0.18152
|1.73443
|0.07657
|1.78025
|-
|2
|1
|3
|2
|3.01217
|1.70966
|0.19388
|1.66175
|0.05624
|1.80606
|-
|2
|1
|3
|3
|2.09997
|1.74945
|0.14493
|1.68277
|0.05446
|1.7922
|-
|2
|1
|3
|4
|2.36683
|1.71741
|0.12244
|1.71407
|0.06775
|1.75721
|-
|2
|1
|3
|5
|1.56776
|1.75755
|0.08776
|1.76946
|0.04244
|1.79675
|-
|2
|1
|3
|6
|1.63824
|1.75452
|0.09422
|1.76794
|0.04181
|1.80604
|-
|2
|1
|3
|7
|0.74114
|1.83421
|0.08039
|1.78306
|0.02347
|1.85596
|-
|2
|1
|4
|1
|1.47047
|1.78588
|0.17271
|1.69379
|0.06511
|1.74985
|-
|2
|1
|4
|2
|2.22168
|1.72985
|0.20701
|1.59429
|0.08178
|1.71455
|-
|2
|1
|4
|3
|2.50108
|1.69618
|0.16828
|1.61962
|0.08598
|1.70516
|-
|2
|1
|4
|4
|1.97141
|1.7202
|0.1446
|1.66357
|0.06856
|1.73201
|-
|2
|1
|4
|5
|1.17054
|1.75879
|0.1172
|1.69234
|0.04624
|1.75806
|-
|2
|1
|4
|6
|1.74755
|1.70968
|0.12562
|1.67603
|0.0629
|1.72333
|-
|2
|1
|4
|7
|0.52482
|1.80155
|0.07345
|1.75615
|0.02671
|1.79288
|-
|2
|1
|5
|1
|1.76464
|1.76219
|0.24301
|1.59094
|0.07156
|1.73136
|-
|2
|1
|5
|2
|1.99594
|1.73438
|0.1984
|1.5954
|0.06489
|1.73449
|-
|2
|1
|5
|3
|1.8804
|1.72362
|0.13019
|1.67977
|0.06783
|1.71916
|-
|2
|1
|5
|4
|1.83337
|1.71477
|0.11197
|1.70244
|0.05764
|1.73194
|-
|2
|1
|5
|5
|1.49752
|1.72615
|0.13128
|1.65461
|0.04656
|1.7433
|-
|2
|1
|5
|6
|1.3042
|1.7305
|0.07173
|1.75315
|0.04482
|1.7399
|-
|2
|1
|5
|7
|2.00868
|1.67669
|0.12298
|1.64761
|0.09175
|1.64669
|-
|2
|1
|6
|1
|0.84993
|1.75972
|0.12918
|1.74026
|0.0328
|1.74802
|-
|2
|1
|6
|2
|1.93666
|1.67406
|0.16606
|1.59943
|0.04535
|1.7106
|-
|2
|1
|6
|3
|2.12115
|1.64964
|0.19988
|1.50821
|0.05229
|1.68986
|-
|2
|1
|6
|4
|0.68831
|1.73901
|0.09674
|1.6838
|0.01696
|1.75787
|-
|2
|1
|6
|5
|1.13081
|1.69479
|0.06413
|1.72559
|0.04936
|1.67757
|-
|2
|1
|6
|6
|0.5893
|1.72537
|0.02598
|1.80138
|0.01591
|1.74082
|-
|2
|1
|6
|7
|0.72519
|1.71955
|0.03157
|1.78405
|0.02889
|1.71972
|-
|2
|1
|7
|1
|1.85937
|1.66064
|0.2416
|1.49676
|0.06807
|1.63599
|-
|2
|1
|7
|2
|1.8527
|1.64892
|0.2374
|1.43845
|0.06336
|1.6431
|-
|2
|1
|7
|3
|1.56905
|1.66084
|0.15434
|1.55598
|0.04336
|1.68109
|-
|2
|1
|7
|4
|0.74968
|1.69857
|0.13496
|1.56636
|0.02871
|1.6933
|-
|2
|1
|7
|5
|1.08222
|1.65925
|0.10847
|1.613
|0.03305
|1.67829
|-
|2
|1
|7
|6
|1.1124
|1.68059
|0.14267
|1.57525
|0.04416
|1.6776
|-
|2
|1
|7
|7
|0.88031
|1.6751
|0.10534
|1.60483
|0.04216
|1.66444
|-
|2
|1
|8
|1
|0.62802
|1.72402
|0.19225
|1.54631
|0.03247
|1.69368
|-
|2
|1
|8
|2
|0.83902
|1.68303
|0.15492
|1.53421
|0.05922
|1.61411
|-
|2
|1
|8
|3
|1.33727
|1.63407
|0.19835
|1.43309
|0.05874
|1.61141
|-
|2
|1
|8
|4
|1.06381
|1.64762
|0.11026
|1.58762
|0.04019
|1.64574
|-
|2
|1
|8
|5
|1.13714
|1.61716
|0.13322
|1.53166
|0.05648
|1.59149
|-
|2
|1
|8
|6
|1.19134
|1.60463
|0.11089
|1.54864
|0.06258
|1.56912
|-
|2
|1
|8
|7
|1.58872
|1.60204
|0.066
|1.64659
|0.04748
|1.63282
|-
|2
|2
|1
|1
|3.46775
|1.78609
|0.28956
|1.68515
|0.15003
|1.72171
|-
|2
|2
|1
|2
|5.69879
|1.67614
|0.3725
|1.5045
|0.19774
|1.64659
|-
|2
|2
|1
|3
|5.18985
|1.66571
|0.40124
|1.40574
|0.17828
|1.65793
|-
|2
|2
|1
|4
|3.43435
|1.74182
|0.20332
|1.66994
|0.11075
|1.76221
|-
|2
|2
|1
|5
|2.48643
|1.76219
|0.13714
|1.7396
|0.09636
|1.75624
|-
|2
|2
|1
|6
|1.41151
|1.82292
|0.15415
|1.6725
|0.06549
|1.80013
|-
|2
|2
|1
|7
|0.9096
|1.8409
|0.08811
|1.7823
|0.03467
|1.85275
|-
|2
|2
|2
|1
|1.85358
|1.83615
|0.28355
|1.64765
|0.06055
|1.83138
|-
|2
|2
|2
|2
|3.81188
|1.74978
|0.25972
|1.62799
|0.11238
|1.7646
|-
|2
|2
|2
|3
|3.16717
|1.76679
|0.29832
|1.53409
|0.09407
|1.78959
|-
|2
|2
|2
|4
|2.33664
|1.78934
|0.22694
|1.60101
|0.07273
|1.80371
|-
|2
|2
|2
|5
|2.01675
|1.79303
|0.10664
|1.79792
|0.06062
|1.8184
|-
|2
|2
|2
|6
|1.80809
|1.80081
|0.13659
|1.70935
|0.07335
|1.79213
|-
|2
|2
|2
|7
|1.01661
|1.8295
|0.0548
|1.84688
|0.03414
|1.84213
|-
|2
|2
|3
|1
|2.01474
|1.8142
|0.21867
|1.74325
|0.05359
|1.83088
|-
|2
|2
|3
|2
|3.53989
|1.71985
|0.28196
|1.60868
|0.10823
|1.73763
|-
|2
|2
|3
|3
|3.38412
|1.69907
|0.27409
|1.56164
|0.11042
|1.71397
|-
|2
|2
|3
|4
|2.2171
|1.74622
|0.16076
|1.70107
|0.07372
|1.75906
|-
|2
|2
|3
|5
|1.11799
|1.80944
|0.11087
|1.75678
|0.03792
|1.81891
|-
|2
|2
|3
|6
|1.40464
|1.76033
|0.10048
|1.72933
|0.05342
|1.75745
|-
|2
|2
|3
|7
|0.11328
|1.8972
|0.04052
|1.87101
|0.00787
|1.88753
|-
|2
|2
|4
|1
|2.59777
|1.74476
|0.28154
|1.66509
|0.10763
|1.71072
|-
|2
|2
|4
|2
|3.53853
|1.69511
|0.38311
|1.46839
|0.13243
|1.66523
|-
|2
|2
|4
|3
|2.80538
|1.70587
|0.26686
|1.55787
|0.1126
|1.68024
|-
|2
|2
|4
|4
|2.18191
|1.72068
|0.18333
|1.65612
|0.085
|1.71029
|-
|2
|2
|4
|5
|1.23383
|1.7716
|0.12824
|1.71179
|0.04845
|1.76628
|-
|2
|2
|4
|6
|0.85652
|1.79279
|0.0763
|1.79314
|0.03563
|1.78528
|-
|2
|2
|4
|7
|0.97995
|1.77178
|0.0797
|1.7577
|0.03846
|1.77043
|-
|2
|2
|5
|1
|2.47016
|1.74985
|0.32061
|1.60073
|0.10455
|1.71058
|-
|2
|2
|5
|2
|3.76194
|1.68979
|0.32787
|1.54675
|0.11781
|1.69109
|-
|2
|2
|5
|3
|2.61421
|1.70766
|0.20307
|1.64866
|0.08315
|1.71378
|-
|2
|2
|5
|4
|1.6809
|1.74028
|0.16795
|1.66491
|0.06202
|1.73305
|-
|2
|2
|5
|5
|1.31241
|1.75722
|0.14383
|1.68302
|0.05338
|1.74562
|-
|2
|2
|5
|6
|1.66563
|1.71781
|0.12721
|1.69231
|0.06147
|1.72101
|-
|2
|2
|5
|7
|0.87471
|1.74991
|0.07882
|1.71706
|0.04173
|1.73246
|-
|2
|2
|6
|1
|1.70055
|1.72832
|0.20839
|1.67759
|0.06001
|1.71779
|-
|2
|2
|6
|2
|3.20558
|1.65143
|0.33676
|1.47797
|0.09642
|1.6546
|-
|2
|2
|6
|3
|1.5827
|1.71538
|0.19719
|1.62038
|0.05324
|1.71254
|-
|2
|2
|6
|4
|1.7692
|1.69473
|0.14854
|1.66225
|0.05758
|1.69946
|-
|2
|2
|6
|5
|1.33003
|1.70542
|0.10726
|1.69398
|0.04565
|1.7096
|-
|2
|2
|6
|6
|1.01266
|1.71155
|0.09376
|1.70285
|0.04005
|1.70822
|-
|2
|2
|6
|7
|0.9856
|1.70091
|0.06454
|1.73063
|0.0394
|1.69796
|-
|2
|2
|7
|1
|2.02441
|1.67788
|0.30435
|1.5407
|0.08673
|1.63673
|-
|2
|2
|7
|2
|1.43949
|1.71143
|0.30098
|1.47963
|0.06527
|1.67295
|-
|2
|2
|7
|3
|1.68946
|1.66442
|0.24777
|1.47116
|0.06594
|1.64834
|-
|2
|2
|7
|4
|1.10967
|1.68591
|0.15663
|1.60109
|0.04949
|1.67069
|-
|2
|2
|7
|5
|0.77866
|1.70882
|0.11248
|1.64389
|0.03402
|1.70215
|-
|2
|2
|7
|6
|0.67502
|1.69719
|0.10289
|1.62419
|0.03507
|1.67744
|-
|2
|2
|7
|7
|0.65216
|1.70336
|0.05545
|1.73388
|0.02233
|1.72102
|-
|2
|2
|8
|1
|1.33877
|1.67358
|0.18369
|1.64385
|0.06055
|1.63818
|-
|2
|2
|8
|2
|0.71697
|1.71038
|0.25461
|1.49037
|0.04798
|1.66397
|-
|2
|2
|8
|3
|2.13197
|1.62429
|0.2393
|1.47673
|0.08136
|1.6065
|-
|2
|2
|8
|4
|1.16932
|1.66188
|0.13759
|1.60108
|0.0463
|1.64856
|-
|2
|2
|8
|5
|1.48369
|1.62387
|0.12547
|1.58988
|0.06919
|1.5925
|-
|2
|2
|8
|6
|1.18879
|1.65442
|0.10031
|1.62813
|0.07392
|1.58846
|-
|2
|2
|8
|7
|0.58052
|1.68546
|0.02696
|1.7382
|0.01982
|1.70519
|}
</center>
</div>
</div>

== Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme ==
<div class="mw-collapsible mw-collapsed">
<div>
=== Abstract ===
Based on comments on imprecision of the estimation method for 24-hour fat % in AM/PM milk recording schemes the regression formula was extended and re-estimated. Non-linearity for the existing effects of protein % of the milk sample, interval before sampling, milk amount of sample, milk amount of previous milking and interval before the previous milking was incorporated by using polynomials. Extensions were made by adding the effects of time of sampling, parity and month of sampling as class variables and lactation stage as polynomial. In total a reduction of the standard deviation of the difference between true and estimated 24-hour fat % of 2.4% was reached (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

'''''Keywords''''': estimation, fat %, AM/PM.

=== Introduction ===
The AM/PM milk recording routine is based on only one morning (a.m.) or evening (p.m.) milk sample which are collected in an alternating way. A condition to take part in this AM/PM milk recording in The Netherlands is that on farm electronic milk measurements (EMM) are available. EMM-data consists of time of milking and milk quantity of every milking. Based on one milk sample and the EMM-data the 24-hour fat % is estimated (Peeters & Galesloot, 2002<ref name=":2">Peeters, R. and P. Galesloot, 2002.Estimating daily fat yield from a single milking on test day for herds with a robotic milking system. J. Dairy Sci. 85, 682-688.</ref>). Also for farms with an automatic milking system (AMS) this estimation is used when only one milk sample is available for analysis on milk composition.

Based on comments from farmers on fluctuations in 24-hour fat % preliminary research was conducted. This showed that the current estimation caused an underestimation of 24-hour fat % based on an a.m.-sample of 0.09% while the estimate based on a p.m.-sample was overestimated by 0.05%. Possible causes for this fluctuation are differences in milk-fat synthesis between day- and night-time as was shown by Gilbert et al. (1972) <ref>Gilbert, G.R., G.L. Hargrove and M. Kroger, 1972. Diurnal variations in milk yield, fat yield, milk fat % and milk protein % by the test interval method. J. Dairy Sci. 56, 409-410.</ref>and Lee & Wardorp (1984)<ref>Lee, A.J. and Wardorp, 1984. Predicting daily milk yield, fat percent, and protein percent from morning or afternoon tests. J. Dairy Sci. 67, 351-360.</ref>. Other factors of imprecision in the current estimation can be caused by lactation stage and parity, two factors that are accounted for in the method of Liu et al. (2000)<ref>Liu, Z., R. Reents, F. Reinhardt and K Kuwan, 2000. Approaches to estimating daily yield from single milk testing schemes and use of a.m.-p.m. records in test-day model genetic evaluation in dairy cattle. J. Dairy Sci. 83, 2672-2682.</ref>.

The objective of this research is to re-estimate the regression formula which is used to estimate the 24-hour fat %s in AM/PM milk recording and AMS recordings with only one sample. By testing for non-linearity of current effects and introducing new explanatory variables the aim is to increase the accuracy of the estimated 24-hour fat %.

=== Material and Methods ===
The data needed for the objective had to meet a number of criteria. The most important criteria were that the data comprised:

* differences in interval between milking times;
* different milking times;
* multiple samples per cow per herd test date;
* milking time and quantity of all milkings;

Only data of farms that use an AMS met all of these criteria. Therefore the research was conducted on data of all farms that used an AMS from January 20th 2001 until July 1st 2004. Records with only one sample per herd test date were excluded from the analysis.

In order to estimate as well as validate the new regression formula the each herd test date was assigned at random into two separate datasets. Dataset 1 was used for estimation and contained 371.528 samplings on 50.591 cows on 537 farms. Dataset 2 was used for validation and contained 371.885 milkings on 50.643 cows on 538 farms. Some characteristics of variables of both datasets are presented in Table 1.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" |'''''Table 1. Characteristics of variables in dataset 1 (estimation) and dataset 2 (validation).'''''
|-
| rowspan="2" |'''Variable'''
| colspan="2" |'''Dataset 1 (estimation)'''
| colspan="2" |'''Dataset 2 (validation)'''
|-
|'''Mean'''
|'''Std'''
|'''Mean'''
|'''Std'''
|-
|Sample milk amount (kg)
|10.1
|3.1
|10.1
|3.1
|-
|Sample fat (%)
|4.40
|0.76
|4.41
|0.76
|-
|Sample protein (%)
|3.49
|0.35
|3.49
|0.35
|-
|Time at sampling
|12.29
|7.24
|12.31
|7.24
|-
|Interval before sample (min)
|520
|154
|521
|155
|-
|Interval before prev. milking (min)
|526
|158
|527
|159
|}
</center>

=== Methods ===
The analysis started with the currently used regression formula which uses the effects: fat %, protein %, milk amount of sampling, interval before sampling, milk amount of the previous milking and interval before the previous milking (Peeters & Galesloot, 2002<ref name=":2" />). All these effects are considered to be linear. As an extra check of the data this regression formula was re-estimated and compared to the currently used regression formula. In order to estimate the regression formula first of all the 24-hour fat % was determined by using a weighted average of all milk samples for that cow on that herd test date.

Subsequently, a number of changes to the regression formula were tested for their effect on the accuracy of the 24-hour fat %. The changes that are tested are:

# non-linearity of the current effects;
# effect of time at sampling;
# effect of lactation stage;
# effect of parity;
# month of milk recording;

The effects were all tested in a similar way by plotting the residuals of the regression formula without the effect that is tested to the tested effect. Based on this plot a possible relation between residual and effect becomes clear and the best way of incorporating the effect is shown. The conclusion if an effect had a positive effect on the accuracy of the regression formula was based on the standard deviation of the difference between estimated and true 24-hour fat %. Also the correlation between the two fat %s and the b-factor (regression coefficient) of the linear regression between the two fat %s were considered.

=== Results ===
The regression coefficients of the re-estimated regression formula differed slightly from the estimates by Peeters & Galesloot (2002)<ref name=":1" />, probably due to the different dataset.

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %.
[[File:Imagefig1.png|center|thumb|''Figure 1a: Average residual per class for the variables sample fat %'']]
[[File:Imagefig1b.png|center|thumb|''Figure 1b: Sample protein %'' ]]
[[File:Imagefig1c.png|center|thumb|''Figure 1c : Interval before sampling'']]
[[File:Imagefig1d.png|center|thumb|''Figure 1d : Interval before previous milking'']]
[[File:Imagefig1e.png|center|thumb|''Figure 1e : Sample milk amount'']]
[[File:Imagefig1f.png|center|thumb|''Figure 1f: Milk amount before sampling'']]

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %. Of all variables, only fat % of the milk sample (Figure 1a) seemed to be linear. A 2nd order polynomial fitted the interval before the previous milking. The other variables, i.e. protein % of the milk sample, interval before sampling, milk amount of sample and milk amount of the previous milking were described by a 3rd order polynomial. For all variables except fat % of the sample higher order polynomials were found significant. This however was caused by the large amount of data and no longer a possible biological effect since it also had no effect on the accuracy of the estimation.

The effect of time of sampling showed a large amount of variability over time. Using a polynomial to fit the data was therefore difficult. Estimation of the effect by hourly intervals was a good alternative as is shown in Figure 2. Lactation stage had mainly an effect in the first 50 days of lactation as is shown by Figure 3. A 3rd order polynomial fitted the data properly.
[[File:Imagefig2.png|center|thumb|''Figure 2. Average residual per class for time of sampling (minutes after midnight).'']]
[[File:Imagefig33.png|center|thumb|''Figure 3. Average residual per class for lactation stage (days).'']]

The effects of parity and month of milk sampling were both considered as class variables. For parity the effects of parity 1 to 6 and 7 or higher were considered. Table 2 shows that mainly for the lower parities the estimated 24-hour fat % was overestimated. Also the months May to October, usually the pasture period, showed an overestimation of 24-hour fat %.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" |'''''Table 2. Effect of parity and month of sampling on estimated 24-hour fat % (*100).'''''
|-
|'''Parity'''
|'''Estimate'''
|'''Month of sampling'''
|'''Estimate'''
|-
|1
|<nowiki>-6.58</nowiki>
|January
|<nowiki>-0.24</nowiki>
|-
|2
|<nowiki>-3.56</nowiki>
|February
|<nowiki>-0.28</nowiki>
|-
|3
|<nowiki>-1.42</nowiki>
|June
|<nowiki>-0.54</nowiki>
|-
|4
|<nowiki>-0.48</nowiki>
|April
|<nowiki>-0.27</nowiki>
|-
|5
|<nowiki>-0.35</nowiki>
|May
|<nowiki>-2.07</nowiki>
|-
|6
|<nowiki>-0.35</nowiki>
|June
|<nowiki>-3.36</nowiki>
|-
|7+
|<nowiki>-0.00</nowiki>
|July
|<nowiki>-4.32</nowiki>
|-
|
|
|August
|<nowiki>-5.52</nowiki>
|-
|
|
|September
|<nowiki>-4.74</nowiki>
|-
|
|
|October
|<nowiki>-2.24</nowiki>
|-
|
|
|November
|<nowiki>-0.97</nowiki>
|-
|
|
|December
|<nowiki>-0.00</nowiki>
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" |'''''Table 3. Statistics of the difference between true and estimated 24-hour fat % for six regression formulas (current, re-estimated + five steps), each also including preceding steps.'''''
|-
|style="text-align: left;"|'''Regression'''
|'''Std.'''
|'''Min'''
|'''Max'''
|'''Cor'''
|'''b-factor'''
|-
|style="text-align: left;"|Current, re-estimated
|0.2856
|<nowiki>-1.840</nowiki>
|2.224
|0.898
|0.807
|-
|style="text-align: left;"|Non-linearity
|0.2820
|<nowiki>-1.890 </nowiki>
|2.198
|0.901
|0.812
|-
|style="text-align: left;"|Time of sampling
|0.2817
|<nowiki>-1.877 </nowiki>
|2.211
|0.901
|0.813
|-
|style="text-align: left;"|Lactation stage
|0.2803
|<nowiki>-1.883 </nowiki>
|2.196
|0.902
|0.814
|-
|style="text-align: left;"|Parity
|0.2794
|<nowiki>-1.887 </nowiki>
|2.179
|0.903
|0.816
|-
|style="text-align: left;"|Month of sampling
|0.2788
|<nowiki>-1.868 </nowiki>
|2.175
|0.903
|0.817
|}
</center>

Table 3 shows some statistics of the difference between the true and estimated 24-hour fat % based on dataset 2 (validation) of the different regression formulas. Each of the five changes to the regression formula had a (minor) positive effect on either the standard deviation of the difference between the true and estimated 24-hour fat % (Std.), the correlation (Cor) between the two fat %s, the b-factor of the linear regression between the two fat %s or a combination of the these. All changes together reduced the standard deviation with 2.4% from 0.2856 to 0.2788, increased the correlation from 0.898 to 0.903 and increased the b-factor from 0.807 to 0.817.

=== Conclusions ===
The regression formula to estimate the 24-hour fat % based on one milk sample was improved. Improvements were first of all considering non-linearity of the variables by using polynomials for protein % of the milk sample (3rd order), interval before sampling (3rd order), milk amount of sample (3rd order), milk amount of previous milking (3rd order) and interval before the previous milking (2nd order). Secondly, adding the effects of time of sampling (class variable), lactation stage (3rd order polynomial), parity (class variable) and month of sampling (class variable) gave a further reduction of the difference between true and estimated 24-hour fat %. The total reduction in standard deviation of the difference between true and estimated 24-hour fat % is 2.4% (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

== Appendix 3 - A unified Python implementation of standardized 305 day yield calculation methods ==
The ICAR guideline is translated into an open-source Python package that can serve as a reference implementation for 305-day yield calculation. In addition to implementing the methods described in the original guideline (with the exception of the multi-trait method, which will be added in future work), the package incorporates 14 lactation-curve models, including traditional parametric models, Bayesian fitting approaches, and an AI-based model. The package also provides tools to derive biologically relevant lactation characteristics such as time to peak, peak yield, cumulative yield, and persistency. The package is publicly available through PyPI and can be installed directly using pip install lactationcurve (van Leerdam et al., 2026). Extensive documentation was developed alongside the package to improve transparency and reproducibility [https://bovi-analytics.github.io/bovi/lactationcurve.html https://bovi-analytics.github.io/bovi/lactationcurve.html.]

Through a companioning website (https://tools.bovi-analytics.org<nowiki/>/), users can upload milk-recording data in CSV format, fit and visualize the implemented lactation-curve models, and compare different cumulative milk-yield methodologies on both test-day and fully daily-recorded lactations using metrics such as RMSE, Pearson correlation, MAPE, and MAE. Reference datasets are provided to allow organizations to benchmark their own calculations against alternative methodologies. In addition, downloadable PDF reports summarize the results through detailed statistics and scatterplots, both overall and stratified by parity.
</div>
</div>

Section 02 – Cattle Milk Recording

2026-07-22T17:24:02Z

Cmosconi: /* Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme */

= Overview =
<div class="mw-collapsible mw-collapsed">
<div>
== Introduction ==
Information about milk production traits is very important for managing and breeding dairy herds. The milk recording process starts with the collection of animal identification, a calving date of milking cows, the amount of milk given and the date with time or time frame of a day. A milk sample may be taken. The obtained milk sample is analysed for milk constituents. The results of the analysis plus the data about milk yield and time of milking are stored in a database. Subsequently a number of parameters, cumulative yields and indices are calculated and stored in the database and, finally, reported to the farmer

This Section 2 of the ICAR Guidelines focuses on the milk recording process for dairy cattle.

== Scope ==
Figure 1 gives a pictorial summary of the main elements of this guideline.

In summary, this section of the ICAR Guidelines covers the milk recording process from the enrolment of a herd for milk recording, through to the delivery of information which a herd owner can use to assist in a range of decisions.
[[File:Scope of Section 2 - Dairy cattle milk recording..png|thumb|Figure 1. Scope of Section 2 -Dairy cattle milk recording.|center|524x524px]]

Not covered in this section are:
# Standards and guidelines for ICAR approval of milk recording devices. Please consult [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices|Section 11]] for this subject.
# Standards and guidelines for ICAR approval of ID devices. Please consult [[Section 10 – Identification Device Certification|Section 10]] for this subject.
# Standards and guidelines for preparation of milk samples and for quality assurance of milk analysis. Please consult [[Section 12 – Milk Analysis|Section 12]] for this subject.
# Standards and guidelines for in-line milk analysis on the farm. Please consult [[Section 13 – On-farm Milk Analysis|Section 13]] for this subject.

== Enrolment ==

Enrolment of new herds in the recording process should involve an agreement between the farmer and the recording organisation regarding technical and financial questions such as:

# General information about the recording programme itself, i.e.
#* Herd and cow identification.
#* Scope of recorded data, including database setup as required by the user.
#* Scheduling recording.
#* Data capture and processing.
#* Recording methods and intervals.
#* Milk measuring and meters.
#* Sampling and sample transport.
#* Reports (outcomes) and supporting decisions.
# Definition of supervision scheme and other quality assurance and plausibility checking steps.
# Fee structure and invoicing.
# Approval of technicians by milk recording organisations (MROs) so as to give them free access to farms for all recording and supervision actions.

In cases where the owner of the recorded cows or his employees carry out the recording itself, it is up to the organisation to decide upon, and provide for, any necessary training.

== Standard and Guidelines for Milk Recording ==
These standards and guidelines for milk recording are valid for all milking systems, including AMS where applicable.
====General Standards and Guidelines for milk recording====
#ICAR-approved (electronic) milk meters and sampling devices must be used on the recording day (see [https://wiki.icar.org/index.php/Section_11_%E2%80%93_Testing,_Approval_and_Checking_of_Measuring,_Recording_and_Sampling_Devices#Procedure_1:_Procedure_for_Application_for_Testing_of_Measuring,_Recording_and_Sampling_Devices_or_Sensor_Systems Procedure 1 of Section 11 - Guidelines for Testing, Approval and Checking of Milk Recording Devices]). The list of approved milk meters, jars and AMS and automatic milk sampler/tray combinations sampling devices can be found on the [https://www.icar.org/index.php/certifications/icar-certifications-for-milk-meters-for-cow-sheep-goats/ ICAR web page].
#Milk weights are recorded for each milking of the recording period. The measurement may be done using any of the ICAR approved recording devices, or by weighing. The minimum accuracy of the measurement is 0.2 kg.
#Where milk constituents are analysed, the equipment used must meet ICAR standards for accuracy. Please consult [[Section 12 – Milk Analysis|Sections 12]] and [[Section 13 – On-farm Milk Analysis|Section 13]] of the Guidelines for details.
#The accuracy of the equipment used for milk recording and sampling must be checked by an agency approved by the member organisations, on a regular and systematic basis using methods approved by ICAR. The list of methods is given in [[Section 11 – Testing, Approval and Checking of Measuring, Recording and Sampling Devices#Procedure 6: Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices|Procedure 6 of Section 11]] - Evaluation of Installation and Routine Calibration Procedures for Recording and Sampling Devices.
#All analyses of the constituents of a milk sample must be carried out on the same milk sample.
#These samples should ideally represent the 24-hour milking period.
#If milk samples do not represent a 24-hour period, the results of milk analyses must be corrected to a 24-hour period by a method approved by ICAR (see [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]).
#In cases where the duration of recording deviates from 24 hours, the results must be converted into 24-hour yields. Only approved 24-hour yield calculation methods can be used. The appropriate methodology is described in [[Section 02 – Cattle Milk Recording#Procedure 1: Computing 24-hour Yields|Standard methods for calculating 24 hour yields]]
#As date of recording, we recommend to use the date on which the last sample was taken. As alternative, the date of the first sample can be used.
#Calculation methods
##The quantities of milk and milk constituents shall be calculated according to one of the methods outlined in this section of the ICAR Guidelines (see [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Standard methods for calculating 24 hour yields]).
##Member organisations should keep the ICAR Secretariat informed about the calculation methods being used by the records processing operations in their organisation or country and shall be responsible for ensuring that the records are corrected and calculated as specified in this section of the ICAR Guidelines.
====Standards and Guidelines for milk recording using AMS====
This subsection covers systems where milk weights, milk quality or other traits of the cows are monitored constantly and automatically. This can be done in both automatic and manually operated milking systems.

Requirements:
*Animal identification is automatic and reliable. Farm transponders can also be used for automatic identification if they are linked to the cow’s official identification in farm software.
*All individual milkings must be recorded from all AMSs in the farm and transmitted to the recording database for calculation, interrupted milkings included.
*For official milk recording purposes, the data file obtained from electronic milk meters must contain the following: 1) Cow ID, 2) Milking time stamp, 3) Milk weight and 4) Sampling stamp to mark the milking where the sample comes from.
*All milkings within the recording period may be sampled, and in this case the samples should be analysed separately. Alternatively, a one-milking sample can be taken for each cow, followed by fat correction calculation.
*All cows in milk on the recording day have to be sampled. The sampling device must remain in operation until all cows are sampled. When the number of available sampling devices is smaller than the number of AMS units, sampling may need to be prolonged beyond one day to allow complete sampling of all cows. In that case, the sampling device has to be moved between AMS units.
*During sampling, the automatic sampler must be monitored to make sure there are vials left for the next cows.
*24-hour yield calculations must be carried out by a MRO, independently of the AMS manufacturer. This is done in order to guarantee harmonisation of calculation methods between the different brands of equipment and software.
*Data of all milkings over a given time period must be collected for the 24-hour milk yield calculation. A 96-hour data collection period is recommended.
Recommendations:
#Ideally, data of all milkings should be collected and used to compute lactation yield.
#Description of formats to exchange data recorded by an AMS can be requested from the manufacturer or the ICAR ADE data exchange standard for milking data can be used.
#In the case of milk recording method B (see [[Section 02 – Cattle Milk Recording#Recording|chapter 1.4 "Recording]]") with AMS, the milk recording organization should make sure that the farmer knows how to load or transfer data.
#Data can be extracted by: 1) manual operation by MRO Technician’s or Farmer (file extraction), 2) automated system and data transfer through an Application Programming Interface (API), 3) another data transfer and exchange system.
#Raw milk recording data from the AMS must be easily accessible for MRO data processing.
#For official milk recording purposes, the data file obtained from electronic milk meters may also contain the following: 1) Vial ID (this is obligatory with M sampling scheme), 2) Milking duration, 3) Milking speed, 4) Incomplete milking in automatic milking systems and 5) Other relevant data measured or reported by the equipment.
#Individual milkings should be tested for milk secretion rate in order to detect interrupted and unrecorded milkings, which in turn have an effect on the calculated 24-hour yields. If there is an interrupted milking or a milking that follows an interrupted milking at the beginning of the recording period, these two milkings must be excluded from the calculations. During the recording period they can be excluded but do not need to be.
#It is recommended to individually sample all milkings within the 24-hour recording period for 24-hour fat content calculation due to the high variability of milking frequency and milk fat content. In cases where sampling all milkings is not possible, please consult Chapter 2 of [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 - Computing 24-hour Yields] (for approved correction calculation methods).
#It is recommended to sample only milkings with a preceding interval longer than 4 hours.
====Authorisation to record====
It is recommended that professional milk recording technicians are trained and certified before they carry out recordings on their own. Ideally, such training includes a period of supervised work with a certified technician. Where such a certification system is in place, it is not allowed to record without an authorisation.

It is also recommended that frequent training is given to milk recording technicians on new technologies and equipment, safety instructions and data quality issues.

In B and C recording, farmers or their employees doing the practical recording need to be capable of operating the recording equipment correctly (e.g. milk meters, data capture tools) and are familiar with recording techniques.

It is recommended to have a conformation test from a certified recording agency and that frequent training take place.
====Cows to be recorded====
In a recorded herd, all milk-producing cows must be recorded. If a herd is divided into groups, all animals in the group have to be recorded on the same recording scheme. If different recording schemes are practiced on the farm all cows must be recorded according to the standards for recording and sampling intervals in table 3.

Acceptable reasons for missing data are discussed below, in 5.5. Missing results and/or abnormal intervals are reported [[Section 02 – Cattle Milk Recording#Missing results|here]].

===Identification (ID)===
====Herd ID====
Each herd in milk recording must be allocated a unique permanent identification number.
====Animal ID====
An official milk recording system must be based on a clearly identifiable and unique animal ID. It is recommended that one identification scheme for the whole country is used. Animal identification must also be in accordance with national and international regulation (e.g. EU member countries with EU legislation - 1760/2000 for cattle), and with relevant parts of currently valid ICAR Guidelines. The animal must be marked with an ICAR approved identification device or system. If the ID of imported animals is changed, the connection to the original ID must be maintained. Management numbers for cows can be used aside the official ID.
====Identification of the sample vial====
The sample, the milk weight and the cow ID must be linked at the milking.

Vials can be identified according to:
#Vial placement in the sampling unit.
#Cow or sample ID written on the vials.
#Barcoded vial with printed cow ID.
#Barcoded vial with cow ID registered at the milking.
#RFID vial with cow ID registered at the milking.
=====Sample identification without electronic equipment=====
Samples are identified according to their placement in the sampling unit. Additionally, sample or cow numbers can be written on the vials with a waterproof marker. If this marking is not done, there must be a sure and efficient way to identify sample No. 1 (e.g. different colour) and the sequence of other samples.

Each sampling unit must be connected to a list of samples where cow ID is given for each sample. Each transportation box also has to carry the relevant herd ID’s and, preferably, the sampling dates.
=====Barcoded vials=====
Samples are identified according to the barcode on the vial label.

If the label contains cow and/or herd ID, no electronic equipment is needed at the recording. The samples can be sent to the laboratory without accompanying sample lists or herd ID markings on the box.

If the label contains a random sample ID number, the cow ID must be connected with it on the farm. This is done with a barcode reader and computer programmes making the connection possible.
=====Vials with RFID=====
Samples are identified according to the RFID chip in the vial. This system requires the use of RFID readers and specific computer programmes creating a file where the cow and vial ID’s are connected.
=====Automatic sampling systems=====
In automatic milking systems (AMS), ICAR approved automatic samplers have to be used. Sample identification in these systems can be based on vial placement, barcode or RFID. The file with corresponding cow ID is in the management programme of the milking system. Data transfer is carried out with specific software and via a specific interface from the AMS to the MRO.
=====Sample ID in the laboratory=====
For impartiality and better quality, it is recommended that the samples are identified without cow ID and sent to the laboratory anonymously and the analysis results are merged afterwards in the data processing centre.
====Connection of the sample to milking and 24 h yield====
=====Sample and milk weight from the same milking=====
The ideal situation is that the sample and milk weight represent the same milking.
=====Sample from one milking, milk weight from two=====
A corrected analysis is routinely attached to the 24-hour yield.
=====Sample from one milking, milk weight from two or more, corrected by intervals=====
In this case, a 24-hour-yield is also combined with a one-milking sample, but the 24‑hour yield is obtained by correcting the recorded milkings according to the length of the preceding milking intervals. For example, if a cow has produced 20 kg milk in two milkings and the preceding intervals total 20 hours, her 24-hour yield is calculated as 20 kg * (24 h/20 h) = 24 kg. A corrected analysis is attached to this 24‑hour yield.
=====Sample from one milking or day, milk weight from several days=====
With electronic milk meters, it is possible to use the milk production from several days. This gives better accuracy of milk yield estimation; the highest accuracy with uncorrected milk weights is reached using a 4-day average. The problem is that the sample results become disconnected from the milk yield and a loss in fat and protein yield accuracy will occur. Ideally, fat and protein production should be connected to the recording day even in AMS.

In this case, there are three options to connect samples to the 24-hour yield:
#Milk weight is estimated from a longer measurement period but for fat and protein yield estimation only the milk yield on sampling day is used.
#Information only from the recording day for constituents in milk and milk yield estimation.
#Combination of multiple day milk yield with constituents from sampling. See ICAR procedures for using data from more than one day (Lazenby ''et al''., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>, estimation of fat and protein yield (Galesloot and Peeters , 2000)<ref name=":1">Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>.
The analysis data are merged with milk weights in the laboratory or data processing centre and the date of the analysis must be known.

=== Traits to be recorded ===

==== Definition of milking speed and box time ====

===== Introduction =====
Automated Milking Systems (AMS) do measure many traits. The definition of these traits might be different per brand of AMS. Data of these traits is often used by e.g. milk recording organisations, herdbooks or management software providers. When organisations store these data in their databases and use for certain services, it is important to know how these traits are defined.

These definitions could be used by milk recording organisations etc. to take into account differences between traits measured by different brands of AMS. These definitions could also be used by manufacturers of AMS to take into account for product development, to get more alignment in trait definitions between different brands of AMS.

Aim of this document is to propose a harmonized definition of some traits measured by AMS.

At this stage, the traits milking speed and box time are taken into account. Traits related to teat coordinates are described in Section 5 (Conformatoin Recording) of the ICAR guidelines.

==== Average milking speed ====
Definition = AverageMilkingSpeed (gr/min) = {TotalMilkYield / TotalMilkingTime}

* Total milk yield (kg) = Sum of all quarter level milk yields (kg)
* Total milking time = Last Take-off time (of any teat) - Begin of milk flow (of any teat)

Recommendations for manufacturers:

* Exclude any pre-treatment time from milking time.
* Provide take-off settings (threshold in gr/min at take-off, user-defined or default) and settings for the beginning of the measurement period, as milking time will be influenced by take-off settings and by the definition of the beginning of the milk flow.

Recommendations for data users:

* Don't report milking sessions with kick-off´s, interrupted and re-attached milkings because milking time will vary for these milkings.

==== Box time ====
Different types of box time:

* Milking
* Feed-only
* Pass-through
* Selection
* Training

Definition = {End box time - Begin box time} (HH:MM:SS)

* Begin box time = datetime of recognition of animal
* End box time = datetime when cow has exited the box (which might be different from opening of the gate), best to detect when cow has actually left the box

Additional data is needed to understand the status and completeness of the milking visit (Wethal and Heringstad, 2019). Registered issues during the milking are e.g.

* ff: at least 1 teat cup kicked off
* TeatNotFound: unable to find at least 1 of the teats for milking
* IncompleteMilking/FailedMilking: Minimum of 1 teat was registered as incompletely milked.
* The expected milk yield for a milking session depends on previous milkings. Settings like yield less than 80% of expectation for a teat, the milking session would be recorded as having an incompletely milked teat.
* Manual interaction like teat manually attached or milking finished manually.

Recommendations for manufacturers:

* Make the codes available that express if a milking was successful and the cause if the milking was not successful.
* Uniform names and definitions for interrupted, incomplete or failed milkings as well.

Recommendations for data users:

* Check the availability of a code that expresses if a milking was successful and the cause if the milking was not successful. The meaning of the code can be used to consider if the box time record has to be used for the intended purpose or not.
* To check if there is any extra box time due to feeding concentrates, e.g. through user specific settings such as 'PriorityFeeding'.

=== Traits to be recorded ===
In official milk recording, the following data have to be recorded, wherever available:

# Identification of each cow in the herd, even if they remain in the herd for a very short time.
# Birth date, sex, breed and parents of each animal when known.
# All services and embryo flushings and transfers: date, recipient, sire, dam of the embryo.
# All animal deaths and movements between farms and owners.
# Recording dates and locations.
# Milk yields for each cow and recording date.
# Fat content in milk for each cow and sampling date.

It is recommended to record also the following:

# Protein content in milk for each cow and sampling date.
# Milk somatic cell count for each cow and sampling date.
# Other results obtained from milk analysis.
# Milking duration and milking speed where possible.
# Milking times during recording.
# Recording methods and respective symbols used in records.
# Information about cow during the rearing period.

=== Recording method ===
The recording method for the herd consists of using five different symbols for:

# Responsibility for the practical recording.
# Sampling scheme.
# Recording interval.
# Sampling interval (if different from the above).
# Number of milkings per day (especially any deviation from 2x milking).

The symbols in Table 2 should be used:<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Symbols for milk recording schemes.''
|- style="background-color:#efefef; text-align:center;"

|'''Responsibility for recording'''
|'''Sampling scheme'''
|'''Recording interval (weeks)'''
|'''Sampling interval (weeks)'''
|'''Number of milkings per day'''
|-
| style="text-align:center;" | A
| style="text-align:center;" | P
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | B
| style="text-align:center;" | E
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | C
| style="text-align:center;" | Z
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" |
| style="text-align:center;" | T
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" |
| style="text-align:center;" | M
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:center;" | R x
|-
| style="text-align:center;" |
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | etc.
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | S x
|}
</center>

As an example: Recording method is CP36, 2x means that this is a recording where records/ samples are taken partly by the owner (farmer), and partly by a technician from the MRO, where the recording frequency is every 3 weeks, where the sampling frequency is every 6 weeks, and where the number of milkings per day is 2. If a national nomenclature system is used, it should be possible to transfer this system into ICAR nomenclature.

The reference milk recording method is by a representative of the recording organisation, measuring and sampling every four weeks, with proportional sampling and two milkings per day (AP44, 2x).

Recording other than by the reference method must be indicated using the appropriate symbols.

It is recommended that a limit is set for changing the recording method e.g. so that normally it is only possible to change the method twice per year.

It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

In the next sections the symbols are explained:
====Responsibility for the recording====
This symbol indicates who is responsible for measuring the milk yields and taking samples in the herd.
#Representative of the MRO (Method A; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Farmer or his/her representative (Method B; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
#Mixed responsibility (Method C; see '''[https://wiki.icar.org/index.php/Section_01_%E2%80%93_General_Rules#Performance_recording_of_milk Section 1 Chapter 3 - Performance recording of milk]''')
====ICAR Standards for sampling schemes====
=====Proportional sampling (P)=====
Samples and milk weights are taken at each milking during the recording day. The sampled amount corresponds to the milk yield of each milking. This is achieved by the use of a pipette in equal number of pipetting at each milking or of a specially designed tool which ensures proportional sampling to create one mixed sample. This is the default sampling scheme with no necessary correction to the analysis results, all other schemes must be reported.
=====Equal measure sampling (E)=====
Samples and milk weights are taken at each milking during the recording day. The amount of the sample is measured to be equal at each milking and mixed into one sample. The analysis results for fat should be corrected if one of the milking intervals is shorter than 10 or longer than 14 hours.
=====Multiple sampling (M)=====
Samples are taken at more than one milking during the recording day while milk weights are taken at each milking or over several days. Samples from different milkings are not mixed but they are kept in distinct vials so that each cow has at least two samples. The analysis results must be corrected to correspond to the 24-hour fat and protein yields. For example: a cow is milked 3x during 24 hours and 2 or 3 separate samples are taken, kept and analysed in different vials. This is the gold standard for AMS. It produces the most accurate results but is more expensive.
=====One-milking sampling with milk weights from more than one milking (Z)=====
Samples are taken from one milking during the recording day while milk weights are taken at each milking or over several days. The analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Alternated one-milking recording (T)=====
Samples and milk weights are taken during one milking, alternating between morning and evening milkings. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====Constant one-milking recording (C)=====
Samples and milk weights are taken during one milking, constantly during morning or evening milking. The milk weights and analysis results must be corrected using one of the methods described in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield.]

=====In-line analysis recording (I)=====
Milk is not sampled but its constituents are continuously analysed by a stationary analyser.
====ICAR Standards for recording and sampling intervals====

<center>
{| class="wikitable"
! colspan="5" style="text-align:left;" | ''Table 2. Standards for recording and sampling intervals.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| rowspan="2" style="text-align:center;" |'''Recording or sampling interval (weeks)'''
| rowspan="2" style="text-align:center;" |'''Minimum number of recordings or samplings per year'''
| colspan="2" style="text-align:center;" |'''Interval between recordings or samplings (days)'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| rowspan="10" style="text-align:center;" |Reference method
| style="text-align:center;" |1
| style="text-align:center;" |44
| style="text-align:center;" |4
| style="text-align:center;" |10
|-
| style="text-align:center;" |2
| style="text-align:center;" |22
| style="text-align:center;" |10
| style="text-align:center;" |18
|-
| style="text-align:center;" |3
| style="text-align:center;" |15
| style="text-align:center;" |16
| style="text-align:center;" |26
|-
| style="text-align:center;" |4
| style="text-align:center;" |11
| style="text-align:center;" |22
| style="text-align:center;" |37
|-
| style="text-align:center;" |5
| style="text-align:center;" |9
| style="text-align:center;" |32
| style="text-align:center;" |46
|-
| style="text-align:center;" |6
| style="text-align:center;" |8
| style="text-align:center;" |38
| style="text-align:center;" |53
|-
| style="text-align:center;" |7
| style="text-align:center;" |7
| style="text-align:center;" |44
| style="text-align:center;" |60
|-
| style="text-align:center;" |8
| style="text-align:center;" |6
| style="text-align:center;" |50
| style="text-align:center;" |70
|-
| style="text-align:center;" |9
| style="text-align:center;" |5
| style="text-align:center;" |55
| style="text-align:center;" |75
|-
| style="text-align:center;" |Daily
| style="text-align:center;" |310
| style="text-align:center;" |1
| style="text-align:center;" |3
|}
</center>

====ICAR standards for number of milkings per day====

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 3. Symbols for number of milkings per day.''
|- style="background-color:#efefef; text-align:center;"
|'''Number of milkings per day'''
|'''Symbol'''
|-
| style="text-align:center;" | Once per day milking
| style="text-align:center;" | 1 x
|-
| style="text-align:center;" | Two milkings
| style="text-align:center;" | 2 x
|-
| style="text-align:center;" | Three milkings
| style="text-align:center;" | 3 x
|-
| style="text-align:center;" | Four milkings
| style="text-align:center;" | 4 x
|-
| style="text-align:center;" | Continuous milking (e.g. AMS)
| style="text-align:center;" | R x
|-
| style="text-align:center;" | Regular milkings not at the same times on each day (e.g. 10 milkings per week)
| style="text-align:center;" | 1.4x
|-
| style="text-align:center;" | Shown as the average number of milkings per day.
| style="text-align:center;" |
|-
| style="text-align:center;" | Animals that are both milked and suckled. (Number of times milked to prefix the S)
| style="text-align:center;" | S x
|}
</center>

Where a herd is dry for a period of the year, the minimum number of recordings should be adjusted proportionately to the production period.

Minimum number of herd recordings should be at least 85% of the normal number of recordings.

=== Missing results and/or abnormal intervals ===
{{anchor|Missing_results}}A recorded 24-hour yield is the best estimate of the yield and the constituents of the milk, weighed, sampled and recorded within 24 hours on the day of recording.
#When herds are normally milked at intervals such that the recording day is other than 24 hours, the yields shall be adjusted to a 24-hour interval using the following procedure (or other procedures approved by the ICAR):
#*Divide 24 by the interval, then multiply by the yield. For example:
#**For a 25 hour interval (24/25) x 35 kg = 33.6 kg
#**For a 20 hour interval (24/20) x 35 kg = 42.0 kg
#A recording is a set of daily test values for a given animal on a given day of recording, one or some or all of them can be missed (missing values)
#Missing values can be due to:
#*Out of range.
#*Sickness.
#*Disaster.
#*No sample analysis results.
#The number of the official and complete (milk, fat and protein) recordings in the lactation or other accumulated yield should be reported.
#Permitted range of the daily recorded values is given in Table 5. Outside of these ranges, the daily recorded<ref>'''Note:''' High fat breeds have breed average higher than 5.0 for fat %.</ref> value will be considered as a missing value.

<center>
{| class="wikitable"
! colspan="7" style="text-align:left;" | ''Table 5. Permitted range of the daily recorded values.''
|- style="background-color:#efefef; text-align:center;"
| rowspan="2" style="text-align:center;" |
| colspan="2" style="text-align:center;" |'''Milk (kg)'''
| colspan="2" style="text-align:center;" |'''Fat %'''
| colspan="2" style="text-align:center;" |'''Protein %'''
|-
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
| style="text-align:center;" |'''Min'''
| style="text-align:center;" |'''Max'''
|-
| style="text-align:center;" | Main Dairy Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 1.5
| style="text-align:center;" | 9.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 7.0
|-
| style="text-align:center;" | High Fat1 Cattle Breeds
| style="text-align:center;" | 3.0
| style="text-align:center;" | 99.9
| style="text-align:center;" | 2.0
| style="text-align:center;" | 12.0
| style="text-align:center;" | 1.0
| style="text-align:center;" | 9.0
|}
</center>1Note: High fat breeds have breed average higher than 5.0 for fat %The true daily recorded values collected from animals labelled by the farmer as sick, injured or under treatment must be used in the computation of the lactation record unless the milk yield is less than 50% of the previous milk yield or less than 60% of the predicted yield. In such a case, the whole set of daily recorded values may be considered as missing.

Estimates of the missing values of a daily recording can be computed by using interpolation procedures or by more sophisticated procedures approved by ICAR

== Samples ==

=== Representative sample ===
The milk sample has to represent the complete milking linked to it. This is achieved by mixing the milk thoroughly or pouring it into another vessel right before sampling.

Sampling scheme P requires using a pipette for making the sample proportional between different milkings.

With sampling scheme E, it is advisable to use a measuring cup to make sure the sample parts actually are equal.

Immediately after sampling, the vials have to be preserved, capped, shaken and marked. Samples should be stored cool and dark.

=== Transport ===
Samples should be transported for analysis to a laboratory as soon as possible after sampling.

The samples need to be packed for transport and handled during transport in a manner that guarantees that sample IDs are not compromised or mixed. It is also recommended to protect the packages from external interference.

The packing material must be clean and disposable or easy to clean.

During transportation, it is recommended that the temperature of the samples stays below +10°C.

== Database ==
Storing the recorded data in a milk recording database is an indispensable part of the recording. It is recommended to use the quickest possible means to store the data in the database in order to ensure up-to-date breeding values and management applications. Where computerised data capture is possible, it should not take more than five days after the recording to have the complete recording data set in the database.

The application of the Guidelines in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2 - Computing 24-hour Yield], together with other parts of the Guidelines, ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

The guidelines on storage of data collected by the milk recording process are:

# For every recording, cow identification (ID), 24-hour milk yield or individual milk yields with a minimum of 0.2 kg (or the equivalent thereof) milk accuracy and recording date have to be stored.
# Where possible, it is advisable to store each milking separately. The data stored can include milk yield, time and date of milking, and milking scheme.
# Analysed results of the milk sample are stored, namely: sample ID, fat content (or percentage), sample status, sample type. Optional data can be stored on protein and/or lactose content, somatic cell count and additional analyses.
# Analysis results can be linked to one or more milkings of the cow.
# In case of storage or performance problems it might be necessary to remove old data of individual cow milkings from the database.
# Recording day information is the yield over 24 hours and should at least be kept in the database for the current lactation and the previous lactation.
# If recording day information is changed after batch processing it should be marked with a user-ID and time stamp.
# Yields are stored in kg or lbs or, in the case of fat and protein contents, in percent units.

The necessary additional information about how the results have been obtained include:

# Who did the recording (certified technician, farmer etc.).
# Herd and/or cow milking frequency.
# How many milkings were measured.
# How many milkings were sampled.
# Sampling scheme when sampling.
# Daily yield calculation method used.
# Recording and sampling intervals.
# It is recommended to store the Recording method ICAR code on event level, which is for every single cow milking stored in the database. The recording method for an accumulated yield is derived from the recording method of the underlying single milkings, in which case the recording method with the highest frequency is used to calculate the accumulated yield.

Basic checks for recording data:

# Farm (herd) ID: identified by a unique key.
# Animal ID: has to be unique in database.
# Format of animal ID: compliant to international standards of identification and registration.
# Recording date: less than or equal to today, greater than last recording date.
# Milk yield: stored with one decimal.
# 24 hour milk yield within range ( Table 5).
# Fat and protein content: e.g. within a range of +/- 3 standard deviation of population average (Table 5).
# Calving date: greater than birthday of cow (e.g. greater than birthday of cow + 20 months).
# Calving date: less than or equal to today.
# Sample analysis

This section of the ICAR Guidelines examines how observations are performed on farms and how data are collected, analysed and reported back to farmers. It forms an integral part with other sections of the ICAR Guidelines. It ensures that samples are analysed to the relevant degree of accuracy for the purposes of milk recording, breeding value prediction and other areas of usage. ICAR members operate in a range of situations, ranging from places with almost fully automated recording systems to areas with no roads and electricity. Therefore, the guidelines only demand standards that can be followed, irrespective of production situations and recommend more advanced options, where possible or required. Under the guidelines some practices might not be permitted while other practices are tolerated but not recommended.

== Yield calculations ==
This section covers 24-hour yields and accumulated yields for milk, fat, protein and somatic cells. It also describes the procedure for acceptance of new methods not previously mentioned in the guidelines.

The basic requirements for all calculation methods are that rounding shall only take place at the last step of the computation.

=== Lactation period ===

==== Commencement of the lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, is considered to commence is:

# The day that the cow calves (calving date), or
# In the absence of a calving date, the best estimate of the day that the cow commenced milk production.

A (valid) calving is defined as a parturition taking place:

# After the mid-point of the gestation period if a service has been recorded, or,
# After at least 75% of the normal gestation period has elapsed since the previous calving recorded if no service event has been recorded.

Any parturition falling outside the above definition shall be recorded as an abortion and shall not start a new lactation period.

For cows of dairy breeds the normal gestation length shall be deemed to be 280 days unless more specific breed information is available for use.

If the first recording is done on the calving date or within the first 4 days after calving, the milk yield and constituents at the first recording should not form part of the official lactation record, especially for automated milking systems (AMS) with multiple recorded days.

==== Completion of lactation period ====
The day that the lactation period, as recorded by the member or according to the ICAR Guidelines, has been completed is or:

# The day that the cow ceases to give milk (goes dry) or
# The day the cow gives less than 3.0 kg/day or 1.0 kg/milking in a recording (unless recorded sick) or
# When it is common practice not to record the dry-off date, the day of the midpoint between the last recording with the cow in milk and the first recording day with the animal dry may be assumed to be the dry-off date.

The lactation period ends on whichever date above occurs first.

Cows may be recorded as absent or sick on the recording day, without the lactation period being defined as terminated.

=== Production period ===
In the case where yield records are calculated on the basis of a period of production, usually a year, the record should be expressed as a ‘production period record‘ (symbol PP).

The production period begins the day after the end of the previous production period and ends as defined by the length (in days) of the production period.

=== Additional notes ===
For any ICAR method the interval between two consecutive recordings must routinely fulfil the value for the acceptable range on the herd level.

If the first recording occurs within 14 days from calving, then no adjustment is required to the first recorded value when computing the accumulated record. If the first recording occurs 15 to 95 days from calving, then an adjustment procedure may be applied.

If the 305th day of a lactation falls before the last recording, the interpolation method should be used also for the last period to compute the yields.

=== Standard methods for calculating 24 hour yields ===
The ICAR approved methods are presented in '''[https://www.icar.org/Guidelines/02-Procedure-1-Computing-24-Hour-Yield.pdf Procedure 1 of Section 2]'''. They include:

1. Methods for calculating daily yields from AM/PM milkings:

# Method of Delorenzo and Wiggans (1986)<ref>Delorenzo, M.A., and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. [https://www.journalofdairyscience.org/article/S0022-0302(86)80678-6/pdf J Dairy Sci 69; 2386]</ref>
# Method of Liu et al. (2019). Please note that in 2022 the method of Liu et al. (2000)<ref name=":0">Liu, Z., R. Reents, F. Reinhardt and K. Kuwan. 2000. Approaches to Estimating Daily Yield from Single Milk Testing Schemes and Use of a.m.-p.m. Records in Test-Day Model Genetic Evaluation in Dairy Cattle. [https://www.journalofdairyscience.org/article/S0022-0302(00)75161-7/pdf J. Dairy Sci. 83:2672-2682].</ref> has been updated to the method of Liu et al. (2019). We recommend to organisations that currently have implemented the method of Liu et al. (2000)<ref name=":0" /> to update to method of Liu et al. (2019).
# Method of Kyntäjä et al. (2021)<ref name=":3">1. Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. [https://www.icar.org/Documents/technical_series/ICAR-Technical-Series-no-25-Virtual-Meeting/Kyntaja.pdf ICAR Technical Series no. 25: 171-175.]</ref>

2. Methods to estimate 24h yield from Automatic Milking Systems:

# Using data on more than one day (Lazenby et al., 2002)<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Using data on 1 day (Bouloc et al., 2002)<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>
# Estimation of fat and protein yield (Galesloot and Peeters, 2000)<ref>Peeters, R. and P.J.B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. [https://www.journalofdairyscience.org/article/S0022-0302(02)74124-6/pdf J Dairy Sci. 2002 Mar;85(3):682-8].</ref>
# Sampling period (Hand et al., 2004<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D.F. 2004. Comparison of Protocols to Estimate 24 Hour Percent Fat and Protein. Presented at 34th ICAR session, Sousse, Tunisia, June, 2004. Proceedings of the 34th ICAR Meeting EAAP Publication No. 113:219-224</ref>; Bouloc et al., 2004)

3. Standard methods to estimate 24h yield from electronic milk meters:

# Estimation of 24-hour milk yield
# Using data on more than one day (Hand et al., 2006)<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. [https://doi.org/10.3168/jds.S0022-0302(06)72240-8 J. Dairy Sci. 89:1723-1726]</ref>
# Estimation of 24-hour fat and protein yield

=== Standard methods for calculating accumulated yields ===
The ICAR approved methods are presented in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_2_%E2%80%93_Computing_of_Accumulated_Lactation_Yield Procedure 2 of Section 2]. They include:

# Test Interval Method (TIM) (Sargent, 1968)<ref>Sargent, F.D., V.H. Lyton, and O.G. Wall, Jr . 1968. Test interval method of calculating Dairy Herd Improvement Association records. [https://doi.org/10.3168/jds.S0022-0302(68)86943-7 J. Dairy Sci. 51:170].</ref>
# Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987)<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. [https://doi.org/10.1016/0301-6226(87)90049-2 Livest. Prod. Sci. 17:l].</ref>
# Best prediction (VanRaden, 1997)<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. [https://doi.org/10.3168/jds.S0022-0302(97)76268-4 J. Dairy Sci. 80:3015-3022].</ref>
# Multiple-Trait Procedure (MTP) (Schaeffer and Jamrozik, 1996)<ref>Schaeffer, L.R. and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. [https://doi.org/10.3168/jds.S0022-0302(96)76578-5 J. Dairy Sci. 79:2044-2055.]</ref>

=== Procedure to approve new methods ===

# All parties interested in seeking approval for any new accumulated yield calculation method will notify the ICAR Secretariat and provide a description of the proposed method.
# These parties will provide a detailed report including statistical details, scientific references and other relevant data to the ICAR Dairy Cattle Milk Recording Working Group.
# The ICAR Dairy Cattle Milk Recording Working Group will then consider the proposal and recommend that it be conditionally approved, approved or rejected.
# The final steps will consist of approval by the General Assembly and publication in the guidelines. .

== Reporting ==
This subsection covers reports, data files, statistics and calculated key figures provided to farmers for breeding and management purposes.

It is recommended that farmers are given reports after each recording and at the end of the recording year or another longer recording period. These reports should contain data on both cow and herd level. In bigger herds, it is also advisable to present results by management groups or otherwise chosen cow groups within the herd. The reporting may be done on paper, through web pages and/or in the form of data files or electronic reports.

Where data files are distributed or direct access given to the results in the database, care must be taken that data ownership is clearly defined. This also includes defining who has access to data and how this access can be authorised.

ICAR members are advised to prepare annual statistics in a reasonable timeframe after closing the recording year. The minimum data requirements are what is needed for the ICAR [https://my.icar.org/stats/list Dairy Cattle Yearly Enquiry on-line database].

<center>
{| class="wikitable"
! colspan="3" style="text-align:left;" | ''Table 5. Examples of key figures for herd to be used by farmers and other users.''
|- style="background-color:#efefef; text-align:center;"
|style="text-align:left |'''Key figure'''
|style="text-align:left |'''Explanation'''
|-
| style="text-align:left;" | 12-month rolling average yield
| style="text-align:center;" | Total milk, fat and protein produced during the 365 (366) days preceding the recording divided by the average number of cows for the same period.
|-
| style="text-align:left;" | Average 305-day yield
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations finished during the reporting period divided with the number of finished 305-day lactations.
|-
| style="text-align:left;" | Average 305-day yield within a period
| style="text-align:center;" | Total milk, fat and protein produced within 305-day lactations during the reporting period divided with the average number of cows on a 305-day lactation within the reporting period.
|-
| style="text-align:left;" | Average annual yield
| style="text-align:center;" | Total milk, fat and protein produced during the recording year divided by the average number of cows for the same recording year.
|-
| style="text-align:left;" | Average calving interval
| style="text-align:center;" | The average preceding intervals of all calvings second and more during the reporting period.
|-
| style="text-align:left;" | Average fat, protein or lactose contents in milk
| style="text-align:center;" | Total fat, protein and lactose yields divided by the total milk yield, usually expressed with two decimals.
|-
| style="text-align:left;" | Average lactation yield
| style="text-align:center;" | Total milk, fat and protein produced within lactations of any length finished during the reporting period divided with the number of finished lactations.
|-
| style="text-align:left;" | Average lactation yield within a period
| style="text-align:center;" | Total milk, fat and protein produced during the reporting period divided with the average number of cows in milk within the reporting period.
|-
| style="text-align:left;" | Average number of cows
| style="text-align:center;" | Average number of cows in the herd (or group) on a given day during the reporting period. Usually expressed with one decimal.
|-
| style="text-align:left;" | Average somatic cell count
| style="text-align:center;" | The average of all individual cow somatic cell counts weighted for individual milk yields.
|-
| style="text-align:left;" | Daily milk, fat and protein yields
| style="text-align:center;" | 1) Total daily milk, fat and protein yields divided by number of cows, or 2) Total daily milk, fat and protein yields divided by number of cows in milk.
|-
| style="text-align:left;" | Energy Corrected Milk (ECM)
| style="text-align:center;" | Calculated according to a national standard.
Example from the Nordic countries:

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + milk yield, kg * 0.7832)/3.14

or, if lactose has been analysed

ECM = (fat yield, kg * 38.3 + protein yield, kg * 24.2 + lactose yield * 16.54 + milk yield, kg * 0.0207)/3.14.

From solids expressed as %:

ECM = [(fat content, % * 383 + protein content, % * 242 + 783.2)/3140]* milk yield, kg

or, if lactose has been analysed

ECM = [(fat content, % * 383 + protein content, % * 242 + lactose content, % * 165.4 + 20.7)/3140]* milk yield, kg.
|-
| style="text-align:left;" | Number of lactations
| style="text-align:center;" | Total number of finished lactations in the herd (or group) during the reporting period.
|-
| style="text-align:left;" | Reporting period
| style="text-align:center;" | The period presented in the given report. The most usual options are: one day, one recording interval, lactation, rolling 365 days, recording or calendar year, and the cow’s lifetime.
|}
</center>

== Decisions ==

As a result of the recording process and reports prepared on the basis of its results, decisions can be made on one or more of the following:

=== Short term impact: day-to-day management decisions taken on farms ===

# Decisions about bulk milk quality.
# Feeding decisions - daily diet based on group or individual performance.
# Pasture management decisions.
# Grouping decisions - placing cows in different management or feeding groups.
# Culling decisions - decisions on the sale or slaughter of cattle.
# Mating decisions.
# Decisions regarding programmes of certification for milk and milk products.
# Decisions based on data flow from MRO’s to farms and vice versa.

=== Medium-term impact ===

# Farmers’ decisions based on advisory services, veterinarians, independent experts and other services.
# Decisions about production planning on farms (herd development).

=== Long-term impact ===
# Breeding programme and selection decisions - breeding partners informed by genetic evaluation ([[Section 09 – Dairy Cattle Genetic Evaluation|Section 9)]] based on milk recording results.
# Decisions based on herd book and breeder association activities and deciding on business actions related to breeding animals, i.e. in some countries animal recording data are required for international trade with breeding animals.

=== Strategic decisions ===
# Research programmes concerning management, recording and breeding.
# Political decisions about possible subsidies in dairy cattle breeding at the governmental level and implementing measurements according to agriculture policy.

== Quality control ==
This Section together with other parts of the Guidelines ensure that data from particular animals are linked with the relevant phenotypes, genomic information and environments to the required accuracy and using the best methods. There is a distinction, however, between the accuracy required for official milk recording and breeding value estimations and other relevant official results and data used for managerial purposes.

=== Bulk tank data comparison ===
It is a recommended practice to compare milk recording data with dairy deliveries and bulk tank milk contents. This can be done on the recording day or over a longer period of time. The calculation is done as follows:

# Comparison ratio = Total recorded milk yield, kg /Total milk produced, kg. This comparison is used where there is a reliable estimate of the farm use of milk.
# Quick comparison ratio = Total recorded milk yield, kg/ Total milk delivered, kg. This comparison is used where farm use of milk is not estimated.
# Content comparison = Recorded average fat / Bulk tank average fat
# Comparison ratio for fat = Total recorded fat yield, kg/ Total fat produced, kg
# Total recorded milk yield, kg = Ʃ (Individual milk yield, kg)
# Total milk delivered, kg = Total milk delivered, litres * milk density kg/litre
# Total milk produced, kg = (Total milk delivered, litres + Milk used or discarded on the farm, litres) * milk density kg/litre
# Total fat produced, kg = Total milk produced, kg x (Bulk tank fat percent/100)
# Recorded average fat = Ʃ [Individual milk yield kg x (Individual fat percent/100)]/Ʃ (Individual milk yield, kg)

The recommended acceptable range for comparison ratios is 0.95 - 1.05, and for quick comparison ratios 0.90 - 1.00, with due regard to herd size.

=== One day bulk tank data comparison ===
Milk yields and fat yields or contents are compared on the recording day. Comparing the contents is routinely possible where every delivery is sampled or by taking a bulk tank sample (see point [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Bulk_tank_data_comparison 1.10] above for how the comparison is done.)

=== Bulk tank data comparison over a longer period ===
Milk yields and fat yields or contents are compared over a longer period of time, e.g. 4 months or 12 months. This option requires a routine to obtain the applicable data from the dairies or milk buyers. Farm use of milk may be taken into account where applicable.

=== Bulk tank sample ===
Bulk tank samples can be used to verify the milk contents analysis obtained in milk recording. A sample is taken from a well-mixed bulk tank on the recording day. It must represent the milk of the whole 24-hour period. Bulk tank fat and protein contents are then compared to the weighted averages of the fat and protein percent obtained from milk recording. Normally, the difference between the values should not be more than 5%.

=== Supervised or repeated recording ===
Supervised recording is a tool designed to verify that individual cow records are reliable. It is based on repeating the herd recording as soon as possible after the original recording, and the obtained results are compared with the original recording. It is obligatory for ICAR Certificate of Quality (CoQ) holders to practice regular supervision, irrespective of recording methods used.

It is recommended that the supervised recording will follow immediately after the original recording, but for a good reason it can be postponed for up to 7 days.

The farmer and any other staff doing the original recording must not know that a supervised recording will follow. The technician who performs the supervised recording should not be the same person who did the original recording.

Usually supervised recording is done by recording the whole herd again, using the same sampling scheme and recording method (or a reference method) as in the previous recording. When herd size exceeds 200 cows, it is also allowed to do a supervised recording to selected, or randomised groups of animals in the herd.

Choosing the herds for supervised recording may be random or based on preselection. Traits for this preselection may include high yield, great increase in yield, presence of bull dams in the herd, and general suspicions about the correctness of herd results.

The traits compared in supervised recording must include milk and fat. Comparing protein is also recommended.

=== Supervision - example of comparison calculations ===

# Milk, fat and protein yields per cow are calculated for both the original and the supervised milking.
# Individual cow records where results between supervised recording and the original recording differ outside the norms might be excused where a good explanation can be given for exclusion (illness, heat, missed milking)
# Deviations (%) are calculated for each cow and yield constituent according to the formula: deviation = (supervised yield/unsupervised yield)*100-100
# Herd averages of the absolute values for each yield constituent are calculated.
# If the supervised recording occurs within 2 days of the original recording, the acceptable difference in herd averages are 7% for milk and protein and 9% for fat.
# If the supervised recording occurs between 3 and 7 days after the original recording, the acceptable difference of the aforementioned herd averages are 9% for milk and protein and 12% for fat.

The limits mentioned in these examples are typically applied by some of the member organisations, and are not meant to be understood as exact norms. Such norms should be laid down by each member organisation.

=== Evaluation of recording data ===
It is recommended that data quality is evaluated for each herd recording day. When such an evaluation is applied, the following features of the data have to be included:

# Person responsible for the recording.
# ICAR approval and calibration status of the recording equipment if owned by the farmer.
# Number of herd recordings per time period and/or recording interval.
# Number of herd samplings per time period and/or sampling interval.

The following features are also recommended to be included if possible:

# Deviation of milk and fat yields from dairy deliveries.
# Deviation of milk and fat yields from previous or predicted yields.
# Standard deviation of individual cow records.
# Number of recorded and/or sampled milkings within the recording day.
# Number of cows missed or not recorded in the recording.
</div>
</div>
= Procedures =
== Procedure 1: Computing 24-hour Yields ==
<div class="mw-collapsible mw-collapsed">
<div>
=== Methods to calculate 24-hour yield for milk yield and fat percentage from a single milking ===

==== Method of Delorenzo & Wiggans (1986)<ref>Delorenzo, M.A. and G.R.Wiggans. 1986. Factors for estimating daily yield of milk, fat, and protein from a single milking for herds milked twice a day. J. Dairy Sci. 69: 2386-2394.</ref> ====
Daily milk (DMY) and fat yield (DFY) estimates are based on measured yield and milking frequency. An adjustment factor accounts for differences in the average milking interval (expressed in decimal hours) between the preceding milking and the measured milking, and the time of day of the measured milking (started in a.m. or p.m.). For 2X milking, an additional adjustment is applied to milk yield for the interaction between milking interval and stage of lactation, with mid lactation (158 DIM) set to zero. Milking interval does not affect protein and solids non fat (SNF) percentages and so the percentages for the sampled milking are used for test-day estimates. Protein yield is calculated from the measured percentage and the adjusted milk yield.

The prediction of DMY and DFY from single milking on morning or evening in herds milked twice a day requires factors, that are the reciprocal of the proportion of total yield expected from single milkings in relation to the milking interval.

We propose to derive these coefficients (intercept, slope, etc.) for each country separately.

===== Adjustment of milking interval =====
The milking interval is the interval between milking time for the observed milking and the milking time preceding the observed milking. The milking interval is divided into 15-minutes classes. Factors for milk and fat yields may be calculated to each class using Equation 1:

''Equation 1. Factors for milk and fat yields.''
[[File:Equation 1.png|none|thumb|397x397px]]

===== Adjustment of lactation stage =====
Because the lactation stage of the cow has an influence on the effect of different milking intervals on milk production a second adjustment is made for every interval class through a covariate of days in milk as addition:

Covariate x (days in milk - 158)

===== Estimating sample day yields =====
Formulas for prediction sample day yields and percentages in herds with two milkings are:

''Equation 2. Equation for predicting 24-hour milk yield.''
[[File:Equation2.png|none|thumb|428x428px]]

''Equation 3. Equation for predicting 24-hour fat percentage.''
[[File:Equation3.png|none|thumb|431x431px]]

''Equation 4. Equation for predicting 24-hour fat yield.''
[[File:Equation4.png|none|thumb]]

''Equation 5. Equation for predicting 24-hour protein yield.''
[[File:Equation5.png|none|thumb|316x316px]]

===== Calculation examples =====

====== Practical Application ======
Two sets of factors are available for estimating DMY from a single milking, each for morning or evening milking sampling. The factors are calculated from the formula as described above and given in Table 1.
<center>
{| class="wikitable"
| colspan="5" align="left" |'''''Table 1. Factor of milk yield and covariate for herds milked twice a day.'''''
|- style="background-color:#efefef;"
| rowspan="2" align="center" |'''Length of milking interval in hours (minutes in decimal)'''
| colspan="2" align="center" |'''Morning milking'''
| colspan="2" align="center" |'''Evening milking'''
|- style="background-color:#efefef;"
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
| align="center" |'''Factor'''
| align="center" |'''Covariate'''
|-
| align="center" |< 9.00
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.594
| align="center" |0.00378
|-
| align="center" |9.00-9.24
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.534
| align="center" |0.00485
|-
| align="center" |9.25-9.49
| align="center" |2.465
| align="center" |0.00710
| align="center" |2.477
| align="center" |0.00486
|-
| align="center" |9.50-9.74
| align="center" |2.411
| align="center" |0.00716
| align="center" |2.423
| align="center" |0.00511
|-
| align="center" |9.75-9.99
| align="center" |2.359
| align="center" |0.00726
| align="center" |2.370
| align="center" |0.00473
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |10.00-10.24
| align="center" |2.310
| align="center" |0.00458
| align="center" |2.321
| align="center" |0.00337
|-
| align="center" |10.25-10.49
| align="center" |2.262
| align="center" |0.00399
| align="center" |2.273
| align="center" |0.00214
|-
| align="center" |10.50-10.74
| align="center" |2.217
| align="center" |0.00294
| align="center" |2.227
| align="center" |0.00000
|-
| align="center" |10.75-10.99
| align="center" |2.173
| align="center" |0.00223
| align="center" |2.183
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |11.00-11.24
| align="center" |2.131
| align="center" |0.00000
| align="center" |2.140
| align="center" |0.00000
|-
| align="center" |11.25-11.49
| align="center" |2.091
| align="center" |0.00000
| align="center" |2.099
| align="center" |0.00000
|-
| align="center" |11.50-11.74
| align="center" |2.052
| align="center" |0.00000
| align="center" |2.060
| align="center" |0.00000
|-
| align="center" |11.75-11.99
| align="center" |2.014
| align="center" |0.00000
| align="center" |2.022
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |12.00
| align="center" |2.000
| align="center" |0.00000
| align="center" |2.000
| align="center" |0.00000
|-
| align="center" |12.01-12.24
| align="center" |1.978
| align="center" |0.00000
| align="center" |1.986
| align="center" |0.00000
|-
| align="center" |12.25-12.49
| align="center" |1.943
| align="center" |0.00000
| align="center" |1.951
| align="center" |0.00000
|-
| align="center" |12.50-12.74
| align="center" |1.910
| align="center" |0.00000
| align="center" |1.917
| align="center" |0.00000
|-
| align="center" |12.75-12.99
| align="center" |1.877
| align="center" |0.00000
| align="center" |1.884
| align="center" |0.00000
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |13.00-13.24
| align="center" |1.846
| align="center" |0.00000
| align="center" |1.852
| align="center" |-0.00190
|-
| align="center" |13.25-13.49
| align="center" |1.815
| align="center" |0.00000
| align="center" |1.822
| align="center" |-0.00231
|-
| align="center" |13.50-13.74
| align="center" |1.786
| align="center" |-0.00167
| align="center" |1.792
| align="center" |-0.00308
|-
| align="center" |13.75-13.99
| align="center" |1.757
| align="center" |-0.00258
| align="center" |1.763
| align="center" |-0.00339
|-
| align="center" |
| align="center" |
| align="center" |
| align="center" |
| align="center" |
|-
| align="center" |14.00-14.24
| align="center" |1.730
| align="center" |-0.00347
| align="center" |1.736
| align="center" |-0.00509
|-
| align="center" |14.25-14.49
| align="center" |1.703
| align="center" |-0.00363
| align="center" |1.709
| align="center" |-0.00471
|-
| align="center" |14.50-14.74
| align="center" |1.677
| align="center" |-0.00332
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |14.75-14.99
| align="center" |1.652
| align="center" |-0.00316
| align="center" |1.683
| align="center" |-0.00454
|-
| align="center" |≥ 15.00
| align="center" |1.628
| align="center" |-0.00235
| align="center" |1.683
| align="center" |-0.00454
|}
</center>

For estimating daily fat percentage there is only one table independent of morning or evening sampling – refer to Table 2.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" |'''''Table 2. Factor of fat percentage for herds milked twice a day.'''''
|- style="background-color:#efefef;"
|'''Length of milking'''

'''interval in hours'''
|'''Fat (percentage'''

'''factor)'''
|-
|< 9.00
|0.919
|-
|9.00-9.24
|0.927
|-
|9.25-9.49
|0.934
|-
|9.50-9.74
|0.941
|-
|9.75-9.99
|0.948
|-
|
|
|-
|10.00-10.24
|0.955
|-
|10.25-10.49
|0.961
|-
|10.50-10.74
|0.968
|-
|10.75-10.99
|0.974
|-
|
|
|-
|11.00-11.24
|0.980
|-
|11.25-11.49
|0.986
|-
|11.50-11.74
|0.992
|-
|11.75-11.99
|0.997
|-
|
|
|-
|12.00
|1.000
|-
|12.01-12.24
|1.003
|-
|12.25-12.49
|1.008
|-
|12.50-12.74
|1.013
|-
|12.75-12.99
|1.018
|-
|
|
|-
|13.00-13.24
|1.023
|-
|13.25-13.49
|1.028
|-
|13.50-13.74
|1.033
|-
|13.75-13.99
|1.037
|-
|
|
|-
|14.00-14.24
|1.042
|-
|14.25-14.49
|1.046
|-
|14.50-14.74
|1.050
|-
|14.75-14.99
|1.054
|-
|≥ 15.00
|1.058
|}
</center>

Milking-interval factors are calculated using Equation 1, where the intercept and slope are as in Table 3.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 3. Slope and intercept for milk yield and fat yield.'''''
|- style="background-color:#efefef;"
| rowspan="2" |'''Trait'''
| colspan="2" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started in a.m.'''
|'''For measured milking started in p.m.'''
|-
|Milk yield
|0.0654
|0.0634
|0.0363
|-
|Fat yield
|0.1965
|0.1939
|0.0254
|}
</center>
The milking interval has no significant influence on protein percentage. Therefore, the protein percentage of the sampled milking is used as the daily protein percentage.

====== Calculation of daily yields from morning milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Data for a cow from morning milking.'''''
|-
|Begin of recording:
|6:15
|(Morning milking)
|-
|Start of preceding milking:
|17:25
|
|-
|Length of milking interval:
|12 hours 50 minutes
|(Expressed as decimal 12.83)
|-
|Milk results at morning:
|12,0
|Milk-kg
|-
|
|4,12
|Fat-percentage
|-
|
|3,45
|Protein-percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 5. Factors for morning milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.877
|-
|The covariate is
|0
|-
|The factor for fat percentage from Table 2 is
|1.018
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 6. Example calculations for morning milking.'''''
|-
|The sample-day milk yield:
|1.877 x 12,0 kg + 0 x (120 - 158) = 22,5 kg
|-
|The sample-day fat percentage:
|1.018 x 4,12 = 4,19
|-
|The sample-day fat yield:
|22,5 kg x 0,0419 = 0,94 kg
|-
|The sample-day protein yield:
|22,5 kg x 0,0345 = 0,78 kg
|}
</center>

====== Calculation of daily yields from evening milking ======
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 7. Data for a cow from evening milking.'''''
|-
|Begin of recording:
|16:48
|Evening milking
|-
|Start of preceding milking:
|6:35
|
|-
|Length of milking interval:
|13 hours 47 minutes
|Expressed as decimal 13.78
|-
|Milk results at evening:
|14,0
|Milk kg
|-
|
|4,00
|Fat percentage
|-
|
|3,40
|Protein percentage
|-
|
|120
|Days in milk
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 8. Factors for evening milking example.'''''
|-
|The factor for milk yield from Table 1 is
|1.763
|-
|The covariate is
|<nowiki>-0,00339</nowiki>
|-
|The factor for fat percentage from Table 2 is
|1.037
|}
{| class="wikitable"
| colspan="2" |'''''Table 9. Example calculations for evening milking.'''''
|-
|The sample-day milk yield:
|1.763 x 14,0 kg - 0,00339 x (120 - 158) = 24,8 kg
|-
|The sample-day fat percentage:
|1.037 x 4,00 = 4,15
|-
|The sample-day fat yield:
|24,8 kg x 0,0415 = 1,03 kg
|-
|The sample-day protein yield:
|24,8 kg x 0,0340 = 0,84 kg
|}
</center>

====== Alternate recording of components and milk yield at both milkings ======
For this plan only the sample-day fat yield has to be calculated with regard to milking interval. The milk yield is the sum of evening and morning milk results.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left" |'''''Table 10. Example data for a cow from both milkings.'''''
|-
|Begin of recording evening:
|17:25
|
|-
|Milk results at evening:
|10:00
|Milk kg (only milking-yield)
|-
|Begin of recording morning:
|6:15
|
|-
|Milk results at morning:
|12:00
|Milk kg
|-
|
|4:20
|Fat percentage
|-
|
|3:50
|Protein percentage
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 11. Factor for fat percentage.'''''
|-
|Length of milking interval:
|12 hours 50 minutes (expressed

as decimal 12.83)
|-
|The factor for fat percentage from Table 2 is
|1.018.
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 12. Example calculation of daily yields.'''''
|-
|The sample-day milk yield:
|10,0 kg + 12,0 kg = 22,0 kg
|-
|The sample-day fat percentage:
|1.018 x 4,20 = 4,28
|-
|The sample-day fat yield:
|22,0 kg x 0,0428 = 0,94 kg
|-
|The sample-day protein yield:
|22,0 kg x 0,0350 = 0,77 kg
|}
</center>

====== Calculation for 3X Milking ======
For 3X herds, a single milking or two consecutive milkings may be weighed. The sample may be collected at one or both of these milkings. Stage of lactation × milking interval adjustments are not used for greater than 2× milking. These AM/PM factors for estimating daily yields in 3X herds should not be confused with factors that adjust 3X records to a 2X basis. Milking-interval factors are calculated using the same formula with the intercept and slope as in Table 13.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" align = "left" |'''''Table 13. Slope and intercept factors for 3X milking.'''''
|- style="background-color:#efefef;"
| rowspan="2" | '''Trait'''
| colspan="3" |'''Intercept'''
| rowspan="2" |'''Slope'''
|- style="background-color:#efefef;"
|'''For measured milking started between 2 a.m. and 9:59 a.m.'''
|'''For measured milking started between 10 a.m. and 5:59 p.m.'''
|'''For measured milking started between 6:00 p.m. and 1:59 a.m.'''
|-
|Milk yield
|0.077
|0.068
|0.066
|0.0329
|-
|Fat yield
|0.186
|0.186
|0.182
|0.0186
|}
</center>
When two milkings are included for sampling, the intercepts and intervals for both milkings are included in determining a factor for calculated estimated milk yield that is applied to the total yield from both milkings as in Equation 6.

''Equation 6. Milking interval factor for 3X milking.''
[[File:Equation6.png|none|thumb|536x536px]]
Milk and fat percent factors are calculated separately based on the number of milkings weighed or sampled.

====== Calculation for 4X - 6X Milking ======
The intercept terms for calculating 3X factors (0.077, 0.068, and 0.066) are multiplied by the factor [3 / (milkings per day)] for use in calculating factors for milking frequencies greater than 3X.

==== Method of Liu et al. (2019) ====
A multiple regression method (MRM) is used for estimating 24-hour daily milk yield (DMY), daily fat yield (DFY) and daily protein yield (DPY) based on partial yields from either morning (AM) or evening (PM) milking. Fat percentage (DFP) or protein percentage (DPP) on a 24-hour daily basis are then derived using the estimated 24-hour daily yields. The MRM can be used as a reference method for estimating daily yields and component percentages.

The method of Liu et al. (2019) is an updated version of the method of Liu et al. (2000). The model is only used for farms with 2 time milkings during 24 hours.

The following formula is used to estimate DMY, DFY, DPY based on partial yields (PMY, PFY,PPY) from either morning (AM) or evening (PM) milking:

''Equation 7. Model for predicting 24-hour yield.''

''yijk = a + bijk * xijk''

where:

yijk is the estimated 24-hour daily yield (DMY, DFY or DPY);

xijk is AM or PM partial daily yield on a test day (PMY, PFY, or PPY).

Subscript '''''i''''' represents class of parity effect with 2 levels: first and higher parities.

Subscript '''''j''''' represents class of length of preceding milking interval with 8 levels for AM milking: < 720 minutes, < 740 minutes, < 760 minutes, < 780 minutes, < 800 minutes, < 820 minutes, < 840 minutes, >= 840 minutes and 8 levels for PM milking: < 600 minutes, < 620 minutes, < 640 minutes, < 660 minutes, < 680 minutes, < 700 minutes, < 720 minutes, >= 720 minutes.

Subscript '''''k''''' represents class of lactation stage with 7 classes: < 60 days, < 120 days, < 180 days, < 240 days, < 300 days, < 360 days, >= 360 days.

'''''a''''' is the estimated intercept for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

'''''b'''''ijk is the estimated slope for the combination of parity class (i), milking interval class (j) and lactation stage class (k) for either AM or PM milking for the given trait.

The factors for '''''a''''' and '''''b'''''ijk can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Appendix_1_-_Adjustment_factors_to_calculate_24-hour_yields_using_the_Liu_method Appendix 1].

For a given yield trait a total number of 112 formulae are to be estimated for calculating 24-hour daily yield based on partial yield from either AM or PM milking. Component percentage for fat (DFP) and protein (DPP), on a 24-hour basis is calculated by dividing estimated fat or protein yield by estimated daily milk yield:[[File:Imagefinal.png|center|thumb|339x339px]]

===== Calculation example with method of Liu et al. (2019) =====
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" align = "left" |'''''Table 14. Data from an evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="6" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="6" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="6" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow'''

'''ID'''
|'''Calving date'''
|'''Lactation number'''
| colspan="2" |'''Milk yield (kg)'''
|'''Fat content (%)'''
|'''Protein content (%)'''
|'''Fat yield (kg)'''
|'''Protein yield (kg)'''
|'''Index1'''
|-
|A
|01.01.2020
|1
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1132
|-
|B
|01.01.2020
|2
| colspan="2" |25,0
|3,98
|3,33
|0,995
|0,8325
|1232
|-
|C
|27.03.2020
|1
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1131
|-
|D
|27.03.2020
|2
| colspan="2" |33,1
|4,03
|3,36
|1,3339
|1,1122
|1231
|-
|
|
|
|
|
|
|
|
|
|
|}
'''1''' Index is marked in the Appendix table.
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 15. Calculation of 24-hour daily yield and components for evening milking.'''''
|-
| colspan="4" |Date of milk testing:
| colspan="3" |23.04.2020
|-
| colspan="4" |Milking time :(AM/PM):
| colspan="3" |16:29 (PM)
|-
| colspan="4" |Length of preceding milking interval:
| colspan="3" |629 minutes, previous milking time 06:00 (AM)
|- style="background-color:#efefef;"
|'''Cow ID'''
|'''DMY (kg)'''
|'''DFY (kg)'''
| colspan="2" |'''DPY (kg)'''
|'''DFP (%)'''
|'''DPP (%)'''
|-
|A
|3,47396+25,0

<nowiki>*</nowiki> 1,98268 = 53,0401 ≈ '''53,0'''
|0,2135+0,995

<nowiki>*</nowiki> 1,68050 = 1,8855975
| colspan="2" |0,10471+0,8325* 1,99092 = 1,7621509
|1,8855975 / 53,04096*100

≈ '''3,55'''
|1,7621509 / 53,04096*100

≈ '''3,32'''
|-
|B
|4,15080+25,0* 1,98520 = 53,7808 ≈ '''53,8'''
|0,3635+0,995

<nowiki>*</nowiki> 1,47515 = 1,8312743
| colspan="2" |0,13952+0,8325* 1,97074 = 1,7801611
|1,8312743 / 53,7808*100

≈ '''3,41'''
|1,7801611 / 53,7808*100

≈ '''3,31'''
|-
|C
|2,80244+33,1

<nowiki>*</nowiki> 2,02183 = 69,72501 ≈ '''69,7'''
|0,17663+1,3339 * 1,72438 = 2,4767805
| colspan="2" |0,11078+1,1122 * 1,96422 = 2,2953855
|2,4767805 / 69,725013*100

≈ '''3,55'''
|2,2953855 / 69,725013*100

≈ '''3,29'''
|-
|D
|3,85525+33,1 * 2,00429 = 70,19725 ≈ '''70,2'''
|0,27991+1,3339 * 1,62403 = 2,4462036
| colspan="2" |0,12863+1,1122* 1,98973 = 2,3416077
|2,4462036 / 70,7197249*100 ≈ '''3,48'''
|2,3416077 / 70,7197249*100 ≈ '''''3,34'''''
|-
|
|
|
|
|
|
|
|}
</center>
'''Note''' that intercepts and slopes of the applied regression formulae are underscored.

===== Fat correction for equal measure sampling =====
With Equal measure sampling, it is advisable to use Equation 8 (or the like) to correct fat contents:

Equation 8. Fat correction for equal measure sampling.

Fat, % = Analysed fat, % + 0.69 – 1.3 x (morning milk/ 24-hour milk)

The relation of morning milk to 24-hour milk is to be calculated to at least four decimals.

==== 1.1 Method of Kyntäjä & Nokka (2021)<ref name=":3" />: 24-hour correction factors for fat percentage ====
This method can be applied to calculate 24-hour correction factors for fat percentage, in case the milk recording is based on two milkings, with at least one known milk yield and one sample. A 24-hour recording day is assumed.

The conventional way to calculate correction factors is based on a data set where all milkings have been recorded and analysed separately. This approach requires a lot of effort and extra analysis, and is not cheap to organise. Organisations that have access to a large number of records may be able to use those data to calculate correction factors even if they have no extra analysis.

Requirements for the data set:

# The data set has to be large enough. Every single factor needs to be based on at least 10,000 or, even better, 100,000 observations.
# Each individual data set must contain at least one preceding milking interval, milk weight, and analysed sample. If it contains more milk weights, intervals etc. that is even better. It is also good to include breed, lactation number, days in milk and other data that may have an effect on the factors.

===== Calculation example of the method of Kyntäjä & Nokka (2021)<ref>Kyntäjä, J. and S. Nokka. 2021. A new approach to predicting the fat content in 2x milking. Proceedings of the 44th ICAR Annual Conference. ICAR Technical Series no. 25: 171-175.</ref> =====

====== The accumulated data set ======
Since 2003, Finland had accumulated a data set of 7.5 million recordings with data on the time of the sampled and preceding milking as reported by the farmer, the lab analysis results, and the 24-hour milk yield. Grouped according to the preceding interval, the analysed fat content gives a nice sigmoid curve with the highest fat content found after a 540 to 630 minutes’ interval (9 to 10.5 hours) and the lowest at 810 to 930 minutes (13.5 to 15.5 hours).
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 16. Average analysed milk fat percentage by preceding interval class, 2003 – 2020.'''''
|- style="background-color:#efefef;"
|'''Interval before'''

'''Sampling (minutes)'''
|'''Number of samples'''
|'''Median interval in the class'''
|'''Average fat content analysed (%)'''
|-
|<510
|93,577
|495
|4.20
|-
|510-539
|19,523
|525
|4.70
|-
|540-569
|111,268
|555
|4.79
|-
|570-599
|253,807
|585
|4.83
|-
|600-629
|1,461,587
|615
|4.75
|-
|630-659
|919,968
|645
|4.66
|-
|660-689
|1,168,683
|675
|4.56
|-
|690-719
|223,877
|705
|4.42
|-
|720-749
|517,447
|735
|4.28
|-
|750-779
|212,428
|765
|4.16
|-
|780-809
|924,014
|795
|4.12
|-
|810-839
|698,463
|825
|4.09
|-
|840-869
|1,104,778
|855
|4.07
|-
|870-899
|154,561
|885
|4.05
|-
|900-929
|77,024
|915
|4.07
|-
|>929
|26,977
|945
|4.13
|}
</center>

The results were also divided into subgroups according to lactation number, phase of lactation, and breed. The effect of the preceding milk interval on milk fat seems to be bigger with older cows and in the beginning of lactation. It was also bigger with Ayrshire cows as compared with Holsteins. At this point, however, the decision was made not to take these factors into account when calculating new correction factors.

====== Calculation of new factors ======
The results above were turned into a simple set of correction factors, dependent solely on the preceding interval. In order to do this, two assumptions were made:

# A 24-hour recording day was assumed. This way, we can deduce the second milking interval from the one we know and mirror the fat percent for that milking.
# Milk secretion rate was assumed to be constant around the 24-hour period. This allows us to deduce the share of the 24-hour yield produced at each milking.

These assumptions allow us to create the new correction factors by mirroring the milk yield and milk fat content in the milking whose actual data we have not got. This way, we get the following formula:

Equation 9. Correction factor.
[[File:Equation9.png|none|thumb|545x545px]]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left" |'''''Table 17. Calculation of the mirrored milking and the correction factors'''''
|- style="background-color:#efefef;"
|'''Interval before sampling (minutes)'''
|'''Average fat in the sampled milking (%)'''
|'''Share of 24-hour milk in the sampled milking'''
|'''Mirrored interval (minutes)'''
|'''Average fat in the mirrored milking (%)'''
|'''Calculated 24-hour average fat(%)'''
|'''Correction factor'''
|-
|<510
|4.21
|0.34
|>929
|4.14
|4.16
|0.989
|-
|510-539
|4.77
|0.36
|900-929
|4.08
|4.33
|0.907
|-
|540-569
|4.82
|0.39
|870-899
|4.05
|4.35
|0.903
|-
|570-599
|4.84
|0.41
|840-869
|4.07
|4.38
|0.906
|-
|600-629
|4.76
|0.43
|810-839
|4.09
|4.37
|0.919
|-
|630-659
|4.66
|0.45
|780-809
|4.12
|4.36
|0.936
|-
|660-689
|4.56
|0.47
|750-779
|4.16
|4.35
|0.953
|-
|690-719
|4.43
|0.49
|720-749
|4.29
|4.36
|0.984
|-
|720-749
|4.29
|0.51
|690-719
|4.43
|4.36
|1.016
|-
|750-779
|4.16
|0.53
|660-689
|4.56
|4.35
|1.046
|-
|780-809
|4.12
|0.55
|630-659
|4.66
|4.36
|1.059
|-
|810-839
|4.09
|0.57
|600-629
|4.76
|4.37
|1.070
|-
|840-869
|4.07
|0.59
|570-599
|4.84
|4.38
|1.076
|-
|870-899
|4.05
|0.61
|540-569
|4.82
|4.35
|1.073
|-
|900-929
|4.08
|0.64
|510-539
|4.77
|4.33
|1.062
|-
|>929
|4.14
|0.66
|<510
|4.21
|4.16
|1.006
|}
</center>

=== Methods to calculate 24-hour yields in Automatic Milking Systems ===

==== General remarks about calculation of 24-hour milk yield ====
It is characteristic for AMS systems that individual cows set their own milking rhythm, thus making it largely irrelevant to use the traditional model of measuring milk yields and sampling at all milkings in the herd during the recording day. In order to determine how much an individual cow’s real 24-hour milk, fat and protein yield is, more complex calculations are required, especially with milk fat that varies considerably from milking to milking. For protein content and cell counts, no correction is needed for a one-milking sample.

The basic idea with calculating a 24-hour milk yield from AMS data is that milk yields per milking are converted into milk yield per time unit (minute or hour) during the preceding interval. This milk yield per time unit is then converted into milk yield in 24 hours. In order to do this, the data set must also contain time stamps for each milking.

How many milkings or how long a measurement period is used for creating 24-hour yields depends on the milk recording organisation. The fewer milkings are used the more random variance there will be in the individual cow milk yields. The absolute minimum is two milkings with preceding intervals, while a measuring period of 96 hours is recommended.

The sampled milking must always be inside the milk yield measurement period. For the calculation of fat and protein yields, it is recommended to use only those milk yields that are from the same period or day. With Z sampling, the 24-hour fat and protein yields may be calculated based on a shorter measurement period than what is used for calculating the 24-hour milk yields.

==== Calculation of milk yield using data of several days (Lazenby ''et al''., 2002<ref>Lazenby, D., E. Bohlsen, K. J. Hand, D. F. Kelton, F. Miglior and K. D. Lissemore. 2002. Methods to estimate 24-hour yields for milk, fat and protein in robotic milking herds. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Automatic Milking Systems (AMS). The average of most recent milk weights can be calculated using a number of preceding milkings or a number of preceding days. If number of milkings is used, the optimal estimate of the milking rate is obtained using an average of current milking together with the 12 most recent milkings back in time. The optimal estimate is the maximum value of the difference curve at which the correlation with the ‘true’ 24-hour milk yield is greatest and the variance across milkings is minimized. If number of days is used, the optimal estimate of the milking rate is obtained using an average of all milkings occurred in the last 96 hours (4 most recent days). In Table 18 the percent of maximum difference for various number of milkings and days is reported. The optimal estimate is independent from stage of lactation and parity.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" align = "left" |'''''Table 18. Percent maximum for different number of days and milkings.'''''
|- style="background-color:#efefef;"
|'''Days'''
|'''Percent Max.'''
|'''Current milking'''

'''+ most recent milkings'''
|'''Percent max.'''
|-
|1
|49.38
|10
|97.85
|-
|2
|77.26
|11
|99.08
|-
|3
|92.34
|12
|99.70
|-
|4
|98.91
|13
|99.81
|-
|5
|98.50
|14
|99.40
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table19.png|center|thumb|911x911px]]
Therefore, 24-hour yield estimation using most recent milkings (1+12) is computed using Equation 10.

''Equation 10. 24-hour yield estimation using 12 previous milkings from AMS.''
[[File:Equation10.png|none|thumb|527x527px]]
and, 24-hour yield estimation using all milkings occurred in the last 96 hours (most recent 4 days), all milking in the last 4 days are included is computed using Equation 11.

''Equation 11. 24 hours yield estimation using milkings from the last 96 hours from AMS''
[[File:Equation11.png|none|thumb|534x534px]]

===== Advantages and disadvantages of this method =====
In terms of Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between milk weights and contents may arise if contents are recorded on one day only. Moreover, some cows may begin or finish their lactation during the period of recording. In this case the computation of milk yield must be adapted. The number of data that need to be validated is higher (for instance, contents have short interval between two milkings).

==== Calculation of milk yield using data on 1 day (Bouloc ''et al''., 2002<ref>Bouloc, N., J. Delacroix and V. Dervishi. 2002. Milk recording and automatic milking systems: features and simplification possibilities of recording procedures. Presented at the 33th biennial Session of ICAR, Interlaken, Switzerland, May 26-31, 2002.</ref>) ====
When the number of milkings is reduced to milkings obtained during one day only, the accuracy of the estimation of the true performance is the same as classical milk recording methods with the same interval between two test days. For instance, Milk Yield estimated from all the milkings recorded during 24 hours, and with an interval between two test days of four weeks has the same accuracy as A4.

==== Calculation of fat and protein yield (Galesloot & Peeters, 2000<ref name=":1" />) ====
Calculation of fat and protein percent must be based on milk weights at time of sampling. The 24-hour protein percentage can be predicted by the protein percentage of the sample without adjustment. However, the 24-hour fat percentage is more difficult to predict, as levels of fat percent are inversely proportional to the amount of milk yield. It is important then to have a close connection between time of samples and actual milk yields.

The Peeters and Galesloot method is a multiple linear regression model for estimating 24-hour fat percent and yields from one-sampled milking during the AMS sampling period. Six different statistical models were tested. This method takes into account fat percent, protein percent, milk weight and milking interval of the sampled milking, milking interval and milk weight of the previous milking (simple model). Another model, based on six different classification of variables (Ca - Cf) such as, time of sampled milking, interval preceding the sampled milking, ratio of fat to protein percent, parity, lactation stage, can be applied (complex model).

===== Simple model =====
24-hour Fat% = b0 + b1* Fat%(n) + b2* Prot%(n) + b3* Int(n) + b4* Int(n-1) + b5* Milk(n) + b6* Milk (n-1) + e

b0= Intercept, b1 to b6 = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, e = Residual effect.

===== Complex model =====
24-hour Fat%i = b0i + b1i* Fat%(n) + b2i* Prot%(n) + b3i* Int(n) + b4i* Int(n-1) + b5i* Milk(n) + b6i* Milk(n-1) + ei

b0i = Intercept, b1i to b6i = Regression coefficients, Int = Milking interval, (n) = Milking sampled, (n-1) = Previous milking, ei = Residual effect

i = subclass of classification for class variables Cx for x = a, b, c, d, e, f

Ca = Day Time of sampled milking (h) 0-5.59, 6.00-11.59, 12.00-17.59, 18.00-23.59

Cb = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440

Cc = Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

Cd = Parity 1, 2, ≥ 3

Ce = Lactation stage 1-99, 100-199, ≥200

Cf = Interval preceding the sampled milking n (min) 0-360, 361-510, 511-700, 701-1440 and Fat%n/Prot%n ratio of fat to protein % of the sampled milking 0-1.10, 1.10-1.25, 1.25-1.40, >1.40

The best prediction of 24-hour fat percent and 24-hour fat yields from this method, includes fat percent, protein percent, milk weight and milking interval of the sampled milking, milk weight and milking interval of the preceding milking and the interaction between milking interval, the ratio of fat to protein percent of the sampled milking (complex model corresponding to Cf classification).

The Peeters and Galesloot method has been updated by Roelofs et al. (2006)<ref>Peeters, R. and P. J. B. Galesloot. 2002. Estimating Daily Fat Yield from a Single Milking on Test Day for Herds with a Robotic Milking System. J Dairy Sci. 85:682-688.</ref>. The Roelofs method is described in [[Section 02 – Cattle Milk Recording#Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme|Appendix 2]] of this Section.

N.B. This method has been developed by CRV. CRV has available a set of parameters, estimated with this method. For more information about costs and advice on application of this method, please contact CRV. ICAR has no benefit from the application of this method or any other method described in these guidelines.

==== Calculation example of 24-hour fat and protein yields with sampling scheme M ====
With this method, all milkings in a 24-hour recording period must be sampled. The obtained separate analysis results are then used to compute a 24-hour yield of milk solids, and a weighted average of their content.

Individual milkings (last 96 hours) and recording day contents:
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left" |'''''Table 20. Calculation of 24-hour fat and protein contents with sampling scheme M.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY/MM/DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat%'''
|'''Protein%'''
|-
|1
|2021/09/09
|20:45
|525
|13.7
|26.1
|
|
|-
|2
|2021/09/10
|5:30
|617
|16.0
|25.9
|
|
|-
|3
|2021/09/10
|15:47
|720
|18.7
|26.0
|
|
|-
|4
|2021/09/11
|3:25
|645
|16.8
|26.0
|
|
|-
|5
|2021/09/11
|14:10
|899
|18.3
|20.3
|
|
|-
|6
|2021/09/11
|23:27
|557
|14.6
|26.2
|
|
|-
|7
|2021/09/12
|10:51
|684
|17.4
|25.4
|4.53
|3.17
|-
|8
|2021/09/12
|19:44
|533
|14.1
|26.5
|4.92
|3.18
|-
|9
|2021/09/13
|1:35
|351
|9.9
|28.2
|5.92
|3.07
|}
</center>

For example, calculation of fat% on recording day:

24-hour Fat% = (9.9 kg milk x 5.92% fat + 14.1 kg milk x 4.92 % fat + 17.4 kg milk x 4.53 % fat) / (9.9 + 14.1 + 17.4) kg milk = 5.00 %

To calculate the 24-hour fat yield, the calculated 24-hour milk yield is multiplied by the fat content thus obtained (5.00 %).

The same method is used for protein, somatic cell count, urea, lactose and other milk constituents.

Estimation of milk contents: It is recommended to set the robot not to take samples if the preceding milking of the individual cow is not more than 4 hours earlier. If such milkings occur the milk sampled from them is not suitable for 24-hour fat calculation.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="8" align = "left"|'''''Table 21. Calculation of 24-hour fat and protein contents with sampling scheme M where one milking interval was shorter than 4 hours.'''''
|- style="background-color:#efefef;"
|'''No.'''
|'''Date'''

'''(YYYY-MM-DD)'''
|'''Time (h:mm)'''
|'''Preceding interval (minutes)'''
|'''Milk yield (kg)'''
|'''Milk secretion rate (g/min)'''
|'''Fat %'''
|'''Protein%'''
|-
|1
|2021/11/12
|20:05
|590
|15.4
|26.4
|
|
|-
|2
|2021/11/13
|6:31
|626
|16.3
|26.0
|
|
|-
|3
|2021/11/13
|17:12
|641
|17.1
|26.7
|
|
|-
|4
|2021/11/14
|4:40
|688
|17.5
|25.4
|
|
|-
|5
|2021/11/14
|15:11
|631
|16.4
|26.0
|
|
|-
|6
|2021/11/15
|2:25
|674
|16.5
|24.5
|
|
|-
|7
|2021/11/15
|9:47
|452
|10.8
|23.9
|
|
|-
|8
|2021/11/15
|18:30
|523
|13.6
|26.0
|4.71
|3.36
|-
|9
|2021/11/15
|21:15
|165
|3.1
|18.8
|5.161
|3.481
|-
|10
|2021/11/16
|7:49
|634
|16.5
|26.0
|4.47
|3.21
|}
1 Time between two consecutive milkings shorter than 4 hours, data not taken into account for calculation of milk contents.
</center>

Calculation of the fat content of milk during the recording day:

24-hour Fat% = (16.5 kg milk x 4.47 % fat + 13.6 kg milk x 4.71 % fat) / (16.5 kg + 13.6 kg) = 4.57 %

The same method is used for protein, somatic cells, urea, lactose and other milk constituents.

=== Methods to calculate 24-hour yields from electronic milk meters ===

==== Using data on more than one day (Hand ''et al''., 2006<ref>Hand, K. J., Lazenby D., Miglior F. and Kelton D. F. 2006. Comparison of Protocols to Estimate Twenty-Four-Hour Fat and Protein Percentages for Herds with a Robotic Milking System. J. Dairy Sci. 89:1723–1726.</ref>) ====
An average of most recent milk weights is used for estimating 24-hour daily milk yield collected from Electronic Milk Meters. The average of most recent milk weights can be calculated using a number of preceding days. Table 22 reports the concordance correlations for a range of multiple-day averages. As soon as at least the 3 preceding days are used in the calculation, the concordance correlation reaches a high value of at least 0.981. There are no significant differences between 3, 4, 5, 6 and 7-day averages. The correlations are independent from stage of lactation and parity. Thus, 24-hour yields can be the average of from 3 to 7 daily milkings previous to the test day when fat and protein samples were taken.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left" |'''''Table 22. Concordance correlations for different multiple-day averages.'''''
|- style="background-color:#efefef;"
|'''Multiple-day average'''
|'''Concordance correlation'''
|-
|1
|0.957
|-
|2
|0.975
|-
|3
|0.981
|-
|4
|0.981
|-
|5
|0.982
|-
|6
|0.981
|-
|7
|0.981
|-
|10
|0.979
|-
|14
|0.977
|}
</center>
===== Example for calculating 24-hour milk yield =====
[[File:Table20.png|center|thumb|923x923px]]

Therefore, 24-hour yield estimation averaging over 5 days is given by Equation 12.

''Equation 12. 24-hour yield estimation averaging over 5 days.''
[[File:Equation12.png|center|thumb|601x601px]]

===== Advantages and disadvantages of this method =====
Concerning Milk Yield, this method leads to a better accuracy of the estimation of the true performance than a performance estimated on a 24-hour basis only. However, problems of disconnection between Milk weights and contents have been shown. The estimation bias increases proportionally to the number of days use to compute the 24-hour average. Thus, this method is recommended only if milk weight is the only variable of interest. If milk contents are of interest then the milk weight should be calculated using the milkings from the same day of sampling.

==== Estimation of 24-hour fat and protein yield ====
Fat and protein yields should be determined from the 24-hour yield on the day of sampling, and not the averaged value.

=== Calculation of daily fat percentage from single samples by Gerke et al., 2025 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Gerke.xlsx here]

Constant access to the automatic milking system (AMS) leads to varying milking frequency of cows and subsequently varying milking interval lengths (MI) and milk yield (MY) of single milkings. This influences milk production and can result in variable milk composition in individual milkings during the day. Therefore, the fat percentage from one sampled milking must be adjusted before it can be used as a daily value. The method described specifies the data required and the calculation procedure for deriving a corrected 24 h milk fat percentage from a single sample on test day (TD) in AMS herds.

==== Model specification ====
The multiple linear regression includes transformation, interaction, and polynomial parameters to model non-linearity and thereby improve prediction accuracy. Beside F% of a single milking (''m'') on TD, the model focused on lactation characteristics and milk recording data of up to 4 preceding milkings. With milking intervals ranging between 4 and 20 hours, the method can be applied to milk recording samples from cows with 2 or 3 milkings whose milking intervals lengths (MI) before sampling accumulate to less than 24 h.

The functional form of the model described below specifies the data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample:[[File:Image A.png|center|thumb|636x636px|'''Data required and the calculation procedure for deriving the estimated 24 h milk fat percentage from a single sample''']]
</div>where:

DF% = estimated 24 h fat percentage on TD

''m'' = sampled milking on TD

''m-x'' = x milkings before the milking where the sample was taken (x: 1-3)

F% = fat percentage of the sampled milking ''m''

MY(''m'') = milk yield (kg) of ''m''

MI(''m'') = length of time interval (min) preceding the sampled milking ''m''

MY(''m''-x) = milk yields of the 1-3 preceding milkings of ''m''

MI(''m''-x) = milking interval length corresponding to MY(''m''-x)

DIM = days in milk on TD ranging between 5 and 330 d

Parity = parity class (e.g primiparous = 1 and multiparous = 0)

Daytime = time-of-day group of ''m'' (e.g. morning/noon/evening)

e = residual error

The method and its implementation are described in detail by Gerke et al. (2025).

==== Calculation and examples ====
The mathematical notation, with the corresponding regression coefficients in Table 1 for calculating the daily fat percentage (DF%):[[File:Calculating the daily fat percentage (DF%).jpg|center|Calculating the daily fat percentage (DF%)|thumb|511x511px]][[File:Calculating the daily fat percentage (DF%) 2.jpg|center|frame|'''Table 1. Coefficients for regression formula.''']]
</div>
[[File:Example data required for estimating 24 h fat percentage (DF%).jpg|alt=Example data required for estimating 24 h fat percentage (DF%)|center|frame|'''Table 2.''' '''Example data required for estimating 24 h fat percentage (DF%)''']]
Based on the data assembled on TD (Table 2), the corrected 24 h fat percentage (DF%) can be calculated using the mathematical formula und its corresponding coefficients listed in Table 1 as shown in the following examples:
[[File:Corrected 24 h fat percentage.jpg|alt=Corrected 24 h fat percentage|center|thumb|661x661px|'''Corrected 24 h fat percentage''']]

=== Reference ===
Gerke, J. S., Kammer, M., Werner, A., Köstler, R., Piepenburg, J., Mayerhofer, M., … Duda, J. (2025). Estimating daily fat percentage from single samples in herds with automatic milking system using a regression model. ''Livestock Science'', ''293'', 105649. doi: 10.1016/j.livsci.2025.105649

=== Calculation of daily fat percentage from single samples by Jenko et al., 2008, 2010 ===
A simulation for such calculation is available [https://www.icar.org/Guidelines/Calculation-daily-fat-percentage-from-single-sample-by-Jenko.xlsx here]

This method estimates daily milk yield (DMY), daily fat yield (DFY), and daily protein yield (DPY) in the alternate one-milking recording (T) scheme. Daily fat percentage (DFP) and daily protein percentage (DPP) are then derived from the daily yield (DY) estimates. Utilizing this method allows us to remove the risk of underestimating high and overestimating low DY and contents.

The following formula is used to estimate the DY from the partial yield (PY) and the estimated PY/DY ratio (y):

DY=PYi/yi

where the subscript i is either morning (a.m.) or evening (p.m.).

The value of y is calculated based on the milking interval in minutes (MI), estimated intercept (µ) and regression coefficients (b1 and b2) for yield traits in a.m. or p.m. milking using the following equations for DMY and DPY:

'''Equation 1. Model for milk yield and protein yield.'''

yi = µ + b1 × MI

and for DFY

'''Equation 2. Model for fat yield.'''

yi = µ + b1 × MI + b2 × MI2

The intercept and regression coefficients can be either estimated from the data with records from both a.m. and p.m. milking or the estimates from Table 1 can be applied.

'''Table 1. Intercept and regression coefficients for calculation of daily yield.'''
{| class="wikitable"
|'''Daily yield'''
|'''Milking'''
|'''µ'''
|'''b1'''
|'''b2'''
|-
|DMY
|a.m.
|0,1081000000
|0,0005503000
|
|-
|
|p.m.
|0,0884200000
|0,0005683000
|
|-
|DPY
|a.m.
|0,1124000000
|0,0005419000
|
|-
|
|p.m.
|0,0966400000
|0,0005593000
|
|-
|DFY .
|a.m.
|0,5903000000
|<nowiki>-0,0005093000</nowiki>
|0,0000005377
|-
|
|p.m.
|0,1574000000
|0,0006705000
|<nowiki>-0,0000002744</nowiki>
|}
Finally, daily fat percentage (DFP) and daily protein percentage (DPP) are calculated from the estimated DY:

DFP=DFY/DMY × 100

DPP=DPY/DMY × 100

==== Calulation example with method of Jenko et al. (2008, 2010) ====
Example of the calculations of daily yields from morning milking and evening milking is presented in tables 3 and 4. Data from the Delorenzo and Wiggans method is used in the calculations (Table 2).

'''Table 2. Data for morning and evening milking.'''
{| class="wikitable"
|'''Milking'''
|'''a.m.'''
|'''p.m.'''
|-
|Beginning of recording
|06:15
|20:22
|-
|Start of preceding milking
|17:25
|06:35
|-
|Milking interval (min)
|770
|827
|-
|'''Milking results'''
|
|
|-
|Milk (kg)
|12,00
|14,00
|-
|Protein (%)
|3,45
|3,40
|-
|Fat (%)
|4,12
|4,00
|}

'''Table 3. Calculation of partial yield (PY) and calculation of y value.'''
{| class="wikitable"
|Trait
|Milking
|PY (%)
|PY (kg)
|y
|-
|Milk
|a.m.
|
|12,00
|0,1081000000 + 0,0005503000 x 770 = 0,531831
|-
|
|p.m.
|
|14,00
|0,0884200000 + 0,0005683000 x 827 = 0,558404
|-
|Protein
|a.m.
|3,45
|12,00 / 3,45 = 0,41
|0,1124000000 + 0,0005419000 x 770 = 0,529663
|-
|
|p.m.
|3,40
|14,00 / 3,40 = 0,48
|0,0966400000 + 0,0005593000 x 827 = 0,559181
|-
|Fat
|a.m.
|

4,12
|12,00 / 4,12 = 0,49
|0,5903000000 -0,0005093000 x 770 + 0,0000005377 x 7702 = 0,516941
|-
|
|p.m.
|

4,00
|12,00 / 4,00 = 0,56
|0,1574000000 +0,0006705000 x 827 - 0,0000002744 x 8272 = 0,524233
|}

'''Table 4. Calculation of daily yield (DY, kg) and daily components (DY, %).'''
{| class="wikitable"
|Trait
|DY
|Milking
|DY (kg)
|DY (%)
|-
|Milk
|DMY
|a.m.
|12,00 / 0,531831 = 22,56356
|
|-
|
|
|p.m.
|14,00 / 0,531831 = 25,07145
|
|-
|Protein
|DPY
|a.m.
|0,41 / 0,529663 = 0,781629
|(0,781629 / 22,56356) x 100 = 3,46
|-
|
|
|p.m.
|0,48 / 0,559181 = 0,851245
|(0,851245 / 25,07145) x 100 = 3,40
|-
|Fat
|DFY
|a.m.
|0,49 / 0,516941 = 0,956395
|(0,956395 / 22,56356) x 100 = 4,24
|-
|
|
|p.m.
|0,56 / 0,524233 = 1,068227
|(1,068227 / 25,07145) x 100 = 4,26
|}

==== References ====

* Jenko, J., Perpar, T., Logar, B., Sadar, M., Ivanovič, B., Jeretina, J., Verbič, J., Podgoršek, P. 2008. Comparison of different models for estimating daily yields from a.m./p.m. milkings in Slovenian dairy scheme. Presented at the 36th ICAR Session, Niagara Falls, New York, United States, June 16-20, 2008.
* Jenko, J., Perpar, T., Gorjanc G., Babnik, D. 2010. Evaluation of different approaches for the estimation of daily yield from single milk testing scheme in cattle, J. Dairy Res., 77 (2010), pp. 137-143; DOI: 10.1017/S0022029909990586

== Procedure 2 – Computing of Accumulated Lactation Yield ==
<div class="mw-collapsible mw-collapsed">
<div>
=== The Test Interval Method (TIM) (Sargent, 1968<ref>Sargent, F. D., V. H. Lyton, and 0. G. Wall, J r . 1968. Test interval method of calculating Dairy Herd Improvement Association records. J. Dairy Sci. 51:170.</ref>) ===
Test Interval Method is the reference method for calculating accumulated yields. Another adaptation of the method is the Centering Date Method where the yields from the preceding recording are used until the mid point of the recording interval and then substituted by the yields from the following recording.

The following equations are used to compute the lactation record for milk yield (MY), for fat (and protein) yield (FY), and for fat (and protein) percent (FP).
[[File:Equation1111.png|none|thumb|653x653px]]
Where:
M1, M2, Mn are the weights in kilograms, given to one decimal place, of the milk yielded in the 24 hours of the recording day.

F1, F2, Fn are the fat yields estimated by multiplying the milk yield and the fat percent (given to at least two decimal places) collected on the recording day.

I1, I2, In-1 are the intervals, in days, between recording dates.

I0 is the interval, in days, between the lactation period start date and the first recording date.

In is the interval, in days, between the last recording date and the end of the lactation period.

The equation applied for fat yield and percentage must be applied for any other milk components such as protein and lactose.

Details of how to apply the formulae are shown in Table 3 using the example data in Table 1, below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" align = "left" |'''''Table 1. Raw data used in example (TIM).'''''
|- style="background-color:#efefef;"
| colspan="6" align = "left"|'''Data:'''

'''Calving March 25'''
|- style="background-color:#efefef;"
|
|'''Date of'''

'''recording'''
|'''Number'''

'''of days'''
|'''Quantity of milk'''

'''weighed in kg'''
|'''Fat'''

'''percentage'''
|'''Fat'''

'''in grams'''
|-
|April
|8
|14
|28.2
|3.65
|1 029
|-
|May
|6
|28
|24.8
|3.45
|856
|-
|June
|5
|30
|26.6
|3.40
|904
|-
|July
|7
|32
|23.2
|3.55
|824
|-
|August
|2
|26
|20.2
|3.85
|778
|-
|August
|30
|28
|17.8
|4.05
|721
|-
|September
|25
|26
|13.2
|4.45
|587
|-
|October
|27
|32
|9.6
|4.65
|446
|-
|November
|22
|26
|5.8
|4.95
|287
|-
|December
|20
|28
|4.4
|5.25
|231
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="2" align = "left"|'''''Table 2. Lactation period summary (TIM).'''''
|-
|Beginning of lactation:
|March 26
|-
|End of lactation:
|January 3
|-
|Duration of lactation period:
|284 days
|-
|Number of testings (weighings):
|10
|}
</center>
<center>
{| class="wikitable"
| colspan="8" |'''''Table 3. Computations using Test Interval Method.'''''
|- style="background-color:#efefef;"
| colspan="3" rowspan="2" |'''Interval'''

'''both days included'''
|
| colspan="2" |'''Daily production'''
| colspan="2" |'''Sum'''
|- style="background-color:#efefef;"
|'''Days'''
|'''Kg milk'''
|'''Grams of fat'''
|'''Kg milk'''
|'''Kg fat'''
|-
|Mar 26
|<nowiki>-</nowiki>
|Apr 8
|14
|28.2
|1 029
|395
|14.410
|-
|Apr 9
|<nowiki>-</nowiki>
|May 6
|28
|(28.2+24.8)/2
|(1 029+856) /2
|742
|26.389
|-
|May 7
|<nowiki>-</nowiki>
|June 5
|30
|(24.8+26.6) /2
|(856+904) /2
|771
|26.400
|-
|June 6
|<nowiki>-</nowiki>
|July 7
|32
|(26.6+23.2) /2
|(904+824) /2
|797
|27.648
|-
|July 8
|<nowiki>-</nowiki>
|Aug. 2
|26
|(23.2+20.2) /2
|(824+778) /2
|564
|20.817
|-
|Aug. 3
|<nowiki>-</nowiki>
|Aug 30
|28
|(20.2+17.8) /2
|(778+721) /2
|532
|20.980
|-
|Aug 31
|<nowiki>-</nowiki>
|Sept. 25
|26
|(17.8+13.2) /2
|(721+587) /2
|403
|17.008
|-
|Sept. 26
|<nowiki>-</nowiki>
|Oct. 27
|32
|(13.2+9.6) /2
|(587+446) /2
|365
|16.541
|-
|Oct. 28
|<nowiki>-</nowiki>
|Nov. 22
|26
|(9.6+5.8) /2
|(446+287) /2
|200
|9.536
|-
|Nov. 23
|<nowiki>-</nowiki>
|Dec. 20
|28
|(5.8+4.4) /2
|(287+231) /2
|143
|7.253
|-
|Dec. 21
|<nowiki>-</nowiki>
|Jan. 3
|14
|4.4
|231
|62
|3.234
|-
|
|
|
|284
|
|
|4973
|190.216
|-
| colspan="8" |
|-
| colspan="8" |Total quantity of milk: 4 973. kg
|-
| colspan="8" |Total quantity of fat: 190 kg
|-
| colspan="8" |Average fat percentage (190.216 / 4973) x 100 = 3.82%
|}
</center>

=== Interpolation using Standard Lactation Curves (ISLC) (Wilmink, 1987<ref>Wilmink, J.B.M. 1987. Comparison of different methods of predicting 305-day milk yield using means calculated from within-herd lactation curves. Livest. Prod. Sci. 17:l.</ref>) ===
With the method 'Interpolation using Standard Lactation Curves' missing test day yields and 305 day projections are predicted. The method makes use of separate standard lactation curves representing the expected course of the lactation, for a certain herd production level, age at calving and season of calving and yield trait. By interpolation using standard lactation curves, the fact that after calving milk yield generally increases and subsequently decreases is taken into account. The daily yields are predicted for fixed days of the lactation: day 0, 10, 30, 50 etc.

The cumulative yield is calculated as follows in :
[[File:Equation2222222.png|none|thumb|474x474px]]
where:

yi = the i-th daily yield;

INTi = the interval in days between the daily yields yi and yi+1;

''n'' = total number of daily yields (measured daily yields and predicted daily yields).

The next example illustrates the calculation of a record in progress. The cow was tested at day 35 and day 65 of the lactation. To determine the lactation yield, daily milk yields are determined for day 0, 10, 30 and 50 of the lactation, by means of the standard lactation curves. The daily yields are in Table 4.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="3" align = "left"|'''''Table 4. Measured and derived daily yields, used to calculate the record in progress in the example (ISLC).'''''
|- style="background-color:#efefef;"
|'''Day of lactation'''
|'''Milk (kg)'''
|'''Note'''
|-
|0
|25.9
|Predicted
|-
|10
|27.8
|Predicted
|-
|30
|31.7
|Predicted
|-
|35
|31.8
|Measured
|-
|50
|32.9
|Interpolated using standard lactation curve
|-
|65
|33.0
|Measured
|}
</center>

Next, the record in progress can be calculated by means of the formula for a cumulative yield as follows:

[(10 - 1) * 25.9 + (10+1) * 27.8] / 2 +

[(20 - 1) * 27.8 + (20+1) * 31.7] / 2 +

[(5 - 1) * 31.7 + (5+1) * 31.8] / 2 +

[(15 - 1) * 31.8 + (15+1) * 32.9] / 2 +

[(15 - 1) * 32.9 + (15+1) * 33.0] / 2 = 2005.3 kg.

This corresponds to the surface below the line through the predicted and measured daily yields (see Figure 1).
[[File:Figure1.png|center|thumb|621x621px|''Figure 1. Example of calculation of record in progress.'']]

=== Best prediction (BP) (VanRaden, 1997<ref>VanRaden, P.M. 1997. Lactation yields and accuracies computed from test day yields and (co)variances by best prediction. J. Dairy Sci. 80:3015-3022.</ref>) ===
Recorded milk weights are combined into a lactation record using standard selection index methods. Let vector y contain M1, M2, to Mn and let E('''y''') contain corresponding the expected values for each recorded day. The E(y) are obtained from standard lactation curves for the population or for the herd and should account for the cow's age and other environmental factors such as season, milking frequency, etc. The yields in '''y''' covary as a function of the recording interval between them (I). Diagonal elements in Var(y) are the population or herd variance for that recording day and off diagonals are obtained from autoregressive or similar functions such as Corr(M1, M2)=0.995I for first lactations or 0.992I for later lactations. Covariances of one observation with the lactation yield, for example Cov(M1, MY), are the sum of 305 individual covariances. E(MY) is the sum of 305 daily expected values. Lactation milk yield is then predicted as Equation 3:
[[File:Equation333333.png|none|thumb|640x640px]]
With best prediction, predicted milk yields have less variance than true milk yields. With TIM, estimated yields have more variance than true yields. The reason is that predicted yields are regressed toward the mean unless all 305 daily yields are observed. With best prediction, the predicted MY for a lactation without any observed yields is E(MY) which is the population or herd mean for a cow of that age and season. With TIM, the estimated MY is undefined if no daily yields are recorded.

Milk, fat, and protein yields can be processed separately using single-trait best prediction or jointly using multi-trait best prediction. Replacement of M1, M2, to Mn with F1, F2, to Fn or P1, P2, to Pn gives the single-trait predictions for fat or for protein. Multi-trait predictions require larger vectors and matrices but similar algebra. Products of trait correlations and autoregressive correlations, for example, may provide the needed covariances.

=== Multiple-Trait Procedure (MTP) (Schaeffer & Jamrozik, 1996<ref>Schaeffer, L.R., and J. Jamrozik. 1996. Multiple-trait prediction of lactation yields for dairy cows. J. Dairy Sci. 79:2044-2055.</ref>) ===
The Multiple-Trait Procedure predicts 305-d lactation yields for milk, fat, protein and SCS, incorporating information about standard lactation curves and covariances between milk, fat, and protein yields and SCS. Test day yields are weighted by their relative variances, and standard lactation curves of cows of similar breed, region, lactation number, age, and season of calving are used in the estimation of lactation curve parameters for each cow. The multiple-trait procedure can handle long intervals between test days, test days with milk only recorded, and can make 305-d predictions on the basis of just one test day record per cow. The procedure also lends itself to the calculation of peak yield, day of peak yield, yield persistency, and expected test-day yields, which could be useful management tools for a producer on a milk recording program.

The MTP method is based upon Wilmink's model in conjunction with an approach incorporating standard curve parameters for cows with the same production characteristics. Wilmink's function for one trait is given by Equation 4.

Equation 4. Wilmink function for one trait (MTP).

y = A + B''t'' ± C''exp'' (-0.05''t'') + ''e''

where y is yield on day t of lactation, A, B, and C are related to the shape of the lactation curve.

The parameters A, B, and C need to be estimated for each yield trait. The yield traits have high phenotypic correlations, and MTP would incorporate these correlations. Use of MTP would allow for the prediction of yields even if data were not available on each test day for a cow.

The vector of parameters to be estimated for one cow are designated:
[[File:Vectro.png|center|thumb]]
where M, F, and P represent milk, fat, and protein, respectively, and S represents somatic cell score. The vector c is to be estimated from the available test-day records. Let c0 represent the corresponding parameters estimated across all cows with the same production characteristics as the cow in question.

Let
[[File:Vector2.png|center|thumb]]

be the vector of yield traits and somatic cell scores on test ''k'' at day ''t'' of the lactation.

The incidence matrix, ''Xk'', is constructed as follows:
[[File:Vector3.png|center|thumb|558x558px]]

The MTP equations are:
[[File:Equation55555.png|none|thumb|560x560px]]
and ''n'' is the number of tests for that cow. ''Rk'' is a matrix of order 4 that contains the variances and covariances among the yields on ''kth'' test at day ''t'' of lactation. The elements of this matrix were derived from regression formulas based on fitting phenotypic variances and covariances of yields to models with ''t'' and ''t2'' as covariables. Thus, element ''ij'' of ''Rk'' would be determined by

rij(t) = ß0ij + ß1ij (t) + ß2ij (t2)

G is a 12 x 12 matrix containing variances and covariances among the parameters in '''ĉ''' and represents the cow to cow variation in these parameters, which includes genetic and permanent environmental effects, but ignores genetic covariances between cows. The parameters for '''''G''''' and '''''Rk''''' vary depending on the breed, but must be known. Initially, these matrices were allowed to vary by region of Canada in addition to breed, but this meant that there could exist two cows with identical production records on the same days in milk, but because one cow was in one region and the other cow was in another region, then the accuracy of their predictions would be different. This was considered to be too confusing for dairy producers, so that regional differences in variance-covariance matrices were ignored and one set of parameters would be used for all regions for a particular breed. Estimation of G is described later.

If a cow has a test, but only milk yield is reported, then

y’k(Mk 0 0 0)

and
[[File:And.png|center|thumb|540x540px]]

The inverse of '''''Rk''''' is the regular inverse of the nonzero submatrix within '''''Rk''''', ignoring the zero rows and columns. Thus, missing yields can be accommodated in MTP.

Accuracy of predicted 305-d lactation totals depends on the number of test-day records during the lactation and DIM associated with each test. Thus, any prediction procedure will require reliability figures to be reported with all predictions, especially if fewer tests at very irregular intervals are going to be frequent in milk recording. At the moment, an approximate procedure is applied that uses the inverse elements of '''(X’R-1X + G-1) -1.'''

==== 1.1 Example calculations ====
Four test day records on a 25 month old, Holstein cow calving in June from Ontario are given in the Table 5 below.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="7" align = "left"|'''''Table 5. Example test day data for a cow (MTP).'''''
|- style="background-color:#efefef;"
|'''Test no.'''
|'''DIM=''t'''''
|'''Exp(-0.05''t'')'''
|'''Milk (kg)'''
|'''Fat (kg)'''
|'''Protein (kg)'''
|'''SCS'''
|-
|1
|15
|0.47237
|28.8
|
|
|3.130
|-
|2
|54
|0.06721
|29.2
|1.12
|0.87
|2.463
|-
|3
|188
|0.000083
|23.7
|0.97
|0.78
|2.157
|-
|4
|250
|0.0000037
|20.8
|
|
|2.619
|}
</center>

Notice that two tests do not have fat and protein yields, and that intervals between tests are irregular and large. The vector of standard curve parameters based on all available comparable cow, is
[[File:Vector4.png|center|thumb]]
The R^(-1)_k matrices for each test day need to be constructed. These matrices are derived from regression equations. The equations for Holsteins were:
<center>
{| class="wikitable" style="text-align: center;"
|''rMM(t) =''
|71.0752 - 0.281201''t'' + 0.0004977''t2''
|-
|''rMF(t) =''
|2.4365 - 0.013274''t'' + 0.0000302''t2''
|-
|''rMP(t) =''
|2.0504 - 0.008286''t'' + 0.0000163''t2''
|-
|''rMS(t) =''
|<nowiki>-1.7993 + 0.013209</nowiki>''t'' - 0.000056''t2''
|-
|''rFF(t) =''
|0.1312 - 0.000725''t'' + 0.000001586''t2''
|-
|''rFP(t) =''
|0.0739 - 0.000386''t'' + 0.000000926''t2''
|-
|''rFS(t) =''
|<nowiki>- 0.0386 + 0.000292</nowiki>''t'' - 0.000001796''t2''
|-
|''rPP(t) =''
|0.066 - 0.000267''t'' + 0.0000005636''t2''
|-
|''rPS(t) =''
|<nowiki>- 0.0404 + 0.000369</nowiki>''t'' - 0.000001743''t2''
|-
|''rSS(t) =''
|3.0404 - 0.000083''t'' - 0.000006105''t2''
|}
</center>

The inverses of the residual variance-covariance matrices for yields for the four test days are as follows:
<center>
{| class="wikitable" style="text-align: center;"
|
|0.0151259
|0
|0
|0.0080354
|-
|'''R^(-1)_1''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0080354
|0
|0
|0.3334553
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.1685584
|0.345947
|<nowiki>-4.851935</nowiki>
|0.0254775
|-
|'''R^(-1)_2''' = =
|<nowiki>-0.345947</nowiki>
|26.830915
|<nowiki>-17.40281</nowiki>
|<nowiki>-0.041445</nowiki>
|-
|
|<nowiki>-4.851935</nowiki>
|<nowiki>-17.40281</nowiki>
|187.18579
|<nowiki>-0.584885</nowiki>
|-
|
|0.0254775
|<nowiki>-0.041445</nowiki>
|<nowiki>-0.584885</nowiki>
|0.3365425
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
|
|0.2620161
|0.1479068
|<nowiki>-7.943903</nowiki>
|0.0316069
|-
|'''R^(-1)_3''' = =
|0.1479068
|54.446977
|<nowiki>-56.01333</nowiki>
|0.3306741
|-
|
|<nowiki>-7.943903</nowiki>
|<nowiki>-56.01333</nowiki>
|317.9609
|<nowiki>-0.92601</nowiki>
|-
|
|0.0316069
|0.3306741
|<nowiki>-0.92601</nowiki>
|0.3654369
|}
{| class="wikitable" style="text-align: center;"
|

|0.0329465
|0
|0
|0.0251039
|-
|'''R^(-1)_4''' = =
|0
|0
|0
|0
|-
|
|0
|0
|0
|0
|-
|
|0.0251039
|0
|0
|0.3981981
|}

Inverse matrix G^(-1) of order 12 is the same for all cows of the same breed:

[[File:Left 6x6.jpg|center|thumb|600x600px|Inverse matrix G^(-1) of order 12]]

</center>
Note that many covariances between different parameters of the lactation curves have been set to zero. When all covariances were included, the prediction errors for individual cows were very large, possibly because the covariances were highly correlated to each other within and between traits. Including only covariances between the same parameter among traits gave much smaller prediction errors.

The elements of the MTP equations of order 12 for this cow are shown in partitioned format also:

'''X’R-1X ='''
<center>[[File:Elements of the MTP equations of order 12.jpg|center|thumb|600x600px|Elements of the MTP equations of order 12]]
</center>
[[File:Equation7.png|center|thumb|632x632px]]

The solution vector for this cow is
[[File:Equation6666.png|center|thumb]]

To predict 305-day yields, Y305
[[File:Equation7777.png|none|thumb|551x551px]]
Equation 6 is used separately for each trait (milk, fat, protein, and SCS). The results for this cow were 7456 kg milk, 301 kg fat, and 239 kg protein. The result for SCS is divided by 305 to give an average daily SCS of 2.477.
</div>
</div>

= Appendices =
== Appendix 1 - Adjustment factors to calculate 24-hour yields using the Liu method ==
<div class="mw-collapsible mw-collapsed">
<div>
In Table 6 the adjustment factors to calculate 24-hour yields, using the Liu method, can be found. The description of the Liu method can be found in [https://wiki.icar.org/index.php/Section_02_%E2%80%93_Cattle_Milk_Recording#Procedure_1:_Computing_24-hour_Yields Procedure 1 of Section 2.]
<center>
{| class="wikitable" style="text-align: center;"
| colspan="10" |'''''Table 1. Adjustment factors to calculate 24-hour yields using the Liu method. Milking time (MT) is either 1 (PM) or 2 (AM), i = parity class, j= milking interval class and k = stage of lactation class.'''''
|- style="background-color:#efefef;"
|'''MT'''
|'''i'''
|'''j'''
|'''k'''
| colspan="2" |'''Milk yield (DMY)'''
| colspan="2" |'''Fat yield (DFY)'''
| colspan="2" |'''Protein yield (DPY)'''
|-
| colspan="4" |
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|'''Intercept'''
|'''Slope'''
|-
|1
|1
|1
|1
|5.29333
|1.83283
|0.30911
|1.43518
|0.18984
|1.77461
|-
|1
|1
|1
|2
|4.17676
|1.97447
|0.2803
|1.56914
|0.12246
|2.00568
|-
|1
|1
|1
|3
|4.26476
|1.95945
|0.18826
|1.82468
|0.12624
|2.0137
|-
|1
|1
|1
|4
|3.41282
|2.01814
|0.25025
|1.64707
|0.12519
|1.99629
|-
|1
|1
|1
|5
|1.79548
|2.22665
|0.06578
|2.09515
|0.05249
|2.24065
|-
|1
|1
|1
|6
|3.7751
|1.95508
|0.12854
|1.93892
|0.11936
|2.00979
|-
|1
|1
|1
|7
|1.544
|2.1478
|0.06425
|2.06779
|0.0569
|2.13851
|-
|1
|1
|2
|1
|5.8584
|1.79409
|0.33193
|1.42953
|0.20756
|1.7288
|-
|1
|1
|2
|2
|5.45524
|1.84258
|0.32877
|1.43235
|0.21332
|1.74001
|-
|1
|1
|2
|3
|4.64052
|1.86706
|0.27155
|1.57017
|0.16439
|1.84539
|-
|1
|1
|2
|4
|2.86835
|2.06209
|0.18647
|1.79403
|0.10803
|2.0193
|-
|1
|1
|2
|5
|2.11336
|2.12055
|0.10435
|1.97206
|0.07193
|2.10651
|-
|1
|1
|2
|6
|2.00673
|2.0636
|0.1386
|1.83336
|0.06892
|2.06532
|-
|1
|1
|2
|7
|1.71752
|2.11269
|0.06501
|2.0379
|0.05569
|2.12881
|-
|1
|1
|3
|1
|2.80244
|2.02183
|0.17663
|1.72438
|0.11078
|1.96422
|-
|1
|1
|3
|2
|3.47396
|1.98268
|0.2135
|1.6805
|0.10471
|1.99092
|-
|1
|1
|3
|3
|2.81702
|2.04348
|0.20754
|1.71868
|0.1127
|1.98403
|-
|1
|1
|3
|4
|3.1989
|1.998
|0.21578
|1.6991
|0.10802
|1.99517
|-
|1
|1
|3
|5
|2.47055
|2.04826
|0.15418
|1.83151
|0.07492
|2.07547
|-
|1
|1
|3
|6
|1.923
|2.07728
|0.11783
|1.89678
|0.06457
|2.08391
|-
|1
|1
|3
|7
|1.85264
|2.0873
|0.13047
|1.86711
|0.071
|2.06917
|-
|1
|1
|4
|1
|2.75042
|1.96631
|0.24794
|1.61741
|0.09248
|1.95376
|-
|1
|1
|4
|2
|2.97505
|1.96711
|0.20029
|1.71842
|0.09381
|1.97081
|-
|1
|1
|4
|3
|2.33365
|2.02986
|0.17021
|1.79996
|0.07631
|2.03167
|-
|1
|1
|4
|4
|3.41505
|1.94107
|0.1845
|1.76799
|0.10989
|1.95456
|-
|1
|1
|4
|5
|2.67488
|1.97797
|0.13433
|1.85893
|0.09432
|1.97755
|-
|1
|1
|4
|6
|1.89907
|2.04841
|0.08715
|1.96251
|0.07132
|2.04225
|-
|1
|1
|4
|7
|1.80326
|2.03554
|0.1251
|1.86477
|0.06072
|2.04747
|-
|1
|1
|5
|1
|2.76763
|1.92863
|0.15754
|1.72474
|0.10187
|1.88749
|-
|1
|1
|5
|2
|3.36896
|1.92048
|0.2236
|1.64149
|0.12369
|1.8823
|-
|1
|1
|5
|3
|2.22763
|2.00452
|0.17614
|1.7474
|0.08019
|1.9782
|-
|1
|1
|5
|4
|2.44625
|1.97049
|0.17217
|1.74753
|0.0889
|1.94647
|-
|1
|1
|5
|5
|2.379
|1.97307
|0.15965
|1.76134
|0.0896
|1.94575
|-
|1
|1
|5
|6
|1.62948
|2.02491
|0.11021
|1.85546
|0.0852
|1.94593
|-
|1
|1
|5
|7
|1.45651
|2.0254
|0.07479
|1.92789
|0.05846
|2.00196
|-
|1
|1
|6
|1
|2.01088
|1.9497
|0.16548
|1.68143
|0.101
|1.85846
|-
|1
|1
|6
|2
|2.96605
|1.93064
|0.25841
|1.52566
|0.12097
|1.86061
|-
|1
|1
|6
|3
|2.2281
|1.96085
|0.19036
|1.69013
|0.08032
|1.9375
|-
|1
|1
|6
|4
|2.39473
|1.952
|0.17854
|1.72423
|0.06863
|1.97582
|-
|1
|1
|6
|5
|2.37955
|1.94127
|0.19579
|1.66419
|0.08447
|1.93156
|-
|1
|1
|6
|6
|0.36203
|2.12393
|0.14291
|1.75822
|0.03845
|2.04562
|-
|1
|1
|6
|7
|1.5702
|1.96794
|0.1336
|1.76796
|0.06449
|1.94829
|-
|1
|1
|7
|1
|3.93654
|1.82772
|0.2359
|1.61894
|0.15032
|1.76054
|-
|1
|1
|7
|2
|4.39662
|1.81581
|0.24969
|1.5881
|0.16909
|1.74794
|-
|1
|1
|7
|3
|3.78325
|1.82778
|0.19228
|1.71802
|0.12368
|1.8268
|-
|1
|1
|7
|4
|3.39116
|1.86302
|0.1969
|1.71838
|0.12282
|1.848
|-
|1
|1
|7
|5
|3.20111
|1.83255
|0.09893
|1.86309
|0.1044
|1.84257
|-
|1
|1
|7
|6
|3.75639
|1.78665
|0.25205
|1.56174
|0.14105
|1.76802
|-
|1
|1
|7
|7
|1.42153
|1.95649
|0.09226
|1.85882
|0.04636
|1.96245
|-
|1
|1
|8
|1
|2.3454
|1.90436
|0.14321
|1.77423
|0.10703
|1.82306
|-
|1
|1
|8
|2
|3.97557
|1.82746
|0.26651
|1.58374
|0.15298
|1.76385
|-
|1
|1
|8
|3
|4.26939
|1.80503
|0.22918
|1.64925
|0.12924
|1.81061
|-
|1
|1
|8
|4
|2.90779
|1.89861
|0.18578
|1.73968
|0.13948
|1.79679
|-
|1
|1
|8
|5
|2.8265
|1.87632
|0.19374
|1.67929
|0.12377
|1.80944
|-
|1
|1
|8
|6
|2.26312
|1.87397
|0.09917
|1.82528
|0.08819
|1.84453
|-
|1
|1
|8
|7
|0.31382
|2.04402
|0.05049
|1.95773
|0.02612
|1.99012
|-
|1
|2
|1
|1
|4.63752
|1.99615
|0.31102
|1.58962
|0.16637
|1.96686
|-
|1
|2
|1
|2
|5.56226
|1.91521
|0.26761
|1.64342
|0.16973
|1.94145
|-
|1
|2
|1
|3
|4.51983
|1.96962
|0.26221
|1.65088
|0.12245
|2.03857
|-
|1
|2
|1
|4
|4.51563
|1.93033
|0.18468
|1.80715
|0.15252
|1.94807
|-
|1
|2
|1
|5
|2.60334
|2.07338
|0.16011
|1.81257
|0.09892
|2.05493
|-
|1
|2
|1
|6
|2.86068
|1.98457
|0.15381
|1.79197
|0.08619
|2.04046
|-
|1
|2
|1
|7
|1.6596
|2.11753
|0.13089
|1.83687
|0.09908
|1.96479
|-
|1
|2
|2
|1
|3.94656
|2.03607
|0.23716
|1.6988
|0.19559
|1.88765
|-
|1
|2
|2
|2
|4.20525
|1.98621
|0.3553
|1.46663
|0.1657
|1.92175
|-
|1
|2
|2
|3
|3.31729
|2.04589
|0.29682
|1.57761
|0.12491
|2.00945
|-
|1
|2
|2
|4
|1.95977
|2.13926
|0.16059
|1.79846
|0.06713
|2.12835
|-
|1
|2
|2
|5
|1.49014
|2.14889
|0.10057
|1.90772
|0.05279
|2.14047
|-
|1
|2
|2
|6
|0.82235
|2.22517
|0.07573
|1.94963
|0.04014
|2.17549
|-
|1
|2
|2
|7
|1.53608
|2.08972
|0.11472
|1.81148
|0.0676
|2.03957
|-
|1
|2
|3
|1
|3.85525
|2.00429
|0.27991
|1.62403
|0.12863
|1.98973
|-
|1
|2
|3
|2
|4.1508
|1.9852
|0.3635
|1.47515
|0.13952
|1.97074
|-
|1
|2
|3
|3
|3.31493
|2.02332
|0.31131
|1.55183
|0.11703
|2.00696
|-
|1
|2
|3
|4
|2.47354
|2.0652
|0.20828
|1.71637
|0.09402
|2.04147
|-
|1
|2
|3
|5
|1.68517
|2.08809
|0.14418
|1.80246
|0.06917
|2.05808
|-
|1
|2
|3
|6
|1.316
|2.12714
|0.11206
|1.87179
|0.04723
|2.12486
|-
|1
|2
|3
|7
|0.4841
|2.20538
|0.04633
|2.02915
|0.02369
|2.18113
|-
|1
|2
|4
|1
|2.82623
|2.01819
|0.25826
|1.69268
|0.11251
|1.97665
|-
|1
|2
|4
|2
|3.24039
|1.9811
|0.36283
|1.50648
|0.11719
|1.96246
|-
|1
|2
|4
|3
|2.4545
|2.03386
|0.19627
|1.75339
|0.09698
|2.00807
|-
|1
|2
|4
|4
|2.46446
|2.01626
|0.17827
|1.76414
|0.08026
|2.02912
|-
|1
|2
|4
|5
|2.11339
|2.00724
|0.14884
|1.77964
|0.07749
|2.00585
|-
|1
|2
|4
|6
|1.51141
|2.04563
|0.11559
|1.82474
|0.06194
|2.02586
|-
|1
|2
|4
|7
|0.95936
|2.09963
|0.07044
|1.95281
|0.03645
|2.0993
|-
|1
|2
|5
|1
|3.36561
|1.97323
|0.2649
|1.65361
|0.13019
|1.92402
|-
|1
|2
|5
|2
|3.66222
|1.95479
|0.35065
|1.51028
|0.14652
|1.89882
|-
|1
|2
|5
|3
|3.20442
|1.96165
|0.28676
|1.58823
|0.12031
|1.93028
|-
|1
|2
|5
|4
|1.78673
|2.0426
|0.17183
|1.75198
|0.0678
|2.02025
|-
|1
|2
|5
|5
|1.61868
|2.01988
|0.11914
|1.80878
|0.06624
|1.99283
|-
|1
|2
|5
|6
|1.30123
|2.02218
|0.10515
|1.80653
|0.05345
|2.00292
|-
|1
|2
|5
|7
|0.65695
|2.08269
|0.06835
|1.89102
|0.0332
|2.0525
|-
|1
|2
|6
|1
|2.3773
|1.9669
|0.24867
|1.6336
|0.08319
|1.94741
|-
|1
|2
|6
|2
|2.82556
|1.95506
|0.31731
|1.51798
|0.12008
|1.89324
|-
|1
|2
|6
|3
|2.7235
|1.94883
|0.30621
|1.5177
|0.09365
|1.93764
|-
|1
|2
|6
|4
|1.77727
|1.98273
|0.17989
|1.69341
|0.07314
|1.95161
|-
|1
|2
|6
|5
|0.81041
|2.05295
|0.13961
|1.74391
|0.04468
|2.01091
|-
|1
|2
|6
|6
|0.72188
|2.0465
|0.09874
|1.79927
|0.03137
|2.03309
|-
|1
|2
|6
|7
|1.21598
|1.97942
|0.07065
|1.87211
|0.04484
|1.98491
|-
|1
|2
|7
|1
|3.55054
|1.89128
|0.27402
|1.61031
|0.10827
|1.89085
|-
|1
|2
|7
|2
|5.0062
|1.81574
|0.3119
|1.54857
|0.18009
|1.76865
|-
|1
|2
|7
|3
|3.95204
|1.84947
|0.30465
|1.53907
|0.16048
|1.789
|-
|1
|2
|7
|4
|2.36233
|1.9168
|0.18751
|1.70412
|0.09531
|1.88355
|-
|1
|2
|7
|5
|1.48851
|1.94443
|0.09973
|1.81041
|0.05904
|1.92497
|-
|1
|2
|7
|6
|1.22525
|1.94454
|0.06617
|1.87082
|0.05516
|1.91259
|-
|1
|2
|7
|7
|1.13847
|1.93756
|0.08109
|1.83388
|0.04706
|1.93165
|-
|1
|2
|8
|1
|4.09874
|1.87708
|0.20312
|1.73434
|0.15506
|1.83083
|-
|1
|2
|8
|2
|4.66403
|1.84302
|0.31808
|1.56093
|0.18049
|1.78288
|-
|1
|2
|8
|3
|3.24375
|1.89351
|0.2827
|1.59546
|0.13583
|1.83427
|-
|1
|2
|8
|4
|2.24175
|1.92084
|0.17795
|1.72611
|0.09636
|1.87438
|-
|1
|2
|8
|5
|1.63783
|1.93625
|0.1225
|1.78642
|0.0659
|1.90934
|-
|1
|2
|8
|6
|2.01753
|1.89095
|0.13742
|1.74752
|0.08289
|1.86553
|-
|1
|2
|8
|7
|0.97568
|1.97215
|0.05926
|1.88807
|0.04057
|1.95672
|-
|2
|1
|1
|1
|3.44076
|1.73133
|0.27759
|1.55037
|0.13323
|1.68913
|-
|2
|1
|1
|2
|4.99596
|1.64527
|0.2322
|1.58033
|0.17533
|1.62422
|-
|2
|1
|1
|3
|3.83372
|1.68144
|0.25087
|1.52033
|0.14525
|1.66706
|-
|2
|1
|1
|4
|3.87034
|1.68102
|0.20979
|1.60153
|0.13627
|1.68885
|-
|2
|1
|1
|5
|1.76134
|1.80424
|0.15241
|1.70485
|0.06231
|1.81524
|-
|2
|1
|1
|6
|0.79304
|1.89072
|0.09906
|1.80312
|0.03277
|1.89435
|-
|2
|1
|1
|7
|1.43535
|1.80614
|0.0593
|1.81589
|0.0407
|1.85002
|-
|2
|1
|2
|1
|3.72284
|1.68499
|0.19226
|1.66567
|0.1237
|1.66453
|-
|2
|1
|2
|2
|4.42667
|1.66508
|0.24314
|1.55652
|0.14361
|1.66251
|-
|2
|1
|2
|3
|2.7019
|1.75871
|0.32717
|1.38452
|0.11056
|1.72312
|-
|2
|1
|2
|4
|2.41538
|1.75937
|0.14575
|1.68355
|0.09038
|1.74138
|-
|2
|1
|2
|5
|1.65412
|1.81649
|0.13926
|1.70623
|0.0597
|1.81378
|-
|2
|1
|2
|6
|2.0843
|1.7735
|0.21052
|1.57508
|0.07244
|1.78566
|-
|2
|1
|2
|7
|1.43238
|1.80651
|0.08031
|1.78712
|0.05269
|1.81727
|-
|2
|1
|3
|1
|2.45314
|1.77068
|0.18152
|1.73443
|0.07657
|1.78025
|-
|2
|1
|3
|2
|3.01217
|1.70966
|0.19388
|1.66175
|0.05624
|1.80606
|-
|2
|1
|3
|3
|2.09997
|1.74945
|0.14493
|1.68277
|0.05446
|1.7922
|-
|2
|1
|3
|4
|2.36683
|1.71741
|0.12244
|1.71407
|0.06775
|1.75721
|-
|2
|1
|3
|5
|1.56776
|1.75755
|0.08776
|1.76946
|0.04244
|1.79675
|-
|2
|1
|3
|6
|1.63824
|1.75452
|0.09422
|1.76794
|0.04181
|1.80604
|-
|2
|1
|3
|7
|0.74114
|1.83421
|0.08039
|1.78306
|0.02347
|1.85596
|-
|2
|1
|4
|1
|1.47047
|1.78588
|0.17271
|1.69379
|0.06511
|1.74985
|-
|2
|1
|4
|2
|2.22168
|1.72985
|0.20701
|1.59429
|0.08178
|1.71455
|-
|2
|1
|4
|3
|2.50108
|1.69618
|0.16828
|1.61962
|0.08598
|1.70516
|-
|2
|1
|4
|4
|1.97141
|1.7202
|0.1446
|1.66357
|0.06856
|1.73201
|-
|2
|1
|4
|5
|1.17054
|1.75879
|0.1172
|1.69234
|0.04624
|1.75806
|-
|2
|1
|4
|6
|1.74755
|1.70968
|0.12562
|1.67603
|0.0629
|1.72333
|-
|2
|1
|4
|7
|0.52482
|1.80155
|0.07345
|1.75615
|0.02671
|1.79288
|-
|2
|1
|5
|1
|1.76464
|1.76219
|0.24301
|1.59094
|0.07156
|1.73136
|-
|2
|1
|5
|2
|1.99594
|1.73438
|0.1984
|1.5954
|0.06489
|1.73449
|-
|2
|1
|5
|3
|1.8804
|1.72362
|0.13019
|1.67977
|0.06783
|1.71916
|-
|2
|1
|5
|4
|1.83337
|1.71477
|0.11197
|1.70244
|0.05764
|1.73194
|-
|2
|1
|5
|5
|1.49752
|1.72615
|0.13128
|1.65461
|0.04656
|1.7433
|-
|2
|1
|5
|6
|1.3042
|1.7305
|0.07173
|1.75315
|0.04482
|1.7399
|-
|2
|1
|5
|7
|2.00868
|1.67669
|0.12298
|1.64761
|0.09175
|1.64669
|-
|2
|1
|6
|1
|0.84993
|1.75972
|0.12918
|1.74026
|0.0328
|1.74802
|-
|2
|1
|6
|2
|1.93666
|1.67406
|0.16606
|1.59943
|0.04535
|1.7106
|-
|2
|1
|6
|3
|2.12115
|1.64964
|0.19988
|1.50821
|0.05229
|1.68986
|-
|2
|1
|6
|4
|0.68831
|1.73901
|0.09674
|1.6838
|0.01696
|1.75787
|-
|2
|1
|6
|5
|1.13081
|1.69479
|0.06413
|1.72559
|0.04936
|1.67757
|-
|2
|1
|6
|6
|0.5893
|1.72537
|0.02598
|1.80138
|0.01591
|1.74082
|-
|2
|1
|6
|7
|0.72519
|1.71955
|0.03157
|1.78405
|0.02889
|1.71972
|-
|2
|1
|7
|1
|1.85937
|1.66064
|0.2416
|1.49676
|0.06807
|1.63599
|-
|2
|1
|7
|2
|1.8527
|1.64892
|0.2374
|1.43845
|0.06336
|1.6431
|-
|2
|1
|7
|3
|1.56905
|1.66084
|0.15434
|1.55598
|0.04336
|1.68109
|-
|2
|1
|7
|4
|0.74968
|1.69857
|0.13496
|1.56636
|0.02871
|1.6933
|-
|2
|1
|7
|5
|1.08222
|1.65925
|0.10847
|1.613
|0.03305
|1.67829
|-
|2
|1
|7
|6
|1.1124
|1.68059
|0.14267
|1.57525
|0.04416
|1.6776
|-
|2
|1
|7
|7
|0.88031
|1.6751
|0.10534
|1.60483
|0.04216
|1.66444
|-
|2
|1
|8
|1
|0.62802
|1.72402
|0.19225
|1.54631
|0.03247
|1.69368
|-
|2
|1
|8
|2
|0.83902
|1.68303
|0.15492
|1.53421
|0.05922
|1.61411
|-
|2
|1
|8
|3
|1.33727
|1.63407
|0.19835
|1.43309
|0.05874
|1.61141
|-
|2
|1
|8
|4
|1.06381
|1.64762
|0.11026
|1.58762
|0.04019
|1.64574
|-
|2
|1
|8
|5
|1.13714
|1.61716
|0.13322
|1.53166
|0.05648
|1.59149
|-
|2
|1
|8
|6
|1.19134
|1.60463
|0.11089
|1.54864
|0.06258
|1.56912
|-
|2
|1
|8
|7
|1.58872
|1.60204
|0.066
|1.64659
|0.04748
|1.63282
|-
|2
|2
|1
|1
|3.46775
|1.78609
|0.28956
|1.68515
|0.15003
|1.72171
|-
|2
|2
|1
|2
|5.69879
|1.67614
|0.3725
|1.5045
|0.19774
|1.64659
|-
|2
|2
|1
|3
|5.18985
|1.66571
|0.40124
|1.40574
|0.17828
|1.65793
|-
|2
|2
|1
|4
|3.43435
|1.74182
|0.20332
|1.66994
|0.11075
|1.76221
|-
|2
|2
|1
|5
|2.48643
|1.76219
|0.13714
|1.7396
|0.09636
|1.75624
|-
|2
|2
|1
|6
|1.41151
|1.82292
|0.15415
|1.6725
|0.06549
|1.80013
|-
|2
|2
|1
|7
|0.9096
|1.8409
|0.08811
|1.7823
|0.03467
|1.85275
|-
|2
|2
|2
|1
|1.85358
|1.83615
|0.28355
|1.64765
|0.06055
|1.83138
|-
|2
|2
|2
|2
|3.81188
|1.74978
|0.25972
|1.62799
|0.11238
|1.7646
|-
|2
|2
|2
|3
|3.16717
|1.76679
|0.29832
|1.53409
|0.09407
|1.78959
|-
|2
|2
|2
|4
|2.33664
|1.78934
|0.22694
|1.60101
|0.07273
|1.80371
|-
|2
|2
|2
|5
|2.01675
|1.79303
|0.10664
|1.79792
|0.06062
|1.8184
|-
|2
|2
|2
|6
|1.80809
|1.80081
|0.13659
|1.70935
|0.07335
|1.79213
|-
|2
|2
|2
|7
|1.01661
|1.8295
|0.0548
|1.84688
|0.03414
|1.84213
|-
|2
|2
|3
|1
|2.01474
|1.8142
|0.21867
|1.74325
|0.05359
|1.83088
|-
|2
|2
|3
|2
|3.53989
|1.71985
|0.28196
|1.60868
|0.10823
|1.73763
|-
|2
|2
|3
|3
|3.38412
|1.69907
|0.27409
|1.56164
|0.11042
|1.71397
|-
|2
|2
|3
|4
|2.2171
|1.74622
|0.16076
|1.70107
|0.07372
|1.75906
|-
|2
|2
|3
|5
|1.11799
|1.80944
|0.11087
|1.75678
|0.03792
|1.81891
|-
|2
|2
|3
|6
|1.40464
|1.76033
|0.10048
|1.72933
|0.05342
|1.75745
|-
|2
|2
|3
|7
|0.11328
|1.8972
|0.04052
|1.87101
|0.00787
|1.88753
|-
|2
|2
|4
|1
|2.59777
|1.74476
|0.28154
|1.66509
|0.10763
|1.71072
|-
|2
|2
|4
|2
|3.53853
|1.69511
|0.38311
|1.46839
|0.13243
|1.66523
|-
|2
|2
|4
|3
|2.80538
|1.70587
|0.26686
|1.55787
|0.1126
|1.68024
|-
|2
|2
|4
|4
|2.18191
|1.72068
|0.18333
|1.65612
|0.085
|1.71029
|-
|2
|2
|4
|5
|1.23383
|1.7716
|0.12824
|1.71179
|0.04845
|1.76628
|-
|2
|2
|4
|6
|0.85652
|1.79279
|0.0763
|1.79314
|0.03563
|1.78528
|-
|2
|2
|4
|7
|0.97995
|1.77178
|0.0797
|1.7577
|0.03846
|1.77043
|-
|2
|2
|5
|1
|2.47016
|1.74985
|0.32061
|1.60073
|0.10455
|1.71058
|-
|2
|2
|5
|2
|3.76194
|1.68979
|0.32787
|1.54675
|0.11781
|1.69109
|-
|2
|2
|5
|3
|2.61421
|1.70766
|0.20307
|1.64866
|0.08315
|1.71378
|-
|2
|2
|5
|4
|1.6809
|1.74028
|0.16795
|1.66491
|0.06202
|1.73305
|-
|2
|2
|5
|5
|1.31241
|1.75722
|0.14383
|1.68302
|0.05338
|1.74562
|-
|2
|2
|5
|6
|1.66563
|1.71781
|0.12721
|1.69231
|0.06147
|1.72101
|-
|2
|2
|5
|7
|0.87471
|1.74991
|0.07882
|1.71706
|0.04173
|1.73246
|-
|2
|2
|6
|1
|1.70055
|1.72832
|0.20839
|1.67759
|0.06001
|1.71779
|-
|2
|2
|6
|2
|3.20558
|1.65143
|0.33676
|1.47797
|0.09642
|1.6546
|-
|2
|2
|6
|3
|1.5827
|1.71538
|0.19719
|1.62038
|0.05324
|1.71254
|-
|2
|2
|6
|4
|1.7692
|1.69473
|0.14854
|1.66225
|0.05758
|1.69946
|-
|2
|2
|6
|5
|1.33003
|1.70542
|0.10726
|1.69398
|0.04565
|1.7096
|-
|2
|2
|6
|6
|1.01266
|1.71155
|0.09376
|1.70285
|0.04005
|1.70822
|-
|2
|2
|6
|7
|0.9856
|1.70091
|0.06454
|1.73063
|0.0394
|1.69796
|-
|2
|2
|7
|1
|2.02441
|1.67788
|0.30435
|1.5407
|0.08673
|1.63673
|-
|2
|2
|7
|2
|1.43949
|1.71143
|0.30098
|1.47963
|0.06527
|1.67295
|-
|2
|2
|7
|3
|1.68946
|1.66442
|0.24777
|1.47116
|0.06594
|1.64834
|-
|2
|2
|7
|4
|1.10967
|1.68591
|0.15663
|1.60109
|0.04949
|1.67069
|-
|2
|2
|7
|5
|0.77866
|1.70882
|0.11248
|1.64389
|0.03402
|1.70215
|-
|2
|2
|7
|6
|0.67502
|1.69719
|0.10289
|1.62419
|0.03507
|1.67744
|-
|2
|2
|7
|7
|0.65216
|1.70336
|0.05545
|1.73388
|0.02233
|1.72102
|-
|2
|2
|8
|1
|1.33877
|1.67358
|0.18369
|1.64385
|0.06055
|1.63818
|-
|2
|2
|8
|2
|0.71697
|1.71038
|0.25461
|1.49037
|0.04798
|1.66397
|-
|2
|2
|8
|3
|2.13197
|1.62429
|0.2393
|1.47673
|0.08136
|1.6065
|-
|2
|2
|8
|4
|1.16932
|1.66188
|0.13759
|1.60108
|0.0463
|1.64856
|-
|2
|2
|8
|5
|1.48369
|1.62387
|0.12547
|1.58988
|0.06919
|1.5925
|-
|2
|2
|8
|6
|1.18879
|1.65442
|0.10031
|1.62813
|0.07392
|1.58846
|-
|2
|2
|8
|7
|0.58052
|1.68546
|0.02696
|1.7382
|0.01982
|1.70519
|}
</center>
</div>
</div>

== Appendix 2 - Renewed estimation method for 24-hour fat percentage in AM/PM milk recording scheme ==
<div class="mw-collapsible mw-collapsed">
<div>
=== Abstract ===
Based on comments on imprecision of the estimation method for 24-hour fat % in AM/PM milk recording schemes the regression formula was extended and re-estimated. Non-linearity for the existing effects of protein % of the milk sample, interval before sampling, milk amount of sample, milk amount of previous milking and interval before the previous milking was incorporated by using polynomials. Extensions were made by adding the effects of time of sampling, parity and month of sampling as class variables and lactation stage as polynomial. In total a reduction of the standard deviation of the difference between true and estimated 24-hour fat % of 2.4% was reached (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

'''''Keywords''''': estimation, fat %, AM/PM.

=== Introduction ===
The AM/PM milk recording routine is based on only one morning (a.m.) or evening (p.m.) milk sample which are collected in an alternating way. A condition to take part in this AM/PM milk recording in The Netherlands is that on farm electronic milk measurements (EMM) are available. EMM-data consists of time of milking and milk quantity of every milking. Based on one milk sample and the EMM-data the 24-hour fat % is estimated (Peeters & Galesloot, 2002<ref name=":2">Peeters, R. and P. Galesloot, 2002.Estimating daily fat yield from a single milking on test day for herds with a robotic milking system. J. Dairy Sci. 85, 682-688.</ref>). Also for farms with an automatic milking system (AMS) this estimation is used when only one milk sample is available for analysis on milk composition.

Based on comments from farmers on fluctuations in 24-hour fat % preliminary research was conducted. This showed that the current estimation caused an underestimation of 24-hour fat % based on an a.m.-sample of 0.09% while the estimate based on a p.m.-sample was overestimated by 0.05%. Possible causes for this fluctuation are differences in milk-fat synthesis between day- and night-time as was shown by Gilbert et al. (1972) <ref>Gilbert, G.R., G.L. Hargrove and M. Kroger, 1972. Diurnal variations in milk yield, fat yield, milk fat % and milk protein % by the test interval method. J. Dairy Sci. 56, 409-410.</ref>and Lee & Wardorp (1984)<ref>Lee, A.J. and Wardorp, 1984. Predicting daily milk yield, fat percent, and protein percent from morning or afternoon tests. J. Dairy Sci. 67, 351-360.</ref>. Other factors of imprecision in the current estimation can be caused by lactation stage and parity, two factors that are accounted for in the method of Liu et al. (2000)<ref>Liu, Z., R. Reents, F. Reinhardt and K Kuwan, 2000. Approaches to estimating daily yield from single milk testing schemes and use of a.m.-p.m. records in test-day model genetic evaluation in dairy cattle. J. Dairy Sci. 83, 2672-2682.</ref>.

The objective of this research is to re-estimate the regression formula which is used to estimate the 24-hour fat %s in AM/PM milk recording and AMS recordings with only one sample. By testing for non-linearity of current effects and introducing new explanatory variables the aim is to increase the accuracy of the estimated 24-hour fat %.

=== Material and Methods ===
The data needed for the objective had to meet a number of criteria. The most important criteria were that the data comprised:

* differences in interval between milking times;
* different milking times;
* multiple samples per cow per herd test date;
* milking time and quantity of all milkings;

Only data of farms that use an AMS met all of these criteria. Therefore the research was conducted on data of all farms that used an AMS from January 20th 2001 until July 1st 2004. Records with only one sample per herd test date were excluded from the analysis.

In order to estimate as well as validate the new regression formula the each herd test date was assigned at random into two separate datasets. Dataset 1 was used for estimation and contained 371.528 samplings on 50.591 cows on 537 farms. Dataset 2 was used for validation and contained 371.885 milkings on 50.643 cows on 538 farms. Some characteristics of variables of both datasets are presented in Table 1.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="5" |'''''Table 1. Characteristics of variables in dataset 1 (estimation) and dataset 2 (validation).'''''
|-
| rowspan="2" |'''Variable'''
| colspan="2" |'''Dataset 1 (estimation)'''
| colspan="2" |'''Dataset 2 (validation)'''
|-
|'''Mean'''
|'''Std'''
|'''Mean'''
|'''Std'''
|-
|Sample milk amount (kg)
|10.1
|3.1
|10.1
|3.1
|-
|Sample fat (%)
|4.40
|0.76
|4.41
|0.76
|-
|Sample protein (%)
|3.49
|0.35
|3.49
|0.35
|-
|Time at sampling
|12.29
|7.24
|12.31
|7.24
|-
|Interval before sample (min)
|520
|154
|521
|155
|-
|Interval before prev. milking (min)
|526
|158
|527
|159
|}
</center>

=== Methods ===
The analysis started with the currently used regression formula which uses the effects: fat %, protein %, milk amount of sampling, interval before sampling, milk amount of the previous milking and interval before the previous milking (Peeters & Galesloot, 2002<ref name=":2" />). All these effects are considered to be linear. As an extra check of the data this regression formula was re-estimated and compared to the currently used regression formula. In order to estimate the regression formula first of all the 24-hour fat % was determined by using a weighted average of all milk samples for that cow on that herd test date.

Subsequently, a number of changes to the regression formula were tested for their effect on the accuracy of the 24-hour fat %. The changes that are tested are:

# non-linearity of the current effects;
# effect of time at sampling;
# effect of lactation stage;
# effect of parity;
# month of milk recording;

The effects were all tested in a similar way by plotting the residuals of the regression formula without the effect that is tested to the tested effect. Based on this plot a possible relation between residual and effect becomes clear and the best way of incorporating the effect is shown. The conclusion if an effect had a positive effect on the accuracy of the regression formula was based on the standard deviation of the difference between estimated and true 24-hour fat %. Also the correlation between the two fat %s and the b-factor (regression coefficient) of the linear regression between the two fat %s were considered.

=== Results ===
The regression coefficients of the re-estimated regression formula differed slightly from the estimates by Peeters & Galesloot (2002)<ref name=":1" />, probably due to the different dataset.

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %.
[[File:Imagefig1.png|center|thumb|''Figure 1a: Average residual per class for the variables sample fat %'']]
[[File:Imagefig1b.png|center|thumb|''Figure 1b: Sample protein %'' ]]
[[File:Imagefig1c.png|center|thumb|''Figure 1c : Interval before sampling'']]
[[File:Imagefig1d.png|center|thumb|''Figure 1d : Interval before previous milking'']]
[[File:Imagefig1e.png|center|thumb|''Figure 1e : Sample milk amount'']]
[[File:Imagefig1f.png|center|thumb|''Figure 1f: Milk amount before sampling'']]

Figure 1a to 1f show the effect of the variables in the regression formula on the difference between the true and estimated 24-hour fat %. Of all variables, only fat % of the milk sample (Figure 1a) seemed to be linear. A 2nd order polynomial fitted the interval before the previous milking. The other variables, i.e. protein % of the milk sample, interval before sampling, milk amount of sample and milk amount of the previous milking were described by a 3rd order polynomial. For all variables except fat % of the sample higher order polynomials were found significant. This however was caused by the large amount of data and no longer a possible biological effect since it also had no effect on the accuracy of the estimation.

The effect of time of sampling showed a large amount of variability over time. Using a polynomial to fit the data was therefore difficult. Estimation of the effect by hourly intervals was a good alternative as is shown in Figure 2. Lactation stage had mainly an effect in the first 50 days of lactation as is shown by Figure 3. A 3rd order polynomial fitted the data properly.
[[File:Imagefig2.png|center|thumb|''Figure 2. Average residual per class for time of sampling (minutes after midnight).'']]
[[File:Imagefig33.png|center|thumb|''Figure 3. Average residual per class for lactation stage (days).'']]

The effects of parity and month of milk sampling were both considered as class variables. For parity the effects of parity 1 to 6 and 7 or higher were considered. Table 2 shows that mainly for the lower parities the estimated 24-hour fat % was overestimated. Also the months May to October, usually the pasture period, showed an overestimation of 24-hour fat %.
<center>
{| class="wikitable" style="text-align: center;"
| colspan="4" |'''''Table 2. Effect of parity and month of sampling on estimated 24-hour fat % (*100).'''''
|-
|'''Parity'''
|'''Estimate'''
|'''Month of sampling'''
|'''Estimate'''
|-
|1
|<nowiki>-6.58</nowiki>
|January
|<nowiki>-0.24</nowiki>
|-
|2
|<nowiki>-3.56</nowiki>
|February
|<nowiki>-0.28</nowiki>
|-
|3
|<nowiki>-1.42</nowiki>
|June
|<nowiki>-0.54</nowiki>
|-
|4
|<nowiki>-0.48</nowiki>
|April
|<nowiki>-0.27</nowiki>
|-
|5
|<nowiki>-0.35</nowiki>
|May
|<nowiki>-2.07</nowiki>
|-
|6
|<nowiki>-0.35</nowiki>
|June
|<nowiki>-3.36</nowiki>
|-
|7+
|<nowiki>-0.00</nowiki>
|July
|<nowiki>-4.32</nowiki>
|-
|
|
|August
|<nowiki>-5.52</nowiki>
|-
|
|
|September
|<nowiki>-4.74</nowiki>
|-
|
|
|October
|<nowiki>-2.24</nowiki>
|-
|
|
|November
|<nowiki>-0.97</nowiki>
|-
|
|
|December
|<nowiki>-0.00</nowiki>
|}
</center>
<center>
{| class="wikitable" style="text-align: center;"
| colspan="6" |'''''Table 3. Statistics of the difference between true and estimated 24-hour fat % for six regression formulas (current, re-estimated + five steps), each also including preceding steps.'''''
|-
|style="text-align: left;"|'''Regression'''
|'''Std.'''
|'''Min'''
|'''Max'''
|'''Cor'''
|'''b-factor'''
|-
|style="text-align: left;"|Current, re-estimated
|0.2856
|<nowiki>-1.840</nowiki>
|2.224
|0.898
|0.807
|-
|style="text-align: left;"|Non-linearity
|0.2820
|<nowiki>-1.890 </nowiki>
|2.198
|0.901
|0.812
|-
|style="text-align: left;"|Time of sampling
|0.2817
|<nowiki>-1.877 </nowiki>
|2.211
|0.901
|0.813
|-
|style="text-align: left;"|Lactation stage
|0.2803
|<nowiki>-1.883 </nowiki>
|2.196
|0.902
|0.814
|-
|style="text-align: left;"|Parity
|0.2794
|<nowiki>-1.887 </nowiki>
|2.179
|0.903
|0.816
|-
|style="text-align: left;"|Month of sampling
|0.2788
|<nowiki>-1.868 </nowiki>
|2.175
|0.903
|0.817
|}
</center>

Table 3 shows some statistics of the difference between the true and estimated 24-hour fat % based on dataset 2 (validation) of the different regression formulas. Each of the five changes to the regression formula had a (minor) positive effect on either the standard deviation of the difference between the true and estimated 24-hour fat % (Std.), the correlation (Cor) between the two fat %s, the b-factor of the linear regression between the two fat %s or a combination of the these. All changes together reduced the standard deviation with 2.4% from 0.2856 to 0.2788, increased the correlation from 0.898 to 0.903 and increased the b-factor from 0.807 to 0.817.

=== Conclusions ===
The regression formula to estimate the 24-hour fat % based on one milk sample was improved. Improvements were first of all considering non-linearity of the variables by using polynomials for protein % of the milk sample (3rd order), interval before sampling (3rd order), milk amount of sample (3rd order), milk amount of previous milking (3rd order) and interval before the previous milking (2nd order). Secondly, adding the effects of time of sampling (class variable), lactation stage (3rd order polynomial), parity (class variable) and month of sampling (class variable) gave a further reduction of the difference between true and estimated 24-hour fat %. The total reduction in standard deviation of the difference between true and estimated 24-hour fat % is 2.4% (0.2856 to 0.2788). The correlation between the two fat %s increased from 0.898 to 0.903, the b-factor of the linear regression between the two fat %s increased from 0.807 to 0.817.

== Appendix 3 - A unified Python implementation of standardized 305 day yield calculation methods ==
The ICAR guideline is translated into an open-source Python package that can serve as a reference implementation for 305-day yield calculation. In addition to implementing the methods described in the original guideline (with the exception of the multi-trait method, which will be added in future work), the package incorporates 14 lactation-curve models, including traditional parametric models, Bayesian fitting approaches, and an AI-based model. The package also provides tools to derive biologically relevant lactation characteristics such as time to peak, peak yield, cumulative yield, and persistency. The package is publicly available through PyPI and can be installed directly using pip install lactationcurve (van Leerdam et al., 2026). Extensive documentation was developed alongside the package to improve transparency and reproducibility [https://bovi-analytics.github.io/bovi/lactationcurve.html https://bovi-analytics.github.io/bovi/lactationcurve.html.]

Through a companioning website (https://tools.bovi-analytics.org<nowiki/>/), users can upload milk-recording data in CSV format, fit and visualize the implemented lactation-curve models, and compare different cumulative milk-yield methodologies on both test-day and fully daily-recorded lactations using metrics such as RMSE, Pearson correlation, MAPE, and MAE. Reference datasets are provided to allow organizations to benchmark their own calculations against alternative methodologies. In addition, downloadable PDF reports summarize the results through detailed statistics and scatterplots, both overall and stratified by parity.
</div>
</div>