Technical note: A mathematical function to predict daily milk yield of dairy cows in relation to the interval between milkings.

The milk production of a dairy cow is characterized by lactation production, which is calculated from daily milk yields (DMY) during lactation. The DMY is calculated from one or more milkings a day collected at the farm. Various milking systems are in use today, resulting in one or many recorded milk yields a day, from which different calculations are used to determine DMY. The primary objective of this study was to develop a mathematical function that described milk production of a dairy cow in relation to the interval between 2 milkings. The function was partly based on the biology of the milk production process. This function, called the 3K-function, was able to predict milk production over an interval of 12h, so DMY was twice this estimate. No external information is needed to incorporate this function in methods to predict DMY. Application of the function on data from different milking systems showed a good fit. This function could be a universal tool to predict DMY for a variety of milking systems, and it seems especially useful for data from robotic milking systems. Further study is needed to evaluate the function under a wide range of circumstances, and to see how it can be incorporated in existing milk recording systems. A secondary objective of using the 3K-function was to compare how much DMY based on different milking systems differed from that based on a twice-a-day milking. Differences were consistent with findings in the literature.