Theoretical Reproductive Performance in a 120 Cow dairy Herd With 40% Estrus Detection Efficiency

AI service 1 2 3 4 5 6
Days postpartum 1 55 - 76 77 - 98 99 - 120 121 - 142 143 - 164 > 164
Total open cows 120 91 69 52 39 30
Normal cows (P = 0.9)2 108 82 62 47 35 27
Detected-mated (P = 0.40)3 43 33 25 19 14 11
Calving, this AI (P = 0.675)4 29 22 17 13 10 7
Cumulative pregnant cows 29 51 68 81 90 97
Days Open 5 1910 1931 1830 1663 1470 1269
Cumulative Days Open 1910 3841 5671 7335 8805 10073

1 Cows mated after a voluntary waiting period of 54 days.
2 Assume 10% of cows are abnormal due to reproductive pathology/acyclicity.
3 Assume that 50% of the normal, cycling cows are detected and mated at each successive estrus.
4 Cows that successfully conceive, complete gestation and calve normally from each insemination. The probability is a combination of 90% chance of conception and 75% chance of successful gestation/parturition. (P = 0.9 x 0.75 = 0.675).
5 Number of cows calving x median days postpartum for this insemination.

Mean Days Open (pregnant cows) = 10073/97 = 103.8

But 23 cows were still open after six inseminations and should be culled for reproductive failure. If these animals remained in the herd for a full year, this would add 23 x 365 = 8395 days open to the total.
Mean Days Open (all cows) = 10073 + 8395/120 = 153.9

Services per Pregnancy (97 cows) = 2.76