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Sequential Sampling in a Sire Proving Program

Department of Animal Breeding and Department of Statistics, Volcani Institute of Agricultural Research, Rehovoth, Israel

ABSTRACT

A procedure is described in which, as the contemporary comparison records of the daughters of a sire become available, their cumulative sum (S_n) is computed and the sire is accepted if S_n exceeds L₁ and rejected if S_n is less than L₀. Otherwise, sampling is continued until a total weight, W, (the truncation point) is reached. At this point the sire is accepted or rejected according to the sign of S_n. Four such plans, based on a within-sire variance (²) of 4.48 kg²/day were designed. For these plans, W = 28, 29, 30, and 35, L₁ = –L₀ = 10.23, 10.91, 11.35, and 11.88, respectively, and the probability of rejecting a sire transmitting at a level of +0.5384 kg/day (u₁) or accepting a sire transmitting at a level of – 0.5384 kg/day (u₀) is 0.10. These plans can be adapted to other u's and ₂'s, say u* and ²* by the relations

When applied to a sample of 24 sires, the truncated plans rendered the same decision as a single sample plan with weight 25, for 22 of the sires, but rendered that decision on the average, on the basis of a total weight of 13–15, depending on the plan.