The Efficiency of Sequential Sampling Plans Based on Prior Distributions and Costs

Abstract

tial test of a simple hypothesis against a simple alternative is optimal in the sense that no other test with the same producer's and consumer's risk can have a smaller expected sample size. The significance of this theorem for applied statistics is limited for two reasons: first, optimality as defined above does not indicate the extent to which sequential tests are superior to tests based on samples of fixed size, and second, the whole 0. C. curve is important for the practical operation of a s.p., not just two of its points. Therefore, more informative than the theorem of Wald and Wolfowitz are numerical computations like that performed by Wald in [7], p. 57. These computations show that under many circumstances sequential tests and fixed-size sample tests with almost coinciding 0. C. curves have (expected) sample sizes in the relation 1: 2. However, these facts do not justify the common belief in the superiority of sequential s.p. over single s.p. in acceptance inspection. If the sample size is small compared with the lot size, the costs of sampling will be only a tiny fraction of the 'costs' connected with the decision to accept or reject the whole lot. Even if small differences between the 0. C. curves of two sampling plans entail relatively small differences in the 'costs' (of acceptance or rejection) these differences can be large compared with the costs of sampling. However, if the sample size is not small compared with the lot size, the difference between the sample sizes gains an importance which cannot be adequately characterized by the costs of sampling. In this case, the sorting of the sample will have a large effect, and the 0. C. curve is not the decisive criterion for the comparison of s.p. In this paper, comparisons between single and sequential s.p. are performed. A special model of acceptance inspection is chosen by which an objective comparison of s.p. in terms of costs can be made. This model will be a reasonable approximation to reality for only parts of the situations in which acceptance inspection is applied. By using this model, we show that the sequential s.p. is not highly superior to the single s.p.