Optimal lot sentencing based on defective counts and prior acceptability

Abstract

Optimal inspection schemes for lot sentencing based on defective counts and prior lot acceptability, which provide appropriate protections to manufacturers and customers, are derived by minimizing the sampling inspection effort. An efficient computational procedure to determine the best test plan is presented. Moreover, an explicit approximation of the optimal scheme is deduced and its accuracy is analyzed. The achieved results practically solve the underlying constrained optimization problem in closed-form. The developed methodology is applied to the design of reliability demonstration test plans using failure count data and posterior odds ratios. Some illustrative examples are also presented. In most practical cases, the suggested approach is quite robust to small deviations in the prior acceptability, and allows the practitioners to substantially reduce the required sample size for screening lots of incoming and outgoing goods, as well as to appreciably improve the evaluations of the actual producer and consumer risks. Furthermore, it provides straightforward ways to combine multiple expert opinions and to update the optimal inspection scheme using the current estimate of the prior lot acceptability. In addition, the proposed test plans usually outperform the noninformative/frequentist schemes in terms of sampling cost and are quasi-optimal when the previous knowledge is slightly modified.