Bayes and Empirical Bayes Two-Stage Procedures for Sampling Inspection

摘要

A batch of M items is inspected for defectives. Suppose there are d defective items in the batch. Let d_0 be a given standard used to evaluate the quality of the population where 0 < d_0 < M. The problem of testing H_0 : d < d_0 versus H_1 : d ≥ d_0 is considered. It is assumed that past observations are available when the current testing problem is considered. Accordingly, the empirical Bayes approach is employed. By using information obtained from the past data, an empirical Bayes two-stage testing procedure is developed. The associated asymptotic optimality is investigated. It is proved that the rate of convergence of the empirical Bayes two-stage testing procedure is of order O(exp(-c~*n)), for some constant c~* > 0, where n is the number of past observations at hand.