A New Approach to Bayesian Sampling Plans

Summary

A large number of papers exists that deal with Bayesian sampling plans. Hald defines Bayesian sampling plans as ”plans obtained by minimizing average costs, consisting of inspection, acceptance and rejection costs”. In order to obtain such a plan one starts with an a priori distribution of the fraction of nonconforming items in the lots, i.e. an assumption about the process curve, and calculates the sampling plan that minimizes the Bayesian risk or cost (if cost parameters are given). However, once these plans have been obtained they are applied in the classical manner just by making acceptance/rejection decisions for the inspected lots. For a Bayesian, the calculation of the a posteriori distribution of the fraction nonconforming in the lot is the essential step of the Bayesian analysis because for him the complete information combining prior knowledge and sample information is incorporated in the a posteriori distribution. Hence, in this paper the lot acceptance decision is directly based on the a posteriori distribution of the fraction nonconforming in the lot and especially the a posteriori estimate of the probability of the fraction of nonconforming items in the lot being larger than the acceptance quality limit pAQL. This Bayesian method is applied to sampling by attributes based on a beta-binomial model.