Designing of Bayesian Multiple Deferred State Sampling Plan Based on Gamma–Poisson Distribution

Abstract

SYNOPTIC ABSTRACTConditional sampling plans such as chain sampling plans can be applied for making decisions on lot disposition utilizing not only information from the lot sampled but also information from preceding lots. The intent in the utilization of prior lot information is to reduce sample size and consequent costs of the decision process. A deferred state sampling plan is a conditional sampling plan in which the decision about previous lots is deferred until successive lots are selected and the outcome of successive lots is observed. In this article, we propose the multiple deferred state sampling plan based on the Bayesian methodology under the gamma–Poisson distribution. Tables of optimal parameters such as the sample size, acceptance numbers, and number of successive lots required to make the decision on the current lot are provided. The optimal parameters are determined using the approach of two points on the operating characteristic curve and by minimizing the average sample number. The advantages of the multiple deferred state sampling plan over the existing sampling plans under gamma–Poisson distribution are also discussed.