Bayesian Methods for Reliability Demonstration Test for Finite Population Using Lot and Sequential Sampling

Abstract

The work proposed a reliability demonstration test (RDT) process, which can be employed to determine whether a finite population is accepted or rejected. Bayesian and non-Bayesian approaches were compared in the proposed RDT process, as were lot and sequential sampling. One-shot devices, such as bullets, fire extinguishers, and grenades, were used as test targets, with their functioning state expressible as a binary model. A hypergeometric distribution was adopted as the likelihood function for a finite population consisting of binary items. It was demonstrated that a beta-binomial distribution was the conjugate prior of the hypergeometric likelihood function. According to the Bayesian approach, the posterior beta-binomial distribution is used to decide on the acceptance or rejection of the population in the RDT. The proposed method in this work could be used to select item providers in a supply chain, who guarantee a predetermined reliability target and confidence level. Numerical examples show that a Bayesian approach with sequential sampling has the advantage of only requiring a small sample size to determine the acceptance of a finite population.