Bayesian sampling plans with interval censoring

Abstract

AbstractsThis paper employs Bayesian approach to establish acceptance sampling plans for life tests with interval censoring. Assume that interval data have a multinomial distribution, and the interval probabilities are random and vary from lot to lot according to a conjugate prior of Dirichlet distribution. A Bayes risk is defined with a suitable loss function and a predictive distribution. Optimal Bayesian sampling plans are determined by minimizing the Bayes risk per lot. An example is used and some optimal Bayesian sampling plans with three equally-spaced intervals are tabulated for illustration. Sensitivity analysis are conducted to evaluate the influence of the parameter of prior distribution, the cost per sampled item and the cost per used unit time on the proposed Bayesian sampling plans.Keywords: reliability, Dirichlet distribution, life test plan, loss function IntroductionAcceptance sampling is one aspect of quality assurance in the applications of quality control. When quality characteristic is the lifetime of item, acceptance sampling plans are developed for lifetime data. Due to saving test time and cost, engineers would like to infer life information of components based on incomplete data through censoring tests, for instance type I censoring test, type II censoring test or hybrid censoring test. Among these censoring tests, type I censoring test is popular in practice because the termination time is known in advance. However, practitioners might only count the failure numbers at some fixed times and did not measure the exact lifetimes during a censoring test for the purpose of administrative convenience. We call such a censoring test as interval censoring test and the collected failure numbers are the interval censoring data or the grouped data.In practice, an interval censoring test is easier to operate than conducting a type I censoring test, but the interval censoring data contain less information than that contained in type I censoring data. Some acceptance sampling plans have been developed with interval censoring data, see, for example, Ehrenfeld (1962), Kendell and Anderson (1971), Seo and Yum (1993), Chen and Mi (1998), Lu and Tsai (2009a, Tsai (2009b), andLin (2010).In acceptance sampling studies, many acceptance sampling schemes have been investigated in the literatures. Among these, the decision theory approach is particularly attractive, more precise and scientific to develop sampling plans based on the economic consideration. The Bayesian methods arise naturally when prior information is available for planning and estimation.