Designing efficient Bayesian sampling plans based on the simple step-stress test under random stress-change time for censored data

Abstract

ABSTRACT This paper studies the problem about how to design an efficient Bayesian sampling plan based on a simple step-stress test with a random stress-change time for censored data. For brevity, the step-stress test with random stress-change time is briefly called SSRSCT. A Bayesian sampling plan (BSP) through the SSRSCT is called BSPA. First, we derive the BSPA with data based on Type-II censoring for a general loss function. Given gamma and noninformative uniform prior distributions, an explicit expression of the Bayes decision function under a certain loss function is derived. By applying a curtailment procedure to the preceding Bayes decision function, a new Bayesian sampling plan, called an efficient Bayesian sampling plan (EBSPA), is constructed. It is shown that the Bayes risk of EBSPA is less than or equal to that of BSPA. This indicates that EBSPA is more efficient than the BSPA. Comparisons among some BSPAs and the proposed EBSPA are given. Monte Carlo simulations are carried out, and results indicate that the EBSPA outperforms those BSPAs. The EBSPA is recommended.