Efficient Bayesian sampling plans for exponential distributions based on joint type-II censored data

This paper studies a method regarding how to design an efficient Bayesian sampling plan based on data collected from two life tests. Regarding the two life tests, one is operated under a normal condition with stress s0, and the other is operated using an accelerated life test with stress s1, where s0<s1. A joint Type-II censoring scheme is applied for collecting data from the two life tests. Based on the collected data, a Bayes decision function δA is derived for a general loss function. A Bayesian sampling plan (BSP) is then constructed. The monotonicity associated with δA is studied, and a monotone explicit expression of δA is derived. Based on this monotone explicit expression, a curtailment procedure is proposed for deriving a curtailed Bayes decision function δC and an efficient Bayesian sampling plan (EBSP) is constructed. It is shown that the Bayes risk of EBSP is less than or equal to that of BSP. This indicates that EBSP is more efficient than BSP. Comparisons among some BSPs and the proposed EBSP are given. The numerical results indicate that, in terms of Bayes risks, the EBSP significantly outperforms the BSP. The EBSP is recommended.