ABSTRACT

This paper studies the problem about how to design a Bayesian sampling plan (BSP) for two exponential distributions linked by the cumulative exposure model through a simple step-stress accelerated life test (ALT). Such a Bayesian sampling plan through the ALT by a simple step-stress procedure is called BSPA. The BSPA with Type-II censoring in a general loss function is derived. Given joint gamma and uniform prior distributions, an explicit Bayes decision function under a certain loss function is derived. Illustrative examples are given to demonstrate how to find the Bayes decision function. A Monte Carlo simulation study is performed for searching the optimal BSPA. Comparison between the proposed BSPA and the conventional BSP is carried out to study the performance of BSPA. The numerical results indicate that the risk reduction of BSPA by applying the accelerated procedure is more significant if the experimental time cost is more expensive.

摘要

本文研究了如何通过简单的阶跃应力加速寿命测试 (ALT) 为累积暴露模型关联的两个指数分布设计贝叶斯抽样计划 (BSP) 的问题。通过 ALT 通过简单的步进应力过程的这种贝叶斯抽样计划称为 BSPA。推导出具有一般损失函数中的 Type-II 删失的 BSPA。给定联合伽马和均匀先验分布，推导出特定损失函数下的显式贝叶斯决策函数。给出了说明性示例以演示如何找到贝叶斯决策函数。执行蒙特卡罗模拟研究以搜索最佳 BSPA。所提出的 BSPA 与传统 BSP 之间的比较是为了研究 BSPA 的性能。