Abstract

In this paper, a decision-theoretic approach is used to obtain the Bayesian sampling plan (BSP) for the generalized Type-II hybrid censoring scheme when lifetimes of sampled units follow a one-parameter exponential distribution. An efficient loss function is used to decide whether to accept or reject the batch. The BSP is obtained by constructing the closed form of the Bayes decision function. It is observed that the closed form of the Bayes decision function cannot be obtained analytically for any arbitrary loss function. A numerical approach is proposed to determine the optimum BSP for an arbitrary loss function. To illustrate this, we consider a higher degree polynomial loss function and obtain the optimum BSP numerically. Some numerical studies have been conducted to check the performance of the optimum BSP in different cases.

摘要

在本文中，当样本单元的生命周期服从单参数指数分布时，使用决策理论方法获得广义 Type-II 混合审查方案的贝叶斯抽样计划 (BSP)。使用有效的损失函数来决定是接受还是拒绝该批次。BSP是通过构造贝叶斯决策函数的封闭形式得到的。据观察，贝叶斯决策函数的封闭形式无法通过分析获得任何任意损失函数。提出了一种数值方法来确定任意损失函数的最佳 BSP。为了说明这一点，我们考虑更高阶的多项式损失函数并在数值上获得最佳 BSP。已经进行了一些数值研究来检查最佳 BSP 在不同情况下的性能。