Joint progressive censoring schemes are quite useful to conduct comparative life-testing experiment of different competing products. Recently, Mondal and Kundu (“A New Two Sample Type-II Progressive Censoring Scheme”, Communications in StatisticsTheory and Methods, 2018) introduced a joint progressive censoring scheme on two samples known as the balanced joint progressive censoring (BJPC) scheme. Optimal planning of such progressive censoring scheme is an important issue to the experimenter. This article considers optimal life-testing plan under the BJPC scheme using the Bayesian precision and D-optimality criteria, assuming that the lifetimes follow Weibull distribution. In order to obtain the optimal BJPC life-testing plans, one needs to carry out an exhaustive search within the set of all admissible plans under the BJPC scheme. However, for large sample size, determination of the optimal life-testing plan is difficult by exhaustive search technique. A meta-heuristic algorithm based on the variable neighborhood search method is employed for computation of the optimal lifetesting plan. Optimal plans are provided under different scenarios. The optimal plans depend upon the values of the hyper-parameters of the prior distribution. The effect of different prior information on optimal scheme is studied.

中文翻译：

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平衡二样本Ⅱ类渐进式删失方案下的贝叶斯最优寿命测试方案

联合渐进式审查方案对于进行不同竞争产品的比较寿命测试实验非常有用。最近，Mondal 和 Kundu（“A New Two Sample Type-II Progressive Censoring Scheme”，Communications in Statistics Theory and Methods，2018 年）在两个样本上引入了一种联合渐进式删失方案，称为平衡联合渐进式删失 (BJPC) 方案。这种渐进式审查方案的最佳规划对实验者来说是一个重要问题。本文考虑使用贝叶斯精度和 D 最优性标准的 BJPC 方案下的最优寿命测试计划，假设寿命遵循威布尔分布。为了获得最优的 BJPC 寿命测试计划，需要在 BJPC 方案下的所有可接受计划的集合中进行详尽的搜索。然而，对于大样本量，通过穷举搜索技术很难确定最佳寿命测试计划。采用基于变量邻域搜索方法的元启发式算法计算最优寿命测试计划。不同场景下提供最优方案。最优计划取决于先验分布的超参数值。研究了不同先验信息对最优方案的影响。