We discuss the development of reliability acceptance sampling plans under progressive Type-I interval censoring schemes in the presence of competing causes of failure. We consider a general framework to accommodate the presence of independent or dependent competing risks and derive the expression for the Fisher information matrix under this framework. We also discuss the asymptotic properties of the maximum likelihood estimators, which are essential in obtaining the sampling plans. Subsequently, we specialize in a frailty model, which allows us to accommodate the dependence among the potential causes of failure. The frailty model provides an independent competing risks model as a limiting case. We then present the traditional sampling plans for both independent and dependent competing risks models using producer and consumer risks. We also consider the design of optimal PIC-I schemes in this context and use a c optimal design criterion, which helps us to obtain more useful reliability acceptance sampling plans in the presence of budgetary constraints. We conduct a comprehensive numerical experiment to examine the impact of the level of dependence among the potential failure times on the resulting sampling plans. We demonstrate an application of the developed methodology using a real-life example and perform a simulation study to study the finite sample properties of the developed sampling plans. The methodology developed in this article has the potential to improve the design of optimal censoring schemes in the presence of competing risks while taking into account budgetary constraints.

翻译：本文探讨在存在竞争失效原因的情况下，基于渐进式I型区间删失方案制定可靠性验收抽样计划的方法。我们构建了一个通用框架，以容纳独立或相依的竞争风险，并推导了该框架下Fisher信息矩阵的表达式。同时讨论了极大似然估计量的渐近性质，这对获取抽样计划至关重要。随后，我们重点研究了脆弱模型，该模型能够处理潜在失效原因之间的相依性。脆弱模型将独立竞争风险模型作为其极限特例。接着，我们基于生产方风险和使用方风险，分别针对独立与相依竞争风险模型提出了传统抽样方案。在此背景下，我们还考虑了最优PIC-I方案的设计，采用c最优设计准则，以在预算约束条件下获得更具实用价值的可靠性验收抽样计划。通过系统的数值实验，我们检验了潜在失效时间间相依程度对最终抽样方案的影响。借助实际案例展示了所提方法的应用，并通过模拟研究考察了所构建抽样方案在有限样本下的性质。本文发展的方法论有望在考虑预算约束的同时，改进存在竞争风险时的最优删失方案设计。