Reliability Acceptance Sampling Plans under Progressive Type-I Interval Censoring Schemes in Presence of Dependent Competing Risks

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.