On Optimal Planning of Progressive Type-I Interval Censoring Schemes under Dependent Competing Risks

This work considers designing of reliability acceptance sampling plan (RASP) when the competing risk data are progressively interval-censored. The methodology uses the asymptotic results of the estimators of parameters of any lifetime distribution under progressive interval censored competing risk data. Therefore, we establish a simplified form of the Fisher information matrix and present the asymptotic properties of the maximum likelihood estimators (MLEs) under a set of regularity conditions. Next, we consider a special case to illustrate the proposed RASP. we assume that the lifetime of the item due to the individual cause follows Weibull distribution. Also, it is assumed that the components are dependent and the gamma frailty model describes the dependent structure between the components. Now, we obtain the optimal RASP in three different ways. First, We present the method for obtaining optimal sample size and acceptance limit using producer's and consumer's risks. Next, we determine the optimal RASP under C-optimal criteria without cost constraints and with cost constraints. Numerical example is performed for both independent and dependent cases. Also, Monte Carlo simulation study is conducted in order to show that the sampling plans meet the specified risks for finite sample size.