Reliability Analysis of Competing Risks with Masked Failure Causes Based on Progressive Type-II Censoring with Random Removals

Abstract

This paper considers the reliability analysis of competing risks model based on progressive Type-II censored data with random removals, where the failure causes cannot be fully observed. Assume that the occurrence time of each failure mode follows Pareto distribution, and the number of systems removed at each failure time follows a binomial distribution. Based on the lifetime data containing masked failure causes, the maximum likelihood estimations of the unknown parameters and reliability function are obtained. In addition, the asymptotic confidence intervals of the unknown parameters are also proposed based on normal approximation to the asymptotic distribution of MLEs. In view of the shortcomings for failure cause is completely masked, the maximum likelihood estimation method fails, the Bayesian estimations of parameters and credible interval of the unknown parameters are obtained under the P,Q-symmetric entropy loss function. At last, some analyses of numerical results under different masking levels and removing probabilities are performed by Monte-Carlo simulations for illustrative purposes. The results show that the accuracy of the estimations decreases with increasing the masking level and has nothing to do with removing probability.