Statistical inference for a repairable system subject to shocks: classical vs. Bayesian

Abstract

Consider a repairable system subject to shocks that arrive according to a non-homogeneous Poisson process (NHPP). As a shock occurs, two types of failure may be happened. Type-I failure occurs with probability q and is rectified by a minimal repair, whereas type-II failure takes place with probability p = 1−q and is removed by replacement. The system is replaced at the nth type I failure or at type II failure, whichever comes first. In the present paper, we find a general representation for the likelihood function of the proposed model. Then, we follow both classical and Bayesian procedures to estimate the model parameters when the time to first failure is a Weibull distribution. Because the Bayesian estimation cannot be obtained in a closed form, we use two approximation methods: Lindley's approximation and MCMC method. Finally, a Monte Carlo simulation is conducted to compare the performance of estimators in classical and Bayesian procedures.