Statistical inference for a repairable system subject to shocks: classical vs. Bayesian. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Kamranfar, H.; Etminan, J.; Chahkandi, M.
• Is Part Of: Journal of statistical computation and simulation. Volume 90:Issue 1(2020)
• Page Start: 112
• Page End: 137
• Publication Date: 2020-01-02
• Subjects: Bayesian inference -- classical inference -- imperfect repair -- MCMC algorithm -- reliability and maintainability; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2019.1673392
• Languages: English
• ISSNs: 0094-9655

Abstract

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.