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

• Published in: Journal of statistical computation and simulation Vol. 90; no. 1; pp. 112 - 137
• Main Authors: Kamranfar, H., Etminan, J., Chahkandi, M.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.01.2020; Taylor & Francis Ltd
• Subjects: Approximation; Bayesian analysis; Bayesian inference; classical inference; Computer simulation; Economic models; imperfect repair; MCMC algorithm; Monte Carlo simulation; Parameter estimation; Poisson density functions; reliability and maintainability; Repair & maintenance; Statistical analysis; Statistical inference; Weibull distribution
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2019.1673392

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.