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.

KEYWORDS:

• Bayesian inference
• classical inference
• imperfect repair
• MCMC algorithm
• reliability and maintainability

Acknowledgments

The authors would like to thank the referees and the editor for their valuable and helpful comments which have greatly improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.