Age Replacement Policy with a Safety Constraint via the Bayesian Method

Abstract

Consider a system that is subject to shocks that arrive according to a non homogeneous Poisson process. As the shocks occur, the system has m + 1 failure modes including the following: (i) a non repairable failure (catastrophic) mode that calls for a replacement and (ii) m repairable failure (non catastrophic) modes that are rectified by minimal repairs. In this article, we propose an age-replacement model with minimal repair based on using the natural conjugate prior of Bayesian method. In addition, a safety constraint is considered to control the risk of occurring catastrophic failures in a specified time interval. The minimum-cost replacement policy is studied in terms of its existence and safety constraint. A numerical example is also presented to illustrate the proposed model.

Keywords:

• Age replacement
• Bayesian method
• Minimal repair
• Natural conjugate prior
• Safety constraint

Mathematics Subject Classification:

• Primary 60K05
• Secondary 90B25, 62N05

Acknowledgment

The authors would like to thank the referees for their insightful comments and suggestions, which greatly enhanced the clarity of the article.