A Bivariate Replacement Policy for a Cold Standby System Under Poisson Shocks

SYNOPTIC ABSTRACT

This study considers a repair-replacement problem for a repairable cold standby system that is composed of two similar components with preventive maintenance. The system may fail because of intrinsic or extrinsic factors such as shocks. The shocks arrive according to a Poisson process. Whenever the magnitude of a shock exceeds a prespecified threshold of the operating component, the operating component fails. We assume that the intrinsic lifetime, the threshold, and the repair time of the operating component are geometric processes. A bivariate repair-replacement policy ( T,N) is adopted for the system, where T is the interval length between preventive maintenances and N is the number of failures of component 1. The explicit expression of the expected long-run cost-per-unit time is derived and the corresponding optimal bivariate policy ( T,N) can be determined analytically or numerically. Finally, three numerical examples are given to validate the theoretical results of the proposed model.

Key Words and Phrases:

• repairable cold standby system
• geometric process
• repair-replacement policy
• long-run cost-per-unit time
• poisson shock

Acknowledgments

This work is supported by the National Science Foundation of China under Grant No. 71173109, the National Science Foundation for the Youth of China under Grant No. 31301229 and the Fundamental Research Fund for the Central University of China under Grant No.Y0201100265.