A Repair Replacement Policy for a Deteriorating Cold Standby System with a Component has Priority in Use and Repair

The purpose of this paper is to apply the two monotone process repair model to a two-component cold standby repairable system with one repairman. Now it may be assumed that the component 2 after repair is as good as new while component 1 follows the geometric process repair, but component 1 has priority in use and repair, and each component after repair is not as good as new. Under these assumptions, by using two monotone processes, we studied a replacement policy N based on the number of repairs of component 1. The problem is to determine an optimal replacement policy N* such that the long-run expected reward per unit time is minimized.