A geometric process repair model for a repairable cold standby system with priority in use and repair

In this paper, a deteriorating cold standby repairable system consisting of two dissimilar components and one repairman is studied. For each component, assume that the successive working times form a decreasing geometric process while the consecutive repair times constitute an increasing geometric process, and component 1 has priority in use and repair. Under these assumptions, we consider a replacement policy image based on the number of repairs of component 1 under which the system is replaced when the number of repairs of component 1 reaches image. Our problem is to determine an optimal policy image such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit equation of the average cost rate of the system is derived and the corresponding optimal replacement policy image can be determined analytically or numerically. Finally, a numerical example with Weibull distribution is given to illustrate some theoretical results in this paper.