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 N based on the number of repairs of component 1 under which the system is replaced when the number of repairs of component 1 reaches N. Our problem is to determine an optimal policy N* 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 N* can be determined analytically or numerically. Finally, a numerical example with Weibull distribution is given to illustrate some theoretical results in this paper.