Replacement problems for a cold standby repairable system

In this paper, a cold standby repairable system consisting of two identical components and one repairman is studifed. Assume that each component after repair is not "as good as new", by using a geometric process, we consider two kinds of repair replacement policy, one based on the working age T of component 1 under which the system is replaced when the working age of component 1 reaches T, and the other based on the failure number N of component 1 under which the system is replaced when the failure number of component 1 reaches N. Our problem is to choose optimal replacement policies T* and N* respectively such that the long-run average cost per unit time of the system is minimized. And we can prove under some mild conditions that the optimal policy N* is better than the optimal policy T*. Finally, a numerical example for policy N is given.