Mathematical model for an optimal replacement policy for cold standby repairable systems

In this paper, a cold standby repairable system consisting of two identical components and one repairman is studied. Assume that the component after repair is not “as good as new”; using the geometric process, we consider two kinds of replacement model as follows: (1) A kind of replacement policy T of the system based on the working age of the component 1; (2) A kind of replacement policy N of the system based on the failure number of the component 1. The explicit expressions of the long-run average benefit per unit time under each replacement policy are calculated, and the corresponding optimal replacement policies can be found analytically or numerically. Finally, we can derive that the policy N is better than the policy T under certain conditions.