In this article, a cold standby repairable system of two identical components with a single repairman is studied. It is assumed that, the performance of the component 1 and the component 2 after repair is not “as good as new”. For most of the deteriorating system, it is reasonable to assume that the consecutive working time of the system decreases after the repair whereas successive repair time of the system increases after the failure. To approach such a stochastic phenomenon, we can consider arithmetico-geometric process repair model. The working time and repair time of the both the components are exponentially distributed random variables. Under these assumptions, by using arithmetico-geometric process model, we consider the replacement policy based on the number of failures of the component 1. Under this policy system is replaced by new one when number of failures of the component 1 reaches to N. The optimal value of N that maximizes long run average reward per unit time of the system is evaluated. The explicit expression for the long run average per unit time of the system is derived. Also, we study the performance of the cold standby repairable system by using arithmetico-geometric process. Lastly to check the applicability of the model, numerical and simulation study has been performed