In this paper, a repairable system consisting of identical component is studied, both the mean time between failure (MTBF) of the component and the repair time are assumed to be exponentially distributed, Additionally, we assume that the component after a repair is “as good as new”. Maintenance strategies and the change of maintenance rate can affect the performance of the system, in order to further study, the influence degree of the change of maintenance rate on the system, maintenance rate function is introduced, and establish a system of availability and cost-effectiveness as the goal of repairable system model. At the same time, system steady-state availability analytical expression and cost-effective analytical expression are obtained by Laplace transform. Finally, numerical examples show that maintenance strategies and maintenance rate function pose significant effects on availability and cost-effective of the system.