We investigate an aperiodic preventive maintenance policy and propose several optimal PM policies which minimize the expected cost over an infinite time span. Park, Jung and Yum (2000) determine the optimal period and the optimal number of PMs based on Can-field's (1986) periodic model. Our techniques to derive the optimal preventive maintenance policies based on our aperiodic PM model is similar to those in Park, Jung and Yum (2000), which can be considered as the special case of our results.