Optimal Random Age Replacement for Availability

An age replacement maintenance policy is considered here, in which a system is restored whenever it fails, or ages without failure up to a preventive maintenance epoch (whichever comes first). The duration of the restoration activity is random, and depends on whether it was precipitated by a failure or by a preventive maintenance action. The case where the preventive maintenance epoch is deterministic has been studied previously, and shown to be optimal in a certain sense. Here, we consider the case where the preventive maintenance epoch is randomized, which is more realistic for many systems. The system availability is the long run proportion of time that the system is operational (i.e., not undergoing repair or preventive maintenance). The optimal rate of preventive maintenance to maximize availability is considered, along with sufficient conditions for such an optimum to exist. The results obtained herein are useful to systems engineers in making critical design decisions.