Narrow Results

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.

For repairable systems, aging properties of the time to first failure cannot adequately reflect its degradation over time — which is influenced by repairs. For such systems, exploring notions of aging under repairs would provide a more relevant description of deterioration in performance. A framework to formulate appropriate notions of aging relative to repair strategies and examine their implications is indicated. Included among such strategies are renewals (perfect repair or, replacements) and minimal repairs, as are the repair schemes of Brown-Proschan and Block-Borges-Savits. We examine some specific notions of repair relative to aging and briefly review recent results on two aging properties under perfect repairs. The concept of efficiency of repair strategies is introduced and illustrated by simple examples. Our final results concern an induced distribution related to perfect repairs and its realizability.