A preventive maintenance policy with sequential checking procedure for a Markov deteriorating system

We consider a repairable system subject to a continuous-time Markovian deterioration while running, that leads to failure. The deterioration degree is measured with a finite discrete scale: repairs follow general distributions: failures are instantaneously detected. This system is submitted to a preventive maintenance policy, with a sequential checking procedure: the up-states are divided into two parts. the "good" up-states and the "degraded" up-states, Instantaneous (and perfect) inspections are then performed on the running system: when it is Court(.] in a degraded up-state. it is stopped to be maintained (for a random duration that depends on the degradation degree of the system) when it is found in a good up-state, it is left as it is. The next inspection epoch is then chosen randomly and depends on the degradation degree of the system by time of inspection. We compute the long-run availability of the maintained system and give sufficient conditions for the preventive maintenance policy to improve the long-run availability. We Study the optimization of the long-run availability with respect to the distributions of the inter-inspection intervals: we show that under specific assumptions (often checked), optimal distributions are non-random. Numerical examples are studied. (C) 2002 Elsevier Science B.V. All rights reserved.