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Asymptotic failure rate of a Markov deteriorating system with preventive maintenance

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Sophie Mercier  and
Michel Roussignol
Sophie Mercier*
Affiliation:
Université de Marne-la-Vallée
Michel Roussignol*
Affiliation:
Université de Marne-la-Vallée
*
∗ Postal address: Laboratoire d’Analyse et de Mathématiques Appliquées (CNRS-UMR 8050), Université de Marne-la-Vallée, 5, boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France.
∗ Postal address: Laboratoire d’Analyse et de Mathématiques Appliquées (CNRS-UMR 8050), Université de Marne-la-Vallée, 5, boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France.
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Abstract

We consider a system with a finite state space subject to continuous-time Markovian deterioration while running that leads to failure. Failures are instantaneously detected. This system is submitted to sequential checking and preventive maintenance: up states are divided into ‘good’ and ‘degraded’ ones and the system is sequentially checked through perfect and instantaneous inspections until it is found in a degraded up state and stopped to allow maintenance (or until it fails). Time between inspections is random and is chosen at each inspection according to the current degradation degree of the system. Markov renewal equations fulfilled by the reliability of the maintained system are given and an exponential equivalent is derived for the reliability. We prove the existence of an asymptotic failure rate for the maintained system, which we are able to compute. Sufficient conditions are given for the preventive maintenance policy to improve the reliability and the asymptotic failure rate of the system. A numerical example illustrates our study.

Keywords

Reliabilitypreventive maintenancesequential checkingMarkov renewal equationasymptotic failure rate

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 1 , March 2003 , pp. 1 - 19
Copyright
Copyright © Applied Probability Trust 2003 

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