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On the Modelling of Imperfect Repairs for a Continuously Monitored Gamma Wear Process Through Age Reduction

Part of: Stochastic processes Operations research and management science

Published online by Cambridge University Press:  30 January 2018

Sophie Mercier  and
I. T. Castro
Sophie Mercier*
Affiliation:
Université de Pau et des Pays de l'Adour
I. T. Castro*
Affiliation:
Universidad de Extremadura
*
∗ Postal address: Laboratoire de Mathématiques et de leurs Applications - Pau (UMR CNRS 5142), Université de Pau et des Pays de l'Adour, Bâtiment IPRA, Avenue de l'Université, BP 1155, F-64013 Pau cedex, France. Email address: sophie.mercier@univ-pau.fr
∗∗ Postal address: Departamento de Matemáticas, Escuela Politécnica, Universidad de Extremadura, Avenida de la Universidad 10003, Cáceres, Spain. Email address: inmatorres@unex.es
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Abstract

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A continuously monitored system is considered, which is subject to accumulating deterioration modelled as a gamma process. The system fails when its degradation level exceeds a limit threshold. At failure, a delayed replacement is performed. To shorten the down period, a condition-based maintenance strategy is applied, with imperfect repair. Mimicking virtual age models used for recurrent events, imperfect repair actions are assumed to lower the system degradation through a first-order arithmetic reduction of age model. Under these assumptions, Markov renewal equations are obtained for several reliability indicators. Numerical examples illustrate the behaviour of the system.

Keywords

Imperfect maintenancegamma processARA1Markov renewal processMarkov renewal equationdelay timemaintenance policy

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 90B25: Reliability, availability, maintenance, inspection

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 4 , December 2013 , pp. 1057 - 1076
Copyright
© Applied Probability Trust 

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