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IMA Journal of Management Mathematics Advance Access published online on July 15, 2008
IMA Journal of Management Mathematics, doi:10.1093/imaman/dpn016
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© The authors 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A maintenance model with minimal and general repair

Michael Jong Kim and Viliam Makis{dagger}

University of Toronto, 5 King's College Road, Toronto M5G 3G8, Canada

{dagger} Email: makis{at}mie.utoronto.ca

Received on 8 January 2008. Accepted on 13 June 2008.

The purpose of this article is to determine optimal maintenance policies for deteriorating systems subject to failure. Complex systems that deteriorate with usage and age are often subject to random failures of several kinds. Since it is costly to repair or replace failed systems, preventive maintenance is usually carried out while the systems are still operational. This article will be useful in providing maintenance engineers with a methodology to model failing systems and efficiently determine optimal maintenance policies. The problem is formulated and solved in a semi-Markov decision framework with the optimality criterion being the minimization of the long-run expected average cost per unit time. The model developed in this article, which is an extension of recent maintenance models, can be applied to systems that have any finite number of major and/or minor failure states and to systems that permit general repair in operational and major failure states. A new computational approach using an embedded technique is developed that is computationally preferable to the standard policy iteration algorithm when determining the optimal maintenance policy for systems with many states.

Keywords: semi-Markov decision process; optimal maintenance policy; embedded decision process; policy iteration algorithm; condition-based maintenance; general repair


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