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Journal of Applied Mathematics and Stochastic Analysis
Volume 13, Issue 4, Pages 321-346

A model for a dynamic preventive maintenance policy

Université de Marne-la-Vallée, Equipe d'Analyse et de Mathématiques Appliquées Cité Descartes, 5 Boulevard Descartes, Charnps-sur-Marne, Marne-la-Vallée Cedex 2 77454, France

Received 1 August 1999; Revised 1 June 2000

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper exhibits a stochastic model which describes the evolution of a material submitted to inspections. When an inspection takes place, a decision depending on the observed state of the material is taken. If the material is in “not too bad” state, no service is rendered, only the date of the next inspection is chosen. If the material is in a “bad” working state, a service takes place. Roughly speaking, the failure rates of the material are constant, the inspection and repair rates are general. We define the average cost function corresponding to the utilization of this material and we show how it can be computed. Then we determine the inspection rates which give the optimal maintenance policy using a simulated annealing algorithm. We observe experimentally that the best durations between inspections are deterministic ones.