Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 4, Pages 321-346
doi:10.1155/S1048953300000307
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 Christiane Cocozza-Thivent. 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.
Abstract
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.