Predictive maintenance : a stochastic approach ; Maintenance prédictive : une approche stochastique

Abstract

The work presented in this thesis deals with the predictive maintenance of one or two-units systems that undergo a stochastic deterioration process. The value of the state of the system is supposed to be known periodically in time and can take an infinite number of values. We first study the optimization of parametric maintenance policies. The goal is to calculate the optimal value of one or more parameters of the policy that minimize the average cost of the maintenance. In two particular cases, for systems with one or two units under a negative exponential deterioration process, it is possible to find analytical expressions of the average expected cost. The comparison of the optimal cost of the parametric maintenance policy with the one of a "classical" preventive policy shows the advantages of the proposed method. However, this approach does not allow in the general case to end up to an analytical expression of the average cost. Moreover, there is no guarantee that the pre-defined parametric policy is optimal among all the possible maintenance policies. We propose then a general model of maintenance. This model, much more compréhensive than ones found in the literautre, is based on the use of dynamic programming. It allows to compute the optimal maintenance policy for systems with one or more units when different levels of maintenance are possible. Under some conditions, it is proved that the optimal maintenance policy is to perform a maintenance when the state of deterioration of the system becomes greater than a limit. This property allows an easy computation of the optimal maintenance cost ; Le travail présenté dans cette thèse concerne la maintenance prédictive de systèmes constitués de une ou deux unités subissant un processus stochastique de détérioration. L'état de ces systèmes est connu de manière discrète dans le temps et peut prendre une infinité de valeurs. Nous nous intéressons tout d'abord à l'optimisation de politiques de maintenance paramétriques. Il s'agit de déterminer la valeur du ou des ...