To ensure a power generation level, the French national electricity supply (EDF) has to manage its producing assets by putting in place adapted preventive maintenance strategies. In this paper, a fleet of identical components is considered, which are spread out all around France (one per power plant site). The components are assumed to have stochastically independent lifetimes but they are made functionally dependent through the sharing of a common stock of spare parts. When available, these spare parts are used for both corrective and preventive replacements, with priority to corrective replacements. When the stock is empty, replacements are delayed until the arrival of new spare parts. These spare parts are expensive and their manufacturing time is long, which makes it necessary to rigorously define their ordering process. The point of the paper is to provide the decision maker with the tools to take the right decision (make or not the overhaul). To do that, two indicators are proposed, which are based on an economic variable called the Net Present Value (NPV). The NPV stands for the difference between the cumulated discounted cash-flows of the purely corrective policy and the one including the overhaul. Piecewise Deterministic Markov Processes (PDMPs) are first considered for the joint modelling of the stochastic evolution of the components, stock and ordering process with and without overhaul. The indicators are next expressed with respect to these PDMPs, which have to be numerically assessed. Instead of using the most classical Monte Carlo (MC) simulations, we here suggest alternate methods based on quasi Monte Carlo simulations, which replace the random uniform numbers of the MC method by deterministic sequences called Low Discrepancy Sequences. The obtained results show a real gain of the quasi Monte Carlo methods in comparison with the MC method. The developed tools can hence help the decision maker to take the right decision.

International audienceTo improve the management of maintenance planning and spare parts ordering of a fleet of components, different investments plans need to be compared. A new investments plan is compared with a reference one through an economic variable called the Net Present Value (NPV). Classically, Monte Carlo simulations are used to assess economic indicators such as the expected NPV and the probability for the NPV to be negative which stands for the probability to regret the performed investments plan. In this document, we propose to use quasi Monte Carlo methods as an alternative to the Monte Carlo (MC) method, which replace the random uniform numbers of the MC method by deterministic sequences with better uniformity properties

L'évaluation d'une stratégie d'investissements en maintenance préventive nécessite la quantification d'indicateurséconomiques permettant de décrire le gain espéré ainsi que les risqueséconomiques associés. Les simulations de Monte-Carlo sont souvent utilisées dans ce cadre. Cependant, elles nécessitent un temps de calcul important pour obtenir des résultats suffisamment précis. Lorsque l'objectif n'est plus simplement d'évaluer une stratégie candidate mais de déterminer la stratégie optimale, les simulations de Monte-Carlo ne sont plus adaptées. En effet, coupléeà un algorithme d'optimisation, cette méthode nécessiterait des calculs trop longs. Nous présentons dans cet article des méthodes alternatives permettant d'obtenir des résultats précis plus rapidement : les méthodes de quasi Monte-Carlo.