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This paper deals with the preventive maintenance (PM) optimization of airconditioning systems used aboard regional trains in France by the SNCF (French Railway Company). Two kinds of PM policies are envisioned: one with a single overhaul in the whole lifetime of the air-conditioning system, another with opportunistic replacements of components that are too old at each system failure. The air-conditioning system is formed of about 20 ageing and stochastically independent components. The envisioned PM policies make them functionally dependent, however. Both PM optimizations are performed with respect to the same cost function, involving the mean number of component replacements on some finite horizon. In view of its numerical assessment, a piecewise deterministic Markov processes (PDMP) model is used, both to model the maintained and the unmaintained system; a deterministic numerical scheme is next proposed, based on finite volume (FV) methods for PDMPs; owing to difficulties in its implementation, an approximation of this scheme is next used, which is much easier to implement than the initial FV scheme. As a result of using this method, it was finally possible to optimize both PM policies, which are both proved to lower the cost function of about 7 per cent.

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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.