Modelling and numerical assessment of a maintenance strategy with stock through piecewise deterministic Markov processes and quasi Monte Carlo methods

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 article, 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 article 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. The net present value stands for the difference between the cumulated discounted cash-flows of the purely corrective policy and the preventive one which including the overhaul. Piecewise deterministic Markov processes 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 piecewise deterministic Markov processes, which have to be numerically assessed. Instead of using the most classical Monte Carlo simulations, we here suggest alternate methods based on quasi Monte Carlo simulations, which replace the random uniform numbers of the Monte Carlo 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 Monte Carlo method. The developed tools can hence help the decision maker to take the right decision.