Piecewise deterministic Markov processes and maintenance modeling: application to maintenance of a train air-conditioning system

Abstract

This paper deals with the preventive maintenance (PM) optimization of air-conditioning 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.