Keywords: maintenance modelling and optimization, degradation process modelling, Bayesian networks, rail maintenance.

Reliability analysis is an integral part of system design and operating. Moreover, it can be an input to optimize maintenance policies. Recently, dynamic Bayesian networks (DBN) have been proved appropriate to represent complex systems and perform reliability studies. Based on this formalism, the Diagnosis and Maintenance team of IFSTTAR-GRETTIA, proposed a semi-Markovian generic approach (named VirMaLab, for Virtual Maintenance Laboratory), that enables the modelling of the degradation process of complex systems (multi-components, multi-states, eventually influenced by contextual variables), diagnosis device properties (good detection and false alarm rates, etc.) and maintenance actions. Finally, this decision support tool enables evaluation and comparision of maintenance strategies for most industrial systems.

This paper first describes the generic approach considered, in three steps:

1. A mathematical model of the degradation process of the system (or its components). Accordingly the user's knowledge of this process (REX data bases, expert advices, theoretical studies, etc.), this modelling is based on a various probabilistic approaches: stochastic processes, Markov chains, semi-Markovian modelling, etc. To overcome the drawback of some eventually non acceptable hypothesis on the exact system's behaviour, induced by most of the "classic" approaches, an original semi-Markovian modelling was proposed and introduced in this paper, named graphical duration models.
2. The modelling of diagnostic devices (good detection rate, false alarms rate, etc.), their setting parameters (auscultations periods, tracked system's states, etc.) and maintenance actions (preventive or corrective) activated by either some defect detections or periodically in the case of systematic maintenance scheduling. When maintenance is performed, the system's state is modified in respect of success rates of each action (from 'As Good As New' actions to imperfect or failed maintenance).
3. Finally, diagnosis and maintenance of the system being characterized by a set of parameters and each action having a defined cost (financial, human, etc.), the last phase consists in quantifying the maintenance policy in terms of safety, cost, availability, service quality etc.

Then, with such a decision support tool, one can evaluate and compare various maintenance strategies and determine, for a given cost functions, the best set of maintenance and diagnosis parameters. The learning of such modelling can be done with both expert advice and REX databases.

The VirMaLab modelling is based on the Bayesian networks formalism, offering many advantages detailed in the paper. As an illustration of the feasibility of the proposed approach, a railway application, dedicated to the optimization of the rail maintenance (compromise renewal-replacement) will be introduced.

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