Résumé
We propose a numerical method to compute the service time of an aluminum structure subject to corrosion. This example is provided by Astrium. The structure is part of a strategic ballistic missile stored in a nuclear submarine missile launcher and is therefore submitted to strong reliability constraints. We study the loss of thickness by corrosion and more precisely, the distribution of the service time of the structure: the time taken by the thickness loss to reach a critical threshold. We model the evolution of the thickness loss by a hybrid process belonging to the class of Piecewise-Deterministic Markov Processes (PDMP). The service time of the structure is thus an exit time for the PDMP. Our approach is based on the special structure of the PDMP, namely the fact that the only source of randomness of the process is a discrete time Markov chain. We propose a suitable discretization algorithm for this Markov chain based on quantization.