Résumé
We present a numerical method to compute the optimal maintenance time for a complex dynamic system. An early intervention may be uselessly costly, but a late one may lead to a partial/complete failure of the system, which has to be avoided. One must therefore find a balance between these two extreme maintenance policies. To achieve this aim, we model the system by a stochastic hybrid process and propose a numerical method to optimize the maintenance time for this kind of processes. Mathematically, this is an optimal stopping problem. We apply our algorithm to the example of maintenance of a metallic structure subject to corrosion.