Optimal stopping for the predictive maintenance of a structure subject to corrosion

We present a numerical method to compute the optimal maintenance time for a complex dynamic system applied to an example of maintenance of a metallic structure subject to corrosion. An arbitrarily 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 too simple maintenance policies. To achieve this aim, we model the system by a stochastic hybrid process. The maintenance problem thus corresponds to an optimal stopping problem. We propose a numerical method to solve the optimal stopping problem and optimize the maintenance time for this kind of processes.