This paper presents 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, the system is modelled by a stochastic hybrid process. The maintenance problem thus corresponds to an optimal stopping problem. A numerical method is proposed to solve the optimal stopping problem and optimize the maintenance time for this kind of process.
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