Optimal stopping for predictive maintenance of a structure subject to corrosion

Benoîte de Saporta (1, 2, 3) , François Dufour (2, 1) , Huilong Zhang (1, 2) , Charles Elegbede (4)

1 IMB - Institut de Mathématiques de Bordeaux
2 CQFD - Quality control and dynamic reliability
3 GREThA - Groupe de Recherche en Economie Théorique et Appliquée
4 ASTRIUM

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.

Domaines: Probabilités [math.PR]; Optimisation et contrôle [math.OC]

Benoîte de Saporta, François Dufour, Huilong Zhang, Charles Elegbede. Optimal stopping for predictive maintenance of a structure subject to corrosion. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2012, 226 (2), pp169-181. ⟨hal-00554759⟩