Résumé
This function is performed by HUMS (Health & Usage Monitoring System). The aim is to implement in the HUMS a program based on observations that can determine the state of the system and propose a maintenance action before failures. So we decompose our problem into two steps: the first step is to detect the degraded state (which announces future failure) using an informative variable and hidden Markov chains. This step was developped in Baysse et al. (2012). The second is to propose an optimal and dynamic maintenance policy, adapted to the state of the system and taking into account both random failures and those related to the degradation phenomenon. We want to estimate the best time to perform maintenance: a maintenance performed too early may be unnecessarily costly and inconvenient for the client but too late may cause the occurrence of a failure that will damage the rest of the equipment and may be responsible for the failure of a mission. So it is necessary to find a balance between these two extreme maintenance policies. First, we model the state of the system by a piecewise-deterministic Markov process: PDMP introduced by Davis (1993). Often the evolution of the system is modeled by stochastic processes such as Markov jump process, semi-Markov process (Cocozza et al. (1997)). There are also tools for modeling such as Stochastic Petri networks (Marsan et al. 1995), dynamic Bayesian networks (Donat et al. 2010). However, the flexibility of modeling by PDMP allows to take into account the dynamic component degradation. The works of Lair et al. (2012) focuses on this topic, they use a finite volume scheme to evaluate the quantities of interest associated with PDMP. Even if there are different methods that optimize maintenance policy, few use optimal stopping. In this paper, we use this method whose principle is to maximize a performance function that takes into account operating time, maintenance costs, repairs and downtime. We use the numerical probability tools developed in de Saporta et al. (2012) in order to compute this conditioned-based time of maintenance. The integration of this method in the HUMS, will be soon implemented in specific optronic equipment by Thales. We present results of simulation in this case. The methodology can be extended to more complicated cases.