If the reliability community remains interested in dynamic reliability theory, it is not really convinced by the ability of already available approaches to treating current problems from within the operational domain, even if the methodological quality of these approaches is undeniable. This paper is in keeping with two papers presented in earlier conferences. Its aim is to show the potentialities of a method that combines the high modelling capacity of the piecewise-deterministic processes with the great computing power inherent in the Monte Carlo simulation. This method has been applied to a well-known test-case example to test its ability to solve common dynamic reliability problems. Two sets of results have been obtained. The first one has been compared to those coming from a Petri-net model to obtain a preliminary validation of the proposed method. The second one, related to a more complex case, has been compared to already published results found in the literature. Contrary to already existing methods, the approach here is an exact Monte Carlo sampling method; it does not need timespace discretization.
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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