^{1,2}, H. Chraibi

^{1}, A. Dutfoy

^{1}and J. Garnier

^{2}

^{1}PERICLES Department, EDF Lab Saclay, 7 Bd Gaspard Monge, 91120 Palaiseau, France

^{2}CMAP (Centre de mathématiques appliquées), École Polytechnique, 91128 Palaiseau, France

A natural way to assess the reliability of a complex industrial system is to carry out numerical simulations that reproduce the behavior of the system. The PyCATSHOO^{1} tool developed by *E\'lectricité De France* (EDF R&D) allows the modeling of such systems through the framework of piecewise deterministic Markov processes (PDMP). These processes have a discrete stochastic behavior (failures, reconfigurations, control mechanisms, repairs, etc.) in interaction with continuous deterministic physical phenomena. It is well known that for sufficiently rare events, crude Monte-Carlo methods require a very large number of simulations to accurately estimate their probability of occurrence. We propose an adaptive importance sampling strategy based on a Cross-Entropy method to reduce the cost of estimating the probability of system failure^{2}. The success of this method depends crucially on the family of instrumental laws used to approximate the optimal law. We construct this family according to the PDMP structure of the system, in particular according to the configuration of its minimal failure groups. Finally, we propose different sensitivity analysis techniques3 to reduce the dimension of the problem and to determine the respective contributions of different component failure modes to the probability of system mission loss. We present an application of this strategy on a test case from the nuclear industry: the spent fuel pool.