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Piecewise deterministic Markov processes (PDMPs) can be used to model complexdynamical industrial systems. The counterpart of this modeling capability istheir simulation cost, which makes reliability assessment untractable withstandard Monte Carlo methods. A significant variance reduction can be obtainedwith an adaptive importance sampling (AIS) method based on a cross-entropy (CE)procedure. The success of this method relies on the selection of a good familyof approximations of the committor function of the PDMP. In this paper originalfamilies are proposed. They are well adapted to high-dimensional industrialsystems. Their forms are based on reliability concepts related to fault treeanalysis: minimal path sets and minimal cut sets. The proposed method isdiscussed in detail and applied to academic systems and to a realistic systemfrom the nuclear industry.

Adaptive importance sampling based on fault tree analysis for piecewise deterministic Markov process