A FAULT-TREE-BASED IMPORTANCE SAMPLING STRATEGY FOR PIECEWISE DETERMINISTIC MARKOV PROCESSES

Piecewise deterministic Markov processes (PDMPs) can be used to model complex dynamical industrial systems. The counterpart of this modeling capability is their simulation cost, which makes reliability assessment untractable with standard Monte Carlo methods. Indeed, the failure of a complex system is a rare event and estimating the probability of its occurrence using a Monte Carlo method requires the simulation of a very large number of trajectories of the underlying process. A significant variance reduction can be obtained with a well-calibrated importance sampling method. It is known that the optimal distribution for importance sampling depends explicitly on the committor function of the PDMP. Fault tree analysis offers us elegant tools to approximate this committor function. We present an adaptive importance sampling (AIS) method based on a cross-entropy (CE) procedure for sequentially refining the approximation of the committor function. The method is tested on a system from the nuclear industry: the spent fuel pool.