  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. A significant variance reduction can be obtained
with 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 family
of approximations of the committor function of the PDMP. In this paper original
families are proposed. They are well adapted to high-dimensional industrial
systems. Their forms are based on reliability concepts related to fault tree
analysis: minimal path sets and minimal cut sets. The proposed method is
discussed in detail and applied to academic systems and to a realistic system
from the nuclear industry.
