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.

翻译：分段确定性马尔可夫过程（PDMP）可用于对复杂动态工业系统进行建模。然而，这种建模能力的代价是其仿真成本较高，这使得标准蒙特卡洛方法难以进行可靠性评估。基于交叉熵（CE）程序的自适应重要性采样（AIS）方法可以显著降低方差。该方法的成功取决于能否选择良好的PDMP通勤函数的近似函数族。本文提出了新颖的函数族，这些函数族非常适用于高维工业系统，其形式基于与故障树分析相关的可靠性概念：最小路集和最小割集。本文详细讨论了所提出的方法，并将其应用于学术系统以及核工业中的实际系统。