Bayesian Network Modeling for Dynamic Fault Tree

A method of calculating the exact top event probability of a fault tree with dynamic gates and repeated basic events is proposed. It is a hybrid of a Bayesian network (BN) and an algebraic technique. At first, modularization is applied to a dynamic fault tree. The detected modules are classified into two types: the parental Markov condition is satisfied, or not. The module with parental Markov condition is replaced to an equivalent single event. The occurrence probability of this event is obtained as the sum of disjoint sequence probabilities. After the contraction, the BN algorithm is applied to the dynamic fault tree in which some repeated events or dynamic gates may be included. The conditional probability tables for dynamic gates are presented. The BN is almost a standard one and has hierarchical and modular features. Numerical example shows that our method works well for a complex system.