Dynamic Fault Tree Analysis Using Bayesian Networks and Sequence Probabilities

A method of calculating the exact top event probability of a fault tree with dynamic gates and repeated basic events is proposed. The top event probability of such a dynamic fault tree is obtained by converting the tree into an equivalent Markov model. However, the Markov-based method is not realistic for a complex system model because the number of states that should be considered in the Markov analysis increases explosively as the number of basic events in the model increases. To overcome this shortcoming, we propose an alternative method in this paper. It is a hybrid of a Bayesian network (BN) and an algebraic technique. First, modularization is applied to a dynamic fault tree. The detected modules are classified into two types: one satisfies the parental Markov condition and the other does not. The module without the parental Markov condition is replaced with an equivalent single event. The occurrence probability of this event is obtained as the sum of disjoint sequence probabilities. After the contraction of modules without parent Markov condition, the BN algorithm is applied to the dynamic fault tree. The conditional probability tables for dynamic gates are presented. The BN is a standard one and has hierarchical and modular features. Numerical example shows that our method works well for complex systems.