Dynamic Fault Tree Analysis for Systems with Nonexponential Failure Components

A method of calculating the top event probability of a fault tree, where dynamic gates and repeated events are included and the occurrences of basic events follow nonexponential distributions, is proposed. The method is on the basis of the Bayesian network formulation for a DFT proposed by Yuge and Yanagi [1]. The formulation had a difficulty in calculating a sequence probability if components have nonexponential failure distributions. We propose an alternative method to obtain the sequence probability in this paper. First, a method in the case of the Erlang distribution is discussed. Then, Tijms's fitting procedure is applied to deal with a general distribution. The procedure gives a mixture of two Erlang distributions as an approximate distribution for a general distribution given the mean and standard deviation. A numerical example shows that our method works well for complex systems.