Reliability analysis of dynamic fault trees with spare gates using conditional binary decision diagrams

Abstract

Dynamic fault trees (DFTs) with spare gates have been used extensively in reliability analysis. The traditional approach to DFTs is Markov-based that may suffer from problems like state–space explosion. Algebraic-structure-based methods consume long computation time caused by the inclusive/exclusive formula. Recently, some combinatorial solutions have been applied to DFTs such as sequential binary decision diagrams (SBDD) and algebraic binary decision diagrams (ABDD). They analyze systems by the minimal cut sequence (MCQ) based on sequence-dependence. We propose an analytical method based on conditional binary decision diagrams (CBDD) for combinatorial reliability analysis of non-repairable DFTs with spare gates. A detectable component state is mined to describe the sequence-dependent failure behaviors between components in the spare gate. Minimal cut set (MCS) instead of MCQ is used for qualitative analysis to locate faults via the component state. Compared to Markov-based methods, our method can generate system reliability result with any arbitrary time-to-failure distribution for system components. Different from SBDD and ABDD, specific operation rules are proposed to eliminate inconsistencies and reduce redundancies when building a CBDD. For quantitative analysis, the CBDD simplifies computation via using the sum of disjoint products. Case studies are presented to show the advantage of using our method.