Reliability analysis of dynamic fault trees with Priority-AND gates using conditional binary decision diagrams

The conditional binary decision diagram (CBDD) is an extension of the BDD by introducing the conditioning event node, which has been applied to analyze the reliability of the dynamic fault tree (DFT). However, the previous CBDD-based method is limited to the DFT with spare gates since the Boolean conditioning event only describes the replacement state in spare gates. Hence, it cannot be available for the DFT with Priority-AND (PAND) gates. To address this issue, a novel Boolean conditioning event is proposed to describe the sequence-dependence failure in the dynamic system modeled by the DFT with PAND gates. A DFT with complex PAND gates can be converted into a conditional fault tree (CFT) by recursively applying derived rules that are based on the proposed conditioning event. As a result, the minimal cut set replaces the minimal cut sequence for qualitative analysis, which can reduce the average space complexity in a general case. Then, the CBDD can be generated based on the CFT and it can be used for evaluation. Finally, case studies demonstrate an extension of the cold spare gate and the advantages of our method.