A Combinatorial Reliability Analysis of Dynamic Fault Trees with Priority-AND Gates

Dynamic fault trees (DFT) with priority-AND (PAND) gates are widely used in modeling systems with sequence-dependent failure behavior. We defined events as Boolean variables, and we show that by adding to a new Boolean operator denoted PRIOR and introducing the conditioning events, it is possible to mode the sequence-dependent failure behaviors between components in the PAND gate. A set of theorems based on PRIOR are provided to express the structure-function in a sum-of-products canonical form. Then, we propose two rules to generate the hybrid binary decision diagram (HBDD) model of the system. The HBDD can be applied to both PAND systems (DFTs model with PAND gates) and static systems (static fault tree models) with any arbitrary component time-to-failure distributions and different component failure parameter values. Also, the combinatorial method can avoid the generation of invalid nodes when building HBDDs. The application and advantages of the proposed solution are illustrated through an analysis of the case study.