Combinatorial Analysis of Dynamic Fault Trees with Priority-AND Gates

This paper focuses on a sub-class of Dynamic Fault Trees (DFTs), called Priority Fault Trees (PFTs), containing only static Boolean logic gates and Priority-AND (PAND) gates. We present a transformation from a PAND gate to an AND gate with some dependent conditioning events, called CAND gate, provided that the dynamic behavior of the system can be modeled by a (semi-)Markov process. With the CAND transformation, the qualitative analysis of a PFT can be reduced from a permutation problem into a combinatorial problem without resorting to the concept of minimal cut sequence. In addition, we discover that the PAND gate cannot model the priority relations between the events whose occurrences are not necessary for the output event. The inability of the PAND gate can be overcome by the proposed CAND gate.