Is Cut Sequence Necessary in Dynamic Fault Trees?

The dynamic fault trees (DFT) is proposed to model sequence dependencies between fault events based on the traditional static fault tree (SFT). In the analysis of DFT, only combinations of basic events may not be suffincient to imply the top event (TE) due to the encoded sequence dependencies of the DFT. The calculation of cut sequences is, however, a permutation problem and is much more complex than the calculation of cut sets in general. In this paper, we demonstrate that for any DFT that can be modeled by a Markov or semi-Markov process, the DFT can be transformed into an equivalent SFT. With the transformation, the analysis of a DFT can be carried out without resorting to the cut sequences anymore, but in terms of the cut sets of the transformed SFT which can be solved with traditionaleffincient combinatorial algorithms. The transformation provides a way to reduce the permutation problem of cut sequences into a combinatorial problem of cut sets.