Universal probabilistic analysis for cut sequences in dynamic fault trees

Cut sequence, an events' sequence failing in a specific order that can induce the top event, is an algebraic approach to overcome the shortcomings of the traditional methods for dynamic fault trees (DFTs) analysis. The former researchers have done a lot of work for cut sequence' qualitative analysis, however, the quantitative probabilistic analysis has not been completely considered, especially for the cut sequence which is generated from the DFT with cascade structure, due to the complex temporal failure logic among events in the cut sequence. To solve the problem, this paper proposed a universal probabilistic analysis method for any form of cut sequences in the DFT. Firstly, temporal failure logic was defined to precisely demonstrate events' logic. Then, dynamic failure behaviors' categories for basic events were given and a universal probabilistic model for calculating any form of cut sequences was put forward. Eventually, an example was utilized to illustrate the effectiveness of the proposed method. The universal quantitative method, with a better manipulability and expansibility, answers how to calculate the sequential events' occurrence frequency, which is the concern of cut sequences' quantitative analysis in the DFT.