Fuzzy fault tree analysis based on Interpretive Structure Model and binary connection numbers

Abstract

Building a fault tree and calculating the sequence of bottom events importance degree are key steps in fault diagnosis. Two improvements are made to the fuzzy fault tree in this study. The first is building the fault tree using Interpretive Structure Modeling (ISM) technology. The second is transforming triangular fuzzy numbers into binary connection numbers (BCN) through the uncertainty theory of set pair analysis, where the certainty coefficient is determined by the median of the triangular fuzzy number and the uncertainty coefficient is determined by the interval value described by the upper and lower limitations. The formula of failure probability of the top event and the formula of probability importance of the bottom event are deduced with the binary connection number. This method reduces the calculation amount. A case study is carried out to verify the feasibility and effectiveness of the method.