Improved fuzzy set approach to fault tree analysis

Abstract

In fault tree analysis, the conventional approach is Monte-Carlo simulation by assuming a probability distribution for the failure probability. However, it is often very difficult to estimate precise failure rates or failure probabilities of individual components or failure events. Moreover, it isn``t used in case available data are insufficient. To overcome these disadvantages, the fuzzy set theory has been applied to fault-tree analysis. But, there is much difference between values estimated with previous fuzzy sets those estimated with Monte-Carlo simulation and previous fuzzy sets have a lot of uncertainty. In addition, in case of the system where components with sufficient data and components with insufficient data are mixed, these aren``t utilized. Because of the difference between the shape of fuzzy set and that of probability distribution, these problems appear. An improved fuzzy set approach to fault tree analysis has been developed. Its shape is made to approximate shape of the probability distribution and represented as μ(x) = f(ln(x)). It was applied to three system of WASH-1400. The results show that values calculated with improved fuzzy set approximate those calculated with Monte-Carlo Method and have better accuracy than values calculated with triangular fuzzy set in the 90% confidence limit for the top event failure probability. Furthermore, in case of FIM(fuzzy importance measure), FIM estimated with improved fuzzy set relatively approximate FIM estimated with probability distribution. Therefore, improved fuzzy set approach shows new possibility, that is, probability method and fuzzy set method may be combined.