ABSTRACT
In the context of interest here, namely that of fault tree analysis, Lindley & Singpurwalla (1986) present a formal probabilistic (Bayesian) procedure for the use of expert opinions, assuming expert input in the form of mean and standard deviation of lognormally distributed failure rates. In Tanaka et al. (1983), Liang & Wang (1991) and Huang et al. (2001), basic event probabilities (chances) are treated as trapezoidal fuzzy numbers and the extension principle is applied to compute the probability (chance) of occurrence of the top event. In order to deal with repeated basic events in fault tree analysis, Soman & Misra (1993) provide a simple method for fuzzy fault tree analysis based on the α-cut method, also known as resolution identity. Another approach to fuzzy fault tree analysis based on the treatment of the system state as a fuzzy variable has been proposed by Huang et al. (2004).
