Fuzzy probability and α-cut based-fault tree analysis approach to evaluate the reliability and safety of complex engineering systems

Reliability and safety are very critical in complex engineering systems such as chemical and nuclear industries. Fault tree analysis (FTA) has been widely applied to evaluate the reliability and safety of complex engineering systems. This approach assumes that systems always have exact component failure probabilities. However, this assumption is not always true in real-world applications. To deal with this, a number of scholars have integrated fuzzy approach into FTA of engineering systems whose component exact probabilities cannot be collected. Furthermore, simple fuzzy arithmetic operations on membership function have also been proposed to quantify Boolean gates for propagating uncertainties from basic event fuzzy probabilities into the top event fuzzy probabilities. In this study, fuzzy arithmetic operations on alpha-cuts, as opposed to simple fuzzy arithmetic operations, are proposed. The significance of the alpha-cut is that each alpha-cut can uniquely represents each fuzzy probability. In order to verify the applicability of the proposed approach, the reliability of the long-term cooling system of the Westinghouse AP1000 to mitigate a large break loss of coolant accident is evaluated and the results are compared to the reliability of the same system quantified by conventional FTA published in qualified scientific journals. The results of the benchmarking confirm that the proposed approach can be practicably implemented to estimate the reliability and safety of complex engineering systems whose basic event reliability are characterized by fuzzy probabilities. To be applied in other complex engineering systems, safety analysts have to concern for some steps, which are particularly developed for a specific application, such as failure possibility distribution and its corresponding fuzzy probability distribution and the selection of a defuzzification technique.