On fault tree analysis with fuzzy probability

Abstract

This paper proposes the Fuzzy Fault Tree Analysis in which the fuzzy probabilities of the basic events are handled. The fuzzy probability, which means the possibility distribution concerning the occurrence of the event, is a fuzzy set on interval [0, 1]. The fuzzy sets theory was defined by L. A. Zadeh in 1965. This application of fuzzy sets theory to the fuzzy fault tree is effective to evaluate the grade of influence to what extent fuzziness of probability concerning basic events spreads the probability of the top event. The membership function are supposed to be of house-shaped in probability calculations. In a sense the machine failure rate or human error rate can be usually specified by a standard point, a lower limit point and an upper limit point. This fuzzy probability can well fit actual cases. The Fuzzy Fault Tree with house-shaped membership function is discussed using a simple example.