Fuzzy set theoretic approach to fault tree analysis

Abstract

Research in conventional fault tree analysis (FTA) is based mainly on failure probability of basic events, which uses classical probability distributions for the failure probability of basic events. In the present paper the probabilistic consideration of basic events is replaced by possibilities, thereby leading to fuzzy fault tree analysis. Triangular and trapezoidal fuzzy numbers are used to represent the failure possibility of basic events. Since a system may have to go through different operating conditions during the design or testing phase. Thus the failure possibility of a basic event will be assigned more than one fuzzy numbers by different experts under various operating conditions. It is also well established that the selection of a fuzzy number to represent a basic event is vital in fault tree analysis. Here we developed an algorithm to find a single fuzzy number for a basic event, wherein more than one fuzzy number is assigned to that particular event. Using this algorithm, we obtain a single fuzzy number, having least variance from all fuzzy numbers assigned to the concerned event. The adequate and appropriate means and procedure for the detection of basic events having key role in the occurrence of top event in system analysis become essential. Here we have put forward an approach to rank the basic events in accordance with their importance in the occurrence of top
event. This approach can be widely used to improve the reliability and to reduce the operating cost of a system. The proposed techniques are discussed and illustrated by taking an example of a nuclear power plant.

Keywords: Fault tree, Triangular and Trapezoidal fuzzy number, Fuzzy importance, Ranking of fuzzy numbers