Reliability Analysis: Fault Tree to Catastrophe Tree

Abstract

In this paper, we propose a method for analyzing a catastrophe tree that is an analog of the classical method for analyzing a fault tree, which does not require knowledge of the probabilities of events. The concept of the possibility of bifurcation, which is estimated by a number in the interval [0,1] using catastrophe theory and corresponds to the membership function of a fuzzy set, is used instead of the concept of the probability of failure. The possibility of bifurcation (or catastrophe) of the system is calculated using specially introduced rules for aggregating the possibilities of bifurcations for various logical operations of the fault tree. The catastrophe analysis method is illustrated using the example of a fault tree for a road accident at a T-junction.