Quantification of fault trees containing mutually exclusive events

Abstract

This paper presents a method for analysing fault trees that contain independent sets of mutually exclusive (disjoint) events of different cardinality. Disjoint events can be used to model several issues, e.g. multistate systems with multistate components, different attack alternatives in security-related studies, and components in phased mission systems. Basic events of coherent and non-coherent binary trees can be considered as belonging to sets of cardinality 2. Each event is associated with a binary variable, and a labelling technique is used to distinguish the variables belonging to different sets. The proposed analysis method is based on the approach of binary decision diagrams (BDDs). The application of the rules for the construction of the BDD is driven by the labels associated with disjoint variables. The BDD is then transformed into a ternary decision diagram (TDD). The TDD represents a straightforward data structure for performing the probabilistic analysis. Equations are provided to determine the system unavailability and the probability of critical states. Numerical examples clarify the application of the proposed equations.