An intrinsic order criterion to evaluate, large, complex fault trees

Abstract

A new efficient algorithm is introduced to evaluate (non) coherent fault trees, obtaining exact lower & upper bounds on system unavailability, with a prespecified maximum error. The algorithm is based on the canonical normal form of the Boolean function, but overcomes the large number of terms needed, by using an intrinsic order criterion (IOC) to select the elementary states to evaluate. This intrinsic order implies lexicographic (truth table) order. The criterion guarantees a priori that the probability of a given elementary system state is always greater than or equal to the probability of another state, for any set of basic probabilities. IOC is exclusively based on the positions of 0 & 1 in the binary n-tuples defining the elementary states. The algorithm does not require any qualitative analysis of the fault tree. The computational cost mainly depends on the basic event probabilities, and is related to system complexity, only because the Boolean function must be evaluated.