Calculations of systems unreliability by algebraic manipulation of failure event

Abstract

Computations of reliability of a given system is an important field of research in reliability engineering. There are many techniques available in the literature. Some of these are based on Boolean algebra's relations. In these papers unions of events have been reduced to give the reliability of a system. Reduction of union of events involve a lot of work and give rise to a large number of terms. In this paper we have adopted a different approach. We first set up some simple algebraic lemmas on intersections and give their proofs. Next we represent the system failure event as the intersection of paths failure events. By applying our lemmas on this intersection of events step by step we are able to expand the system failure event in the form of unions of mutually exclusive events. Simple substitution of probabilities of success or failure, as the case may be, of the events involved in the union of expanded form gives the unreliability of the system. The algorithm is explained by an example.