Calculating the probability of a complex event presented by a given set of critical sets

Abstract

The problem of calculating the probability of a complex event presented by a special form of Boolean function of basic events the probabilities of which are given is considered. The problem is reduced to orthogonalization of a disjunctive normal form in Boolean algebra of basic events. Two algorithms for orthogonalization are suggested and the experimental results of comparison of their efficiencies are given. The application of the problem may be in calculating reliability of an engineering system.