A new method for ordering binary states probabilities in reliability and risk analysis

Abstract

A new method is proposed to select the binary n-tuples of 0s and 1s by decreasing order of there occurrence probabilities in stochastic Boolean models. This method can be applied to evaluate fault trees in Reliability Engineering and Risk Analysis, as well as to many other problems described by a stochastic Boolean structure. The selecting criterion is exclusively based on the positions of 0s and 1s in the binary n-tuples. In this way, the computational cost in sorting algorithms is drastically reduced, because the proposed criterion is independent of the probabilities of the Boolean variables. Every step, the algorithm extends the set of selected binary states, obtaining the binary n-tuples just by adding 0 (1) at the end of all the (some) previously selected binary n — 1-tuples.