Analysis of minimal cut and path sets based on direct partial Boolean derivatives

Principal steps in reliability engineering include estimation of system reliability and identification and quantification of situations which cause a system failure. There are several techniques that can be used to solve these tasks. Some of them are based on minimal cut (path) sets, which represent minimal sets of basic events, whose simultaneous occurrence leads to a failure (repair) of the system. In this article, applications of minimal cut (path) sets in reliability analysis are summarized, and their connection with direct partial Boolean derivatives is studied. In reliability analysis, direct partial Boolean derivatives identify situations in which a failure (repair) of one system component results in a system failure (repair). Therefore, they reveal the influence of one system component on the whole system. However, minimal cut (path) sets define the influence of a simultaneous failure (repair) of a group of system components on the system activity. Therefore, there should be some correlation between direct partial Boolean derivatives and minimal cut (path) sets. This correlation is studied in this article, and as a result, new algorithms for identification of minimal cut (path) sets are proposed based on this correlation.