Journal
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART O-JOURNAL OF RISK AND RELIABILITY
Volume 230, Issue 2, Pages 147-161Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1748006X15598722
Keywords
Minimal cut (path) set; minimal cut (path) vector; structure function; Fussell-Vesely importance; direct partial Boolean derivative
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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.
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