Probability evaluation of system-failure occurrence based on minimal cut-sets

A minimal cut set (MCS) of FTA (fault tree analysis) shows a minimal combination of component failures leading to system failure, based on which system failure probability can be evaluated. However, the conventional inclusion-exclusion method based on MCSs does not necessarily give the system failure occurrence probability. This paper proposes an analytical probability evaluation method of system failure occurrence based on critical states for each basic event. System failure occurrence is caused by a basic event if it occurs at its critical state. Critical states for a basic event can be obtained using logical expression in terms of MCS's. Thus, the system failure occurrence probability can be obtained as the sum of system failure occurrence probabilities caused by basic events. The proposed method assumes any general distribution for component failure probability. An illustrative example shows the details and merits of the method.