Minimal paths and cuts of networks exposed to common-cause failures

A method is suggested for determining the minimal cuts and paths of a general network with common-cause failures. The minimal paths (cuts) are deduced from simple network minimal paths (cuts) obtained for the network if the common-cause failures are ignored, by appropriate manipulations with sets of path (cut) branches and sets of branches interrupted by common-cause failures. Calculation procedures are presented for an effective application of the method, to evaluate the reliability indices of the network by taking into account the statistical dependence of the failure events. Two examples are included