A Novel Cut-Based Universal Generating Function Method

A multistate information network (MIN) is a generalization of the tree-structured multistate-state system that does not satisfy the flow conservation law. The current known universal generating function methods (UGFMs, here called pUGFMs) used to evaluate acyclic MIN (AMIN) reliability are based on the connectedness between node 1 and the targets, i.e. find all possible paths between node 1 and the targets. A novel cut-based UGFM (cUGFM) is proposed for the AMIN reliability problem. The proposed cUGFM is based on the disconnectedness between node 1 and the targets, i.e. find all possible cuts between node 1 and the targets. It provides a flexible, novel method to calculate reliability and unreliability. The computational complexity of the proposed algorithm is also analyzed and compared with the best-known existing methods. Finally, three benchmark examples are given to illustrate how the exact one-to-all-target-subset AMIN reliability is calculated using the proposed cUGFM.