A new efficient algorithm for finding all d-minimal cuts in multi-state networks

Reliability evaluation of multi-state systems gives a reasonable demonstration of system performance, and thus is of great importance to their planning, designing and operation. One of the common methods for reliability evaluation is using d-minimal cuts (d-MCs). This paper proposes a new method to solve the d-MC problem. Specifically, several efforts have been devoted to searching for all d-MCs from two aspects: (i) A new technique is developed to calculate lower capacity bounds of edges which are appropriately used to determine some real d-MCs without any verification, and further to reduce the number of d-MC candidates; (ii) A new approach is put forward to correctly and effectively detect duplicate d-MCs, and the approach brings important insights into the underlying reason why a d-MC derived from one MC can be generated from another MC once again. A simple example and a real case study of the LCD monitor delivery are provided to illustrate the solution procedure, and the utility of the proposed algorithm, respectively. In addition, numerical experiments conducted on four benchmark networks show that the proposed algorithm outperforms a newly developed method in the literature.