Search for all MCs in networks with unreliable nodes and arcs

A simple method is proposed to search for all minimal cutsets (MCs ) for imperfect networks reliability subject to both arc and node failures under the condition that all of the MCs in the network with perfect nodes are given in advance. The proposed method does not require re-enumeration for all of the MCs for additional node failure consideration. All of the MC candidates found in the proposed algorithm are actual MCs without any need for further verification. This algorithm is more effective than the existing algorithm in which every MC candidate is not verified as a MC. No identical MCs are found using the proposed algorithm, which does not duplicate MCs and is more efficient than the existing methods. Only simple concepts are used to implement the proposed algorithm, which makes it easier to understand and implement. With considering unreliable nodes, the proposed method is also more realistic and valuable for reliability analysis in an existing network. The correctness of the proposed algorithm will be analyzed and proven. One example is used to illustrate how all MCs are generated in a network with arc and node failures solved using the proposed algorithm.