Enhancing reliability calculation for one-output k-out-of-n binary-state networks using a new BAT

Evaluation of network reliability is a crucial aspect of system planning, design, and management. A k-out-of-n network is an important extension of the k-out-of-n system, which is a repairable redundancy binary-state system with n parallel components. The system fails if and only if at least k consecutive components fail, where k is an integer between 1 and n. In the proposed problem, at least k units of input flow are required to activate a node to output one unit of flow. This one-output k-out-of-n binary-state network model, along with a novel algorithm proposed to calculate its reliability, is motivated by real-life applications. The binary-addition-tree algorithm (BAT) can address this problem. By modifying the BAT and incorporating the novel cut-based layered-search method (CLSA), a novel algorithm is proposed to calculate the reliability of the proposed k-out-of-n binary-state network. The proposed algorithm is not limited to its original scope. The proposed algorithm has been extended to address additional scenarios. Specifically, it is now capable of solving traditional multi-output k-out-of-n networks. Based on both theoretical and empirical analyses conducted on examples, the proposed algorithm demonstrates greater efficiency and flexibility compared to the traditional BAT.