An improved algorithm for the quickest path reliability problem

. The quickest path reliability problem (QPRP) emerged for extending the quickest path problem to the system reliability. This problem aims to assess the reliability of a multi-state network (MSN) for transmitting a given d units of a commodity from a source node to a destination node through one single path in the network within T units of time. Most of the proposed algorithms in the literature for this problem need all of the network’s minimal paths as an input. Here, we propose a fast algorithm based on the node-child matrix of the network to address the QPRP that does not need any minimal paths in advance. We discuss the correctness of the algorithm and provide two benchmark examples to illustrate the algorithm and explain its superiority compared to some existing algorithms in the literature.