A hybrid algorithm for reliability evaluation of a multi-state system

Multi-state two-terminal reliability for level d (MS2TR(d)) is one of the most important performance indices of a multi-state system. One common method for computing MS2TR(d) is using the multi-state minimal path (named d-MP). In this article, an efficient algorithm is presented to compute MS2TR(d) in terms of d-MPs. The main characteristics of the proposed algorithm include: (1) it requires neither minimal paths nor minimal cuts to be known; (2) it is a hybrid algorithm combining the max-flow method and the implicit enumeration method. Two examples are provided to illustrate the performance of the presented algorithm, and the computational results show that the hybrid algorithm is superior to the best-known method.