A new approach to evaluate reliability of multistate networks under the cost constraint

A multistate network is a system composed of multistate components. The network reliability under the cost constraint for level (d,c) can be computed in terms of (d,c)-MP (MP stands for minimal path) which is a vector such that d units of flow can be transmitted between two specified nodes with the total cost not greater than c. In this study, a new algorithm was developed to evaluate the reliability of multistate networks under cost constraint in terms of the entire (d,c)-MPs. The proposed method is more efficient than the best-known existing algorithm. One example is illustrated to show how all (d,c)-MPs are generated by the proposed algorithm. The reliability of this example is then computed. The computational complexity of the proposed algorithm is also analyzed.