Reliability evaluation of multi-state systems under cost consideration

A more practical and desirable performance index of multi-state systems is the two-terminal reliability for level (d, c) (2TR_d,c), defined as the probability that d units of flow can be transmitted from the source node to the sink node with the total cost less than or equal to c. In this article, a simple algorithm is developed to calculate 2TR_d,c in terms of (d, c)-MPs. Two major advantages of the proposed algorithm include: (1) as of now, it is the only algorithm that searches for (d, c)-MPs without requiring all minimal paths (MPs) and the procedure of transforming feasible solutions; (2) it is more practical and efficient in solving (d, c)-MP problem in contrast to the best-known method. An example is provided to illustrate the generation of (d, c)-MPs by using the presented algorithm, and 2TR_d,c is thus evaluated. Furthermore, the computational experiments are conducted to verify the performance of the presented algorithm.