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. (C) 2011 Elsevier Inc. All rights reserved.