Reliability evaluation of multi-state systems under cost consideration

Abstract 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.