Abstract
The reliability at required demand level d (M2Rd) is usually selected as the most important index of two-terminal multi-state networks (MSNs) whose arcs have independent, discrete, limited and multivalued random capacities. To evaluate M2Rd is a NP-hard problem and is too costly to obtain through traditional techniques. Up to now, only one Monte-Carlo Simulation (RCMCS) is proposed to evaluate M2Rd-Moreover, RCMCS not only requires to overcome NP-hard problems to know all minimal multi-state cuts (d-MCs) in advance, but also its replications all need an exponential number of comparisons. A simple polynomial-time Monte-Carlo Simulation (YehMCS) is proposed in this article to estimate M2Rd without finding any d-MCs. YehMCS can also solve the reliability (C2Rd) for the continue-state networks (CSN) which is a novel generation of MSN. The estimators of YehMCS are compared with RCMCS and exact solutions. The analysis indicates that YehMCS is more practical, efficient and effective for most cases from the proposed experiments.