Abstract
To evaluate the multi-state network reliability at required demand level d (M2R d ) is a NP-hard problem and is too costly to obtain through traditional techniques. A simple polynomial-time Monte-Carlo Simulation (Yeh MCS ) is proposed in this article to estimate M2R d without finding any d-MCs. Yeh MCS can also solve the reliability (C2R d ) for the continue-state networks (CSN) which is a novel generation of MSN. The estimators of Yeh MCS are compared with RC MCS and exact solutions. The analysis indicates that Yeh MCS is more practical, efficient and effective for most cases from the proposed experiments.