A new method for multi-state flow networks reliability estimation based on a Monte Carlo simulation and intersections of sets

The problem of the assessment of a multi-state flow network reliability can be very time-consuming, especially for large networks. Simulation approaches alleviate this problem by generating random capacity vectors and comparing them with d-MPs or d-MCs, for estimation of network reliability. In this study, a new approach to compare randomly generated vectors with a given list of vectors is developed. The presented method is based on intersections of some sets of indices of a given list of vectors. The computational complexity of the presented approach is examined and compared with existing approaches. Two comprehensive examples are provided to estimate the network reliability and compare the effectiveness of the presented method with existing ones. Numerical experiments show that the presented method is usually more efficient than existing ones especially if the network unreliability is estimated using d-MCs.