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The Monte Carlo simulation (MCS) is a statistical methodology used in a largenumber of applications. It uses repeated random sampling to solve problems witha probability interpretation to obtain high-quality numerical results. The MCSis simple and easy to develop, implement, and apply. However, its computationalcost and total runtime can be quite high as it requires many samples to obtainan accurate approximation with low variance. In this paper, a novel MCS, calledthe self-adaptive BAT-MCS, based on the binary-adaption-tree algorithm (BAT)and our proposed self-adaptive simulation-number algorithm is proposed tosimply and effectively reduce the run time and variance of the MCS. Theproposed self-adaptive BAT-MCS was applied to a simple benchmark problem todemonstrate its application in network reliability. The statisticalcharacteristics, including the expectation, variance, and simulation number,and the time complexity of the proposed self-adaptive BAT-MCS are discussed.Furthermore, its performance is compared to that of the traditional MCSextensively on a large-scale problem.

Self-Adaptive Binary-Addition-Tree Algorithm-Based Novel Monte Carlo Simulation for Binary-State Network Reliability Approximation