  The Monte Carlo simulation (MCS) is a statistical methodology used in a large
number of applications. It uses repeated random sampling to solve problems with
a probability interpretation to obtain high-quality numerical results. The MCS
is simple and easy to develop, implement, and apply. However, its computational
cost and total runtime can be quite high as it requires many samples to obtain
an accurate approximation with low variance. In this paper, a novel MCS, called
the self-adaptive BAT-MCS, based on the binary-adaption-tree algorithm (BAT)
and our proposed self-adaptive simulation-number algorithm is proposed to
simply and effectively reduce the run time and variance of the MCS. The
proposed self-adaptive BAT-MCS was applied to a simple benchmark problem to
demonstrate its application in network reliability. The statistical
characteristics, 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 MCS
extensively on a large-scale problem.
