Improved Sampling Plans for Combinatorial Invariants of Coherent Systems

Terminal network reliability problems appear in many real-life applications, such as transportation grids, social and computer networks, communication systems, etc. In this paper, we focus on monotone binary systems with identical component reliabilities. The reliability of such systems depends only on the number of failure sets of all possible sizes, which is an essential system invariant. For large problems, no analytical solution for calculating this invariant in a reasonable time is known to exist, and one has to rely on different approximation techniques. An example of such a method is Permutation Monte Carlo. It is known that this simple plan is not sufficient for adequate estimation of network reliability due to the rare-event problem. As an alternative, we propose a different sampling strategy that is based on the recently pioneered Stochastic Enumeration algorithm for tree cost estimation. We show that, thanks to its built-in splitting mechanism, this method is able to deliver accurate results while employing a relatively modest sample size. Moreover, our numerical results indicate that the proposed sampling scheme is capable of solving problems that are far beyond the reach of the simple Permutation Monte Carlo approach.