Approximating network reliability estimates using linear and quadratic unreliability of minimal cuts

A new algorithm is proposed to approximate the terminal-pair network reliability based on minimal cut theory. Unlike many existing models that decompose the network into a series–parallel or parallel–series structure based on minimal cuts or minimal paths, the new model estimates the reliability by summing the linear and quadratic unreliability of each minimal cut set. Given component test data, the new model provides tight moment bounds for the network reliability estimate. Those moment bounds can be used to quantify the network estimation uncertainty propagating from component level estimates. Simulations and numerical examples show that the new model generally outperforms Esary-Proschan and Edge-Packing bounds, especially for high reliability systems.