System reliability estimation using simulation combined with network reductions

This paper proposes a dynamic Monte Carlo sampling method, called the conditional minimal cut set (COMICS) algorithm, where all arcs are not simulated at each trial and all minimal cut sets need not be given in advance. The proposed algorithm repeats simulating a minimal cut set composed of the arcs which originate from the (new) source node and reducing the network on the basis of the states of simulated arcs until the s-t connectedness is confirmed. We develop the importance sampling estimator, the total hazard estimator and the hazard importance sampling estimator which are all based on the proposed algorithm, and compare the performance of these simulation estimators. It is found that these estimators can significantly reduce the variance of the raw simulation estimator and the usual importance sampling estimator.