A New Monte Carlo Method for Evaluating System-Failure Probability

This paper proposes, under a rare-event assumption, a new ``Coverage Monte Carlo'' method for evaluating the top-event probability of a coherent fault tree. All the min cuts are assumed to be known. A Karp-Luby Monte Carlo (KLM) estimator with minimum variance is derived in a different manner. The KLM evaluates an inclusion-exclusion formula excluding the first sum of products. A new coverage Monte Carlo (NCM) estimator evaluates the formula excluding the first and the second sums of products. The NCM yields an estimator with a smaller variance than the KLM which becomes a linear time procedure in the number of min cuts. Upper bounds on the numbers of trials necessary to attain a given coefficient of variation are derived for KLM and NCM. The bounds can be calculated before any Monte Carlo trials. The KLM requires at least 8 times more trials than the NCM. Given sufficient computer memory to implement an alias sampling method, the NCM requires less computation time than the KLM when an accurate estimate is required. The NCM is more favorable when the deterministic bounding practice based on the first and second sums of products yields a smaller relative error. The NCM is consistent with the fact that deterministic bounds have been computed.