Abstract
This paper proposes a new “Coverage Monte Carlo” for evaluating a failure probability of a system described by a monotonic Boolean function. All the minimal cut sets are assumed to be known. It is first clarified that the Karp-Luby's coverage Monte Carlo evaluates effects of the second and the higher terms of an inclusion-exclusion formula. The first and the second terms, however, can often be calculated by ordinary, deterministic algorithms, and thus the new Monte Carlo is derived to evaluate only contributions of the third and the higher terms. The Monte Carlo estimate always falls in between the known upper (the first term) and lower (the first minus the second term) bounds. It is proven that the proposed Monte Carlo estimator has a smaller variance than the Karp-Luby estimator under reasonable assumptions. The estimator variance and the coefficient of variation can be evaluated before and after Monte Carlo executions. In contrast to the direct Monte Carlo, the coefficient of variation is proven to approach to zero as the system becomes more reliable and hence rare-event characteristics become more dominant. A numerical example is given.
