Estimation of Reliability by Monte Carlo Simulations: Combined with Optimized Parametric Models

Abstract

A new method for efficient Monte Carlo simulations is developed, and used to estimate the reliability of dependent and independent systems. The method consists of parametrized Monte Carlo simulations, where the robust qualities in the simulations are preserved. The parametrized system corresponds to the given system for set parameter values. By using the regularity of system reliability as a function of the parameter, the original system reliability can be predicted accurately with relative small samples. The estimate is obtained by using weighted least squares to fit the parametrized simulations. Even with a small sample size, n = 10^5 , can probabilities in the order 10^-6 to 10^-8 be estimated very accurate. For some systems, even probabilities in the order 10^-12 are estimated with 10% relative difference from the analytic solution.