A fast and robust method for estimating the failure probability of structures

A new approach is presented to estimate quickly and accurately the probability of failure of structures. The approach works by employing first-order reliability methods to determine the closest point to the mean of random variables in a failure region. Then, by presenting sub-intervals in various layers and by grouping the generated samples in a Monte Carlo simulation (MCS), it was possible to reduce the number of structural calculations with controllable error where acceptable accuracy was introduced. Various numerical and engineering examples with complex limit state functions were solved by the proposed approach and the results were compared with those of common reliability methods. The outcome shows the high accuracy of the proposed approach. Furthermore, the number of required structural calculations was significantly reduced compared to normal MCS.