Monte Carlo simulation using Pearson's frequency curves

Abstract

An extension of the direct Monte Carlo simulation method to estimate the probability of failure of structural systems or components is investigated. It utilizes the performance values computed during the simulation process from which a distribution is fitted using Pearson's system of frequency curves. The area under the curve in the failure domain gives the failure probability. This method has the simplicity and versatility of the direct simulation method and overcomes the need for large number of cycles in problems with low failure probability (less than 0.001). The stability, convergence and accuracy of the method is exemplified through a numerical example.