Optimal Importance‐Sampling Density Estimator

Abstract

Importance‐sampling technique has been used in recent years in conjunction with Monte Carlo simulation method to evaluate the reliability of structural systems. Since the efficiency of the importance‐sampling method depends primarily on the choice of the importance‐sampling density, the use of the kernel method to estimate the optimal importance‐sampling density is proposed. This method deviates from the current practice of prescribing the importance‐sampling density from a given parametric family of density functions. Instead, the data obtained from an initial Monte Carlo run are utilized to determine the required importance‐sampling density. The kernel method yields unbiased estimates of the probability of failure. Two measures are developed to quantify the efficiency of the kernel method relative to the basic Monte Carlo method. The first measure, called the