An effcient method for reliability estimation using the combination of asymptotic sampling and weighted simulation

In this paper, an effcient reliability method is proposed. Asymptotic Sampling (AS) and Weighted Simulation (WS) are two basic tools of the presented method. In AS, the standard deviation of the distributions is amplified at several levels to nd an adequate number of failed samples; then, by using a simple regression technique, the reliability index is determined. The WS is another method that uses the uniform distribution for sampling, in which the information about the distributions of the variables is taken into account through the weight indexes. The WS provides interesting exibility where a sample generated for a specific standard deviation can be used as a sample for another standard deviation without having to reevaluate the limit state function. In AS, the deviations of variables are scaled in each step, where one can use the exibility of the WS to decrease the required calls of limit state function. Using this technique results in a new effcient method, so-called Asymptotic Weighted Simulation (AWS). In addition, using the strengths of both AS and WS can be considered another superiority of the hybrid version. Performance of the presented method is investigated by solving several mathematical and engineering examples.