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

In this paper, an efficient reliability method is proposed. The Asymptotic Sampling (AS) and Weighted Simulation (WS) are two main basic tools of the presented method. In AS, the standard deviation of the distributions are amplified at several levels to find an adequate number of failed samples, then by using a simple regression technique, the reliability index is determined. The WS is another method which uses the uniform distribution for sampling, where the information about the distributions of the variables is taken into account through the weight indexes. The WS provides interesting flexibility 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 flexibility of the WS to decrease the required calls of limit state function. Using this technique results in a new efficient 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.