An improved high-moment method for reliability analysis

For reliability analysis, there may be several potential distributions for a random variable due to limited samples available. For the same reason, a distribution may not be available. Simply assuming a normal distribution may result in a large error for the reliability prediction. Moment-based methods use only moments of random variables for reliability analysis and can effectively address the problem of multiple distributions or lack of distributions. The existing moment-based methods, however, may produce large errors or may result in instability in the analysis process. This study extends the high-moment method for higher accuracy of the reliability prediction by including the parameters ignored by the existing high-moment method. The proposed method derives the reliability index from the first four moments of random input variables based on the statistical properties of the standard normal random variable. Compared with the existing method, the proposed method is more accurate and stable for problems for which the distributions of input random variables are unknown. Numerical examples show the improved accuracy from the proposed method.