An improved fourth-order moment reliability method for strongly skewed distributions

High-order statistical moment method uses only moments of random variable for reliability analysis and can widely address the problem of unknown probability distribution. However, for practical cases with strongly skewed distributions, the existing fourth-moment methods may produce large errors or result in instability in the analysis process. Thus, an improved expression of the fourth-order moment reliability index based on the fourth-moment standardization function for strongly skewed distributions is developed. First, the coefficients of the fourth-moment standardization function are modified for strongly skewed distributions by fitting the coefficients of the third-order polynomial transformation, and an improved fourth-moment standardization function is developed. Then, the accuracy of the improved model is demonstrated by analyzing the relative errors between the estimated moments and their target values. Furthermore, the complete reliability index formula is derived according to the monotonic expression of the third-order polynomial transformation. Finally, numerical examples show the improved accuracy achieved by the proposed method. It can be concluded that, compared to the original methods, the proposed method is more accurate and stable for reliability analysis in which the distribution is strongly skewed.