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.

高阶统计矩方法仅使用随机变量的矩进行可靠性分析，可以广泛解决未知概率分布的问题。但是，对于具有严重偏斜分布的实际情况，现有的第四矩方法可能会产生较大的误差或导致分析过程不稳定。因此，开发了基于第四矩标准化函数的强偏分布的四阶矩可靠性指标的改进表达式。首先，通过拟合三阶多项式变换的系数，针对强偏斜分布修改第四矩标准化函数的系数，并开发出改进的第四矩标准化函数。然后，通过分析估计力矩与其目标值之间的相对误差，证明了改进模型的准确性。此外，根据三阶多项式变换的单调表达式，得出了完整的可靠性指标公式。最后，数值算例表明了所提方法的改进精度。可以得出的结论是，与原始方法相比，该方法对于分布严重偏斜的可靠性分析更为准确和稳定。