Probability Sensitivity Estimation with Respect to Distribution Parameters via the Method of Moments

The method of moments (MoM) has been widely applied for reliability analysis, demonstrating both efficiency and accuracy for nonlinear and small failure probability problems. This contribution presents a method for sensitivity analysis based on MoM, called SAMoM. Specifically, the sensitivity index under consideration is the partial derivative of the failure probability with respect to the distribution parameters, including mean, standard deviation, and skewness. Assuming the random variables are independent, the sensitivity index is formulated with the aid of the third moment reliability index. An efficient numerical algorithm is developed for SAMoM, allowing the sensitivity index to be evaluated as a byproduct of reliability analysis with MoM, without requiring any additional structural analyses. Numerical examples demonstrate that SAMoM can accurately estimate the sensitivity of failure probability with respect to the mean and standard deviation. For random variables with skewness of small magnitude, the sensitivity of failure probability with respect to skewness can also be reliably estimated.