Uncertainty Sensitivity Analysis for Reliability Problems with Parametric Distributions

A method of uncertainty sensitivity modeling and assessment for reliability problems involving parametric distributions is presented in the paper. The uncertainty sensitivity is quantified as the first-order derivative of the response function with respect to the distribution parameters instead of uncertain variables themselves. Monte Carlo (MC) simulation is employed as a universal evaluation method. Change of measure is proposed to formulate the likelihood ratio estimator, allowing for evaluation of the sensitivity for multiple values of distribution parameters using one-pass MC simulations. The relation between the likelihood ratio method and importance sampling is discussed, and the bounded variance of the unbiased MC estimator is derived. In addition, the analysis-assisted sensitivity reduction procedure is outlined, and the influence of distribution parameters on the decisionmaking is discussed. The overall method is demonstrated using examples.