Reliability sensitivity analysis with random and interval variables

TLDR

Sensitivity analysis in reliability identifies how changes in uncertain variables affect reliability and pinpoints the most influential variables, but existing methods mainly handle random variables while many engineering problems involve interval variables. This study proposes a sensitivity analysis method that accommodates mixtures of random and interval variables. Six sensitivity indices—covering average reliability, reliability bounds, interval averages, widths, and random variable distribution parameters—are derived from the first‑order reliability method, enabling automatic extraction of sensitivity information immediately after FORM without additional computations. The method is illustrated through two example problems. © 2009 John Wiley & Sons, Ltd.

Abstract

Abstract In reliability analysis and reliability‐based design, sensitivity analysis identifies the relationship between the change in reliability and the change in the characteristics of uncertain variables. Sensitivity analysis is also used to identify the most significant uncertain variables that have the highest contributions to reliability. Most of the current sensitivity analysis methods are applicable for only random variables. In many engineering applications, however, some of uncertain variables are intervals. In this work, a sensitivity analysis method is proposed for the mixture of random and interval variables. Six sensitivity indices are defined for the sensitivity of the average reliability and reliability bounds with respect to the averages and widths of intervals, as well as with respect to the distribution parameters of random variables. The equations of these sensitivity indices are derived based on the first‐order reliability method (FORM). The proposed reliability sensitivity analysis is a byproduct of FORM without any extra function calls after reliability is found. Once FORM is performed, the sensitivity information is obtained automatically. Two examples are used for demonstration. Copyright © 2009 John Wiley & Sons, Ltd.