Analysis of structural reliability under parameter uncertainties

Formulation of structural reliability requires selection of probabilistic or physical models, which usually involve parameters to be estimated through statistical inference — a process that invariably introduces uncertainties in parameter estimates. The measure of reliability that incorporates these parameter uncertainties is termed the predictive reliability index. Methods for computing this measure and the corresponding failure probability are introduced. A simple approximate formula is derived for the predictive reliability index, which requires a single solution of the reliability problem together with parameter sensitivities with respect to mean parameter values. The approach also provides measures of the uncertainties inherent in the estimates of the reliability index and the failure probability, which arise from parameter uncertainties. An illustrative example involving component and system problems demonstrates the influence of parameter uncertainties on the predictive reliability index and the accuracy of the simple approximation formula.