Measures of Structural Safety Under Imperfect States of Knowledge

In assessing structural safety, the state of knowledge is imperfect when uncertainties arise from estimation error or model imperfection. The nature of these uncertainties is fundamentally different from those arising from inherent variabilities. A reliability index under such conditions is a point estimator of safety. Motivated by needs in structural code development, a set of fundamental requirements on the point‐estimator reliability index are formulated. Existing definitions of the reliability index are examined in this light and are found to be deficient in satisfying one or more of the requirements. Based on concepts from Bayesian statistical decision theory, a new reliability index is introduced which satisfies all the stipulated requirements. The index recognizes the fundamental difference between the sources of uncertainty and provides a rational basis for the assessment of structural safety and for development of reliability‐based codes under arbitrary states of knowledge. Methods are also developed for quantifying the uncertainty in the measure of safety arising from the imperfect state of knowledge. Existing reliability methods can be used to compute the probability distribution or variance of the safety measure. A simple example illustrates the main concepts of the paper.