Ignorance Factors Using Model Expansion

The present paper describes a quantitative analysis of the effect of model imprecision on reliability-based design rules. The presence of model uncertainty requires the insertion of additional safety elements in the corresponding design-check criteria. In this paper, this is considered to be achieved by the use of ignorance factors. A method is derived that allows these ignorance factors to be determined on the basis of just one structural reliability analysis performed without the inclusion of model uncertainty. This is based on a sensitivity analysis of uncertain parameters in a limit-state model, and on some basic considerations of the effect of expanding a perfect model to an imperfect one. This “expansion” problem—the addition of random variables—is complementary to the well-known “omission” problem, and, from this point of view, ignorance factors have a function similar to that of omission factors except that the ignorance factors can be used directly in design-check equations subject to model uncertainty. The present paper outlines the derivation of asymptotic expressions for expansion factors for both additive- and multiplicative-model uncertainty parameters. The basic inverse-reliability-problem format provides for the link between model expansion and ignorance factors. Various example applications show that the proposed user-friendly expressions for ignorance factors result in accurate and reliable design rules.