Cutting the double loop: Theory and algorithms for reliability-based design optimization with parametric uncertainty

Parametric uncertainties complicate engineering design—confounding regulated design approaches and degrading the performance of reliability efforts. The simplest means to tackle this uncertainty is double-loop simulation , a nested Monte Carlo method that, for practical problems, is intractable. In this work, we introduce a flexible, general approximation technique that obviates the double loop. This approximation is constructed in the context of a novel theory of reliability design under parametric uncertainty: we introduce metrics for measuring the efficacy of reliability-based design optimization strategies ( epistemic design gap and effective reliability ), minimal conditions for controlling uncertain reliability ( precision margin ), and stricter conditions that guarantee the desired reliability at a designed confidence level. We provide a number of examples with open-source code to demonstrate our approaches in a reproducible fashion.