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Statistical uncertainties complicate engineering design -- confoundingregulated design approaches, and degrading the performance of reliabilityefforts. The simplest means to tackle this uncertainty is double loopsimulation; a nested Monte Carlo method that, for practical problems, isintractable. In this work, we introduce a flexible, general approximationtechnique that obviates the double loop. This approximation is constructed inthe context of a novel theory of reliability design under statisticaluncertainty: We introduce metrics for measuring the efficacy of RBDO strategies(effective margin and effective reliability), minimal conditions forcontrolling uncertain reliability (precision margin), and stricter conditionsthat guarantee the desired reliability at a designed confidence level. Weprovide a number of examples with open-source code to demonstrate ourapproaches in a reproducible fashion.

Cutting the Double Loop: Theory and Algorithms for Reliability-Based Design Optimization with Statistical Uncertainty