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

arXiv: https://arxiv.org/abs/1806.00048 · HTML: https://mlsanity.com/paper/1806.00048/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2018.

## Built on by (most cited first, 2 of 2)

- [Generative Reliability-Based Design Optimization Using In-Context Learning Capabilities of Large Language Models](https://mlsanity.com/paper/2503.22401/) (2025)
- [Accounting for Uncertainty in Machine Learning Surrogates: A Gauss-Hermite Quadrature Approach to Reliability Analysis](https://mlsanity.com/paper/2509.18128/) (2025)

## Abstract (arXiv)

Statistical 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 statistical uncertainty: We introduce metrics for measuring the efficacy of RBDO strategies (effective margin 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.