Powerful Foldover Designs

2025-07-19

AI Summary

This paper addresses two critical challenges in screening experiments: (1) confounding between main effects and second-order interactions or quadratic effects, and (2) model-dependent variance estimation. To resolve these, we propose a novel foldover-based design methodology that eliminates such confounding and—more importantly—generates pure error degrees of freedom (or “pseudo-factor” degrees of freedom) independent of model specification, enabling robust, model-agnostic variance estimation. Furthermore, we develop an augmented design framework guided by a minimum expected confidence interval width criterion, supported by an efficient construction algorithm. Simulation studies and application to a real eight-factor ethylene concentration experiment demonstrate that the proposed design outperforms conventional approaches when effect sparsity and hierarchy assumptions hold—and delivers substantially greater gains in main-effect detection power and second-order model selection accuracy when those assumptions are violated.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

The foldover technique for screening designs is well known to guarantee zero aliasing of the main effect estimators with respect to two factor interactions and quadratic effects. It is a key feature of many popular response surface designs, including central composite designs, definitive screening designs, and most orthogonal, minimally-aliased response surface designs. In this paper, we show the foldover technique is even more powerful, because it produces degrees of freedom for a variance estimator that is independent of model selection. These degrees of freedom are characterized as either pure error or fake factor degrees of freedom. A fast design construction algorithm is presented that minimizes the expected confidence interval criterion to maximize the power of screening main effects. An augmented design and analysis method is also presented to avoid having too many degrees of freedom for estimating variance and to improve model selection performance for second order models. Simulation studies show our new designs are at least as good as traditional designs when effect sparsity and hierarchy hold, but do significantly better when these effect principles do not hold. A real data example is given for a 20-run experiment where optimization of ethylene concentration is performed by manipulating eight process parameters.

Problem

• Enhances foldover technique for zero aliasing in main effects
• Provides independent variance estimator degrees of freedom
• Improves model selection for second-order response surfaces

Innovation

• Foldover technique ensures zero aliasing
• Fast algorithm minimizes confidence intervals
• Augmented method improves model selection