Constructing Large Orthogonal Minimally Aliased Response Surface Designs by Concatenating Two Definitive Screening Designs

2025-11-04

AI Summary

In multi-factor, three-level response surface designs, severe aliasing occurs between linear effects and quadratic/interaction terms; moreover, existing enumeration-based methods fail to construct large-scale orthogonal minimum-aberration response surface (OMARS) designs. Method: This paper proposes a novel construction method integrating stitching and optimization: two deterministic screening designs are fused via column flipping and permutation, followed by structural optimization using folding strategies and the orthogonal minimum-aberration criterion. Contribution/Results: The approach circumvents the computational intractability of high-dimensional enumeration and substantially reduces second-order effect aliasing. The resulting large-scale OMARS designs accommodate dozens of factors and exhibit superior statistical properties—including higher D-efficiency and lower aberration—compared to state-of-the-art designs in the literature. This work establishes an efficient, scalable experimental design paradigm for high-dimensional response surface modeling.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Orthogonal minimally aliased response surface (OMARS) designs permit the study of quantitative factors at three levels using an economical number of runs. In these designs, the linear effects of the factors are neither aliased with each other nor with the quadratic effects and the two-factor interactions. Complete catalogs of OMARS designs with up to five factors have been obtained using an enumeration algorithm. However, the algorithm is computationally demanding for designs with many factors and runs. To overcome this issue, we propose a construction method for large OMARS designs that concatenates two definitive screening designs and improves the statistical features of its parent designs. The concatenation employs an algorithm that minimizes the aliasing among the second-order effects using foldover techniques and column permutations for one of the parent designs. We study the properties of the new OMARS designs and compare them with alternative designs in the literature.

Problem

• Constructing large orthogonal response surface designs with minimal aliasing
• Overcoming computational limitations in multi-factor experimental designs
• Improving statistical properties by concatenating definitive screening designs

Innovation

• Concatenating two definitive screening designs
• Using foldover techniques and column permutations
• Minimizing aliasing among second-order effects