Constructing Large Orthogonal Minimally Aliased Response Surface Designs Through Enumeration and Combination of Weighing Designs

2026-08-05

AI Summary

This study addresses the lack of scalable, efficient response surface designs with both orthogonality and minimal confounding for high-throughput experimentation. The authors propose the Orthogonal Minimal-Aberration Response Surface (OMARS) design framework, which enables, for the first time, complete enumeration of three-level weighing designs up to 24 runs. To overcome the computational barriers of exhaustive search at larger scales, they develop partial enumeration verification and combinatorial construction algorithms that substantially extend the feasible design space beyond current limits. The resulting catalog of OMARS designs spans a wide range of factor counts and weight configurations, supports run sizes that are arbitrary multiples of the base dimension, and provides a theoretically grounded, flexible, and highly efficient experimental design toolkit for high-dimensional screening and response surface modeling.

Abstract

Advances in automation and high-throughput experimentation have enabled larger and more complex studies involving many factors and tests, creating a growing demand for computationally effective design construction methods. Efficient experimental design remains a key challenge in this context, creating a need for frameworks that can generate large experiments while preserving orthogonality and minimal aliasing. Unlike existing approaches which struggle with scalability, this work introduces an algorithmic framework for constructing large Orthogonal Minimally Aliased Response Surface (OMARS) designs by enumerating and combining weighing designs, three-level matrices with orthogonal columns and a fixed number of non-zero entries per column. Complete enumerations of weighing designs are achieved for designs with up to 24 tests, covering multiple numbers of factors and weights corresponding to two or three zeros per factor. In addition, a validated partial enumeration procedure and a combination method extend the catalog to substantially larger designs. The combination method enables the construction of OMARS designs for any test size that is a multiple of selected base sizes. This paper thus provides the methodology for generating large catalogs of high-quality OMARS designs, well-suited for high-dimensional screening and response-surface modelling in complex industrial and scientific experiments.

Problem

• Orthogonal Minimally Aliased Response Surface Designs
• Weighing Designs
• Experimental Design
• High-throughput Experimentation
• Response Surface Modelling

Innovation

• Orthogonal Minimally Aliased Response Surface (OMARS)
• weighing designs
• design enumeration
• experimental design combination
• high-throughput experimentation