Group Strong Orthogonal Arrays with Appealing Two-Dimensional Space-Filling Property

• Published in: Journal of systems science and complexity Vol. 38; no. 4; pp. 1747 - 1765
• Main Authors: Wang, Chunyan, Yang, Jinyu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2025; Springer Nature B.V
• Subjects: Complex Systems; Control; Integers; Mathematics; Mathematics and Statistics; Mathematics of Computing; Operations Research/Decision Theory; Orthogonal arrays; Orthogonality; Statistics; Stratification; Systems Theory; uniformity; Computer experiment; orthogonality; group strong orthogonal array
• ISSN: 1009-6124; 1559-7067
• DOI: 10.1007/s11424-025-3567-z

Space-filling designs are popular for computer experiments. Therein space-filling designs with good two-dimensional projection are preferred as two-factor interactions are more likely to be important than three- or higher-order interactions in practice. Considering two-dimensional projection, the authors propose a new class of designs called group strong orthogonal arrays. A group strong orthogonal array enjoys attractive two-dimensional space-filling property in the sense that it can be partitioned into groups, where any two columns can achieve stratifications on s u 1 × s u 2 grids for any positive integers u 1 , u 2 with u 1 + u 2 = 3, and any two columns from different groups can achieve stratifications on s v 1 × s v 2 grids for any positive integers v 1 , v 2 with v 1 + v 2 = 4. Few existing designs enjoy such appealing two-dimensional stratification property in the literature. And the level numbers of the obtained designs can be s 3 or s 4 . In addition to the attractive stratification property, the proposed designs perform very well under orthogonality and uniform projection criteria, and are flexible in run sizes, rendering them highly suitable for computer experiments.