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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11424_2025_3567_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="63" /> </InlineMediaObject> <EquationSource Format="TEX">${s^{{u_1}}} \times {s^{{u_2}}}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <msup> <mi>s</mi> <mrow> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> </mrow> </mrow> </msup> </mrow> <mo>×</mo> <mrow> <msup> <mi>s</mi> <mrow> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> grids for any positive integers u1, u2 with u1 + u2 = 3, and any two columns from different groups can achieve stratifications on <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11424_2025_3567_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="61" /> </InlineMediaObject> <EquationSource Format="TEX">${s^{{v_1}}} \times {s^{{v_2}}}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <msup> <mi>s</mi> <mrow> <mrow> <msub> <mi>v</mi> <mn>1</mn> </msub> </mrow> </mrow> </msup> </mrow> <mo>×</mo> <mrow> <msup> <mi>s</mi> <mrow> <mrow> <msub> <mi>v</mi> <mn>2</mn> </msub> </mrow> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> grids for any positive integers v1, v2 with v1 + v2 = 4. Few existing designs enjoy such appealing two-dimensional stratification property in the literature. And the level numbers of the obtained designs can be s3 or s4. 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.

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

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发表日期：

2025年7月3日

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Chunyan Wang,
Jinyu Yang

摘要

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 ${s^{{u_1}}} \times {s^{{u_2}}}$ $s^{u_{1}} \times s^{u_{2}}$ grids for any positive integers u₁, u₂ with u₁ + u₂ = 3, and any two columns from different groups can achieve stratifications on ${s^{{v_1}}} \times {s^{{v_2}}}$ $s^{v_{1}} \times s^{v_{2}}$ grids for any positive integers v₁, v₂ with v₁ + v₂ = 4. Few existing designs enjoy such appealing two-dimensional stratification property in the literature. And the level numbers of the obtained designs can be s³ or s⁴. 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.