<p>Computer experiments with both quantitative and qualitative factors occur in many scientific and engineering applications. How to choose suitable designs for such experiments is always an important issue. Recently, to balance the run sizes and design efficiencies to estimate the interactions between any two qualitative factors and the quantitative factors, the doubly coupled design (DCD) was introduced. Orthogonality and maximin distance are two important properties for designs of computer experiments, and mirror-symmetric structure can yield higher-order orthogonality. In this paper, we first propose methods to construct orthogonal DCDs (ODCDs) and mirror-symmetric ODCDs with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$s^t$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>s</mi> <mi>t</mi> </msup> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$(t \ge 3)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>≥</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> runs systematically, where <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$s \ge 2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>s</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> is a prime or prime power. Then, we study the maximin <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$L_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-distance property of the resulting designs. A newly proposed mapping method plays a critical role in these constructions, and it can be widely applied to some existing construction methods as a further step to make the constructed designs mirror-symmetric. Furthermore, we provide two constructions of DCDs with desirable stratification properties. Most of the resulting designs can accommodate the maximum number of qualitative factors and a relatively large number of quantitative factors.</p>

Construction of doubly coupled designs with desirable space-filling properties

期刊论文
发表日期：

2026年5月27日

查看全文

Mengmeng Liu,
Min-Qian Liu,
Jinyu Yang

摘要

Computer experiments with both quantitative and qualitative factors occur in many scientific and engineering applications. How to choose suitable designs for such experiments is always an important issue. Recently, to balance the run sizes and design efficiencies to estimate the interactions between any two qualitative factors and the quantitative factors, the doubly coupled design (DCD) was introduced. Orthogonality and maximin distance are two important properties for designs of computer experiments, and mirror-symmetric structure can yield higher-order orthogonality. In this paper, we first propose methods to construct orthogonal DCDs (ODCDs) and mirror-symmetric ODCDs with $s^t$ $s^{t}$ $(t \ge 3)$ $(t \geq 3)$ runs systematically, where $s \ge 2$ $s \geq 2$ is a prime or prime power. Then, we study the maximin $L_2$ $L_{2}$ -distance property of the resulting designs. A newly proposed mapping method plays a critical role in these constructions, and it can be widely applied to some existing construction methods as a further step to make the constructed designs mirror-symmetric. Furthermore, we provide two constructions of DCDs with desirable stratification properties. Most of the resulting designs can accommodate the maximum number of qualitative factors and a relatively large number of quantitative factors.