Construction of Marginally Coupled Designs by Subspace Theory

TL;DR

This paper introduces a general method for constructing marginally coupled designs combining orthogonal arrays for qualitative factors and Latin hypercubes for quantitative factors, ensuring desirable space-filling properties.

Contribution

It proposes a novel construction method for marginally coupled designs using subspace theory, enhancing design quality for computer experiments with mixed factors.

Findings

Designs for qualitative factors are multi-level orthogonal arrays.

Designs for quantitative factors are Latin hypercubes with space-filling properties.

Theoretical guarantees for low-dimensional space-filling properties are established.

Abstract

Recent researches on designs for computer experiments with both qualitative and quantitative factors have advocated the use of marginally coupled designs. This paper proposes a general method of constructing such designs for which the designs for qualitative factors are multi-level orthogonal arrays and the designs for quantitative factors are Latin hypercubes with desirable space-filling properties. Two cases are introduced for which we can obtain the guaranteed low-dimensional space-filling property for quantitative factors. Theoretical results on the proposed constructions are derived. For practical use, some constructed designs for three-level qualitative factors are tabulated.