Abstract

In computer experiments, it has become a standard practice to select

the inputs that spread out as uniformly as possible over the design space. The

resulting designs are called space-filling designs and they are undoubtedly desirable choices when there is no prior knowledge on how the input variables affect

the response and the objective of experiments is global fitting. When there is

some prior knowledge on the underlying true function of the system or what

statistical models are more appropriate, a natural question is, are there more

suitable designs than vanilla space-filling designs? In this article, we provide an

answer for the cases where there are no interactions between the factors from

disjoint groups of variables. In other words, we consider the design issue when

the underlying functional form of the system or the statistical model to be used

is additive where each component depends on one group of variables from a set of

disjoint groups. For such cases, we recommend using grouped orthogonal arrays.

Several construction methods are provided and many designs are tabulated for

practical use. Compared with existing techniques in the literature, our construction methods can generate many more designs with flexible run sizes and better

within-group projection properties for any prime power number of levels.

Information

Preprint No.SS-2024-0029
Manuscript IDSS-2024-0029
Complete AuthorsGuanzhou Chen, Yuanzhen He, Devon Lin, Fasheng Sun
Corresponding AuthorsFasheng Sun
Emailssunfs359@nenu.edu.cn

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Acknowledgments

The authors would like to thank an Editor, an AE and two referees for their

helpful comments which greatly improved the paper. Chen is supported by

National Natural Science Foundation of China, Grant No. 12401325. He

was supported by National Natural Science Foundation of China, Grant

No. 11701033.

Lin was supported by Discovery Grant from the Natural Sciences and Engineering Research Council of Canada.

Sun is supported by National Natural Science Foundation of China (Nos. 12371259

and 11971098) and National Key Research and Development Program of

China (Nos. 2020YFA0714102 and 2022YFA1003701).

Supplementary Materials

available online includes all the proofs of theoretical results, design tables, and other technical details of the paper.

Supplementary materials are available for download.