Abstract

Latin hypercube designs (LHDs) have been widely used as computer experimental

designs when a linear model is fitted. The symmetric LHD (SLHD), as a special kind of LHDs,

can guarantee that the estimates of second-order effects and main effects are uncorrelated. In

this paper, we propose two methods to construct orthogonal SLHDs (OSLHDs) and nearly

orthogonal SLHDs (NOSLHDs). The first method can generate new designs based on existing

OSLHDs. Some new NOSLHDs with flexible run sizes and good nearly orthogonality can be

constructed. Moreover, the resulting OSLHDs of the second construction method have better

stratification properties than existing OSLHDs.

A case study is provided to highlight the

effectiveness of constructed designs in data collection.

Information

Preprint No.SS-2024-0312
Manuscript IDSS-2024-0312
Complete AuthorsMaria Boufi, Kashinath Chatterjee, Christos Koukouvinos, Min-Qian Liu, Liuqing Yang
Corresponding AuthorsMin-Qian Liu
Emailsmqliu@nankai.edu.cn

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Acknowledgments

The authors thank Editor Huixia Judy Wang, an associate editor and a referee for

their valuable comments. This work was supported by the National Natural Science

Foundation of China (Grant Nos. 12131001, 12371260 and 12401329), and Natural Science Foundation of Hunan Province (2025JJ60007). Liu is affiliated withe NITFID,

LPMC, KLMDASR, and School of Statistics and Data Science at Nankai University.

Yang is affiliated with School of Mathematics and Statistics at Central South University. The authorship is listed in alphabetic order.