June 2022 A new and flexible design construction for orthogonal arrays for modern applications
Yuanzhen He, C. Devon Lin, Fasheng Sun
Author Affiliations +
Ann. Statist. 50(3): 1473-1489 (June 2022). DOI: 10.1214/21-AOS2159


Orthogonal array, a classical and effective tool for collecting data, has been flourished with its applications in modern computer experiments and engineering statistics. Driven by the wide use of computer experiments with both qualitative and quantitative factors, multiple computer experiments, multifidelity computer experiments, cross-validation and stochastic optimization, orthogonal arrays with certain structures have been introduced. Sliced orthogonal arrays and nested orthogonal arrays are examples of such arrays. This article introduces a flexible, fresh construction method, which uses smaller arrays and a special structure. The method uncovers the hidden structure of many existing fixed-level orthogonal arrays of given run sizes, possibly with more columns. It also allows fixed-level orthogonal arrays of nearly strength three to be constructed, which are useful as there are not many construction methods for fixed-level orthogonal arrays of strength three, and also helpful for generating Latin hypercube designs with desirable low-dimensional projections. Theoretical properties of the proposed method are explored. As by-products, several theoretical results on orthogonal arrays are obtained.

Funding Statement

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 Supported by National Natural Science Foundation of China Grant No. 11971098 and National Key Research and Development Program of China (No. 2020YFA0714102).


We extend our sincere thanks to the Editor, Associate Editor and several referees for their constructive comments that lead to numerous improvements over the previous versions.


Download Citation

Yuanzhen He. C. Devon Lin. Fasheng Sun. "A new and flexible design construction for orthogonal arrays for modern applications." Ann. Statist. 50 (3) 1473 - 1489, June 2022. https://doi.org/10.1214/21-AOS2159


Received: 1 December 2019; Revised: 1 December 2021; Published: June 2022
First available in Project Euclid: 16 June 2022

MathSciNet: MR4441128
zbMATH: 07547938
Digital Object Identifier: 10.1214/21-AOS2159

Primary: 62K15
Secondary: 62K05

Keywords: Completely resolvable , computer experiment , difference scheme , Fractional factorial design , nested orthogonal array , sliced orthogonal array

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.50 • No. 3 • June 2022
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