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New recommended designs for screening either qualitative or quantitative factors

  • A. M. Elsawah
  • Kai-Tai FangEmail author
  • Xiao Ke
Regular Article
  • 15 Downloads

Abstract

By the affine resolvable design theory, there are 68 non-isomorphic classes of symmetric orthogonal designs involving 13 factors with 3 levels and 27 runs. This paper gives a comprehensive study of all these 68 non-isomorphic classes from the viewpoint of the uniformity criteria, generalized word-length pattern and Hamming distance pattern, which provides some interesting projection and level permutation behaviors of these classes. Selecting best projected level permuted subdesigns with \(3\le k\le 13\) factors from all these 68 non-isomorphic classes is discussed via these three criteria with catalogues of best values. New recommended uniform minimum aberration and minimum Hamming distance designs are given for investigating either qualitative or quantitative \(4\le k\le 13\) factors, which perform better than the existing recommended designs in literature and the existing uniform designs. A new efficient technique for detecting non-isomorphic designs is given via these three criteria. By using this new approach, in all projections into \(1\le k\le 13\) factors we classify each class from these 68 classes to non-isomorphic subclasses and give the number of isomorphic designs in each subclass. Close relationships among these three criteria and lower bounds of the average uniformity criteria are given as benchmarks for selecting best designs.

Keywords

Design isomorphism Orthogonal designs Level permutation Projection Generalized word-length pattern Hamming distance pattern Uniformity criteria 

Mathematics Subject Classification

62K05 62K15 94B05 

Notes

Acknowledgements

The authors greatly appreciate valuable comments and suggestions of the referees and the Associate Editor that significantly improved the paper. The authors greatly appreciate the kind support of Prof. Ping He during this work. This work was partially supported by the UIC Grants (Nos. R201409, R201712, R201810 and R201912) and the Zhuhai Premier Discipline Grant.

Supplementary material

362_2019_1089_MOESM1_ESM.pdf (221 kb)
Supplementary material 1 (pdf 221 KB)

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceZagazig UniversityZagazigEgypt
  2. 2.Division of Science and TechnologyBNU-HKBU United International CollegeZhuhaiChina
  3. 3.The Key Lab of Random Complex Structures and Data AnalysisThe Chinese Academy of SciencesBeijingChina
  4. 4.Department of MathematicsSouthern University of Science and TechnologyShenzhenChina
  5. 5.Department of MathematicsHong Kong Baptist UniversityKowloon TongHong Kong

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