New recommended designs for screening either qualitative or quantitative factors
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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.
KeywordsDesign isomorphism Orthogonal designs Level permutation Projection Generalized word-length pattern Hamming distance pattern Uniformity criteria
Mathematics Subject Classification62K05 62K15 94B05
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.
- Elsawah AM (2017c) Constructing optimal router bit life sequential experimental designs: new results with a case study. Commun Stat Simul Comput. https://doi.org/10.1080/03610918.2017.1397164
- Elsawah AM, Fang KT (2018) A catalog of optimal foldover plans for constructing U-uniform minimum aberration four-level combined designs. J Appl Stat. https://doi.org/10.1080/02664763.2018.1545013
- Hall M Jr (1961) Hadamard matrix of order 16. Jet Propuls Lab Res Summ 1:21–26Google Scholar
- Hickernell FJ (1998b) Lattice rules: how well do they measure up? In: Hellekalek P, Larcher G (eds) Random and quasi-random point sets. Lecture notes in statistics, vol 138. Springer, New York, pp 109-166Google Scholar
- Sun DX, Wu CFJ (1993) Statistical properties of Hadamard matrices of order 16. In: Kuo W (ed) Quality through engineering design. Elsevier, Amsterdam, pp 169–179Google Scholar
- Wang Y, Fang KT (1981) A note on uniformdistribution and experimental design. Chin Sci Bull 26:485–489Google Scholar
- Yang X, Yang G-J, Su Y-J (2018) Lower bound of a verage centered \(L_2\)-discrepancy for U-type designs. Commun Stat Theory Methods. https://doi.org/10.1080/03610926.2017.1422761