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Matrix Image Method for Ranking Nonregular Fractional Factorial Designs

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Abstract

Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. In this paper, we study matrix image theory and present a new method for distinguishing and assessing nonregular designs with complex alias structure, which works for all symmetrical and asymmetrical, regular and nonregular orthogonal arrays. Based on the matrix image theory, our proposed method captures orthogonality and projection properties. Empirical studies show that the proposed method has a more precise differentiation capacity when comparing with some other criteria.

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Acknowledgements

The authors thank the editor and two referees for their constructive suggestions and careful reading on an earlier version.

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Authors and Affiliations

  1. Department of Statistics, Jiangsu University of Technology, Changzhou, 213001, China

    Xue-ping Chen & Xuan-qing Chen

  2. Department of Statistics, Nanjing Audit University, Nanjing, 211815, China

    Jin-guan Lin

  3. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, 100081, China

    Xiao-di Wang

Authors
  1. Xue-ping Chen
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  2. Jin-guan Lin
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  3. Xuan-qing Chen
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  4. Xiao-di Wang
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Corresponding author

Correspondence to Xue-ping Chen.

Additional information

This work was supported by National Natural Science Foundation of China (Nos. 11601195, 11601538, 11571073), Natural Science Foundation of Jiangsu Province of China (No. BK20160289), Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 16KJB110005) and Jiangsu Qing Lan Project.

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Chen, Xp., Lin, Jg., Chen, Xq. et al. Matrix Image Method for Ranking Nonregular Fractional Factorial Designs. Acta Math. Appl. Sin. Engl. Ser. 34, 742–751 (2018). https://doi.org/10.1007/s10255-018-0783-5

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  • DOI: https://doi.org/10.1007/s10255-018-0783-5

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