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DUAL-OBJECTIVE OPTIMAL MIXTURE DESIGNS

Authors

  • Chongqi Zhang,

    Corresponding author
    1. Guangzhou University, University of California at Los Angeles and Hong Kong Baptist University
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    • Department of Probability and Statistics, Guangzhou University, Guangzhou 510006, China. e-mail: chongqi@gzhu.edu.cn

  • Wengkee Wong,

    1. Guangzhou University, University of California at Los Angeles and Hong Kong Baptist University
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    • Department of Biostatistics, University of California at Los Angeles, Los Angeles CA 90095-1772, USA.

  • Heng Peng

    1. Guangzhou University, University of California at Los Angeles and Hong Kong Baptist University
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    • Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.


  • Acknowledgements. The authors thank the editorial team for their comments on an earlier version of the manuscript. Weng Kee Wong worked on the manuscript when he was a visiting fellow at The Sir Isaac Newton Institute at Cambridge, England, for the six-month workshop on Design and Analysis of Experiments. He thanks the Institute for the support during his visit in the summer of 2011. The whole work was jointly supported by National Nature Sciences Foundation of China (10871054).

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Summary

Mixture experiments are widely used in many industries and particularly in the manufacture of consumer products. Almost all work to date assumes a single study objective, which is unrealistic. Researchers may want to estimate model parameters and make predictions or extrapolations at the same time. We discuss design issues for determining the optimal proportions of the mixture components when there are two or more objectives in the study and there is a large sample size. We present a general methodology for constructing two types of dual-objective optimal design for mixture experiments and discuss the general applicability of the design strategy to more complicated types of mixture design problems, including mixture experiments.

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