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The existence of the strong combined-optimal design

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Abstract

The technique of fold-over is useful for conducting follow-up experiments. Based on the minimum aberration criterion, Li and Lin (2003) developed an algorithm and used computer to search the corresponding optimal foldover designs for 16 and 32 runs in the 2k-p design. In their study, they found that the 210−6 design is the only one that is not a strong combined-optimal design among all the designs. However, they did not interpret the reason causing the phenomenon. This article will explore under what kind of conditions, that the strong combined-optimal design will exist, and the solutions of the related problems.

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References

  1. Box, G.E.P., Hunter, J.S. (1961) The 2k-p fractional factorial designs. Technometrics 3, Part I, 311–352; Part II, 449–458.

    Article  MATH  MathSciNet  Google Scholar 

  2. Box, G.E.P., Wilson, K.B. (1951) On the experimental attainment of optimal conditions. J. Royal Statist. Soc., Ser. B 13, 291–301.

    MathSciNet  Google Scholar 

  3. Chen, H.H., Cheng, C.S. (2003) Doubling and projection: A method of constructing two-level designs of resolutionIV. 2003 experimental design workshop in Taipei.

  4. Chen, H.H., Cheng, C.S. (2004) Aberration, estimation capacity and estimation index. Statist. Sinica 14, 203–215.

    MATH  MathSciNet  Google Scholar 

  5. Daniel, C. (1962) Sequence of fractional replicates in the 2p-q series. J. Amer. Statist. Assoc. 57, 403–429.

    Article  MATH  MathSciNet  Google Scholar 

  6. Davies, O.L., Hay, W.A. (1950) The construction and uses of fractional factorial designs in industrial research. Biometrics 6, 233–249.

    Article  Google Scholar 

  7. Fries, A., Hunter, W.G. (1980) Minimum aberration 2n-p designs. Technometrics 22, 601–608.

    Article  MATH  MathSciNet  Google Scholar 

  8. John, P.W.M. (1971) Statistic design and analysis of experiments. The Macmillan Company, New York, NY.

    Google Scholar 

  9. Montgomery, D.C. (2001) Design and analysis of experiments 5nd ed., John Wiley & Sons, New York.

    MATH  Google Scholar 

  10. Montgomery, D.C., Runger, G.C. (1996) Foldovers of resolution IV experimental designs. J. Qual. Technol. 4, 446–450.

    Google Scholar 

  11. Li, H., Mee, R.W. (2002) Better foldover fractions for resolution III designs. Technometrics 44, 278–283.

    Article  MathSciNet  Google Scholar 

  12. Li, W., Lin, D.K.J. (2003) Optimal foldover plans for two-level fractional factorial designs. Technometrics 45, 142–149.

    Article  MathSciNet  Google Scholar 

  13. Wu, C.F.J., Hadama, M. (2000) Experiment: planning, analysis, and parameter design optimization. John Wiley & Sons, Inc.

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  1. Department of Mathematics, National Kaohsiung Normal University, Taiwan, R.O.C.

    Pen-Hwang Liau

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  1. Pen-Hwang Liau
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Liau, PH. The existence of the strong combined-optimal design. Statistical Papers 48, 143–150 (2007). https://doi.org/10.1007/s00362-006-0320-0

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  • DOI: https://doi.org/10.1007/s00362-006-0320-0

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