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A measure of rotatability for second order response surface designs

  • Regression Models
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Abstract

The concept of rotatability introduced by Box and Hunter (1957,Ann. Math. Statist.,28, 195–241) is an important design criterion for response surface design. Recently, a few measures of rotatability that enable us to assess the degree of rotatability for a given response surface design have been introduced. In this paper, a new measure of rotatability for second order response surface designs is suggested, and illustrated for 3k factorial design and central composite design. Also a short comparison is made between the proposed measure with the previously suggested measures.

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References

  • Box, G. E. P. and Draper, N. R. (1987).Empirical Model-Building and Response Surface, Wiley, New York.

    Google Scholar 

  • Box, G. E. P. and Hunter, J. S. (1957). Multifactor experimental designs for exploring response surfaces,Ann. Math. Statist.,28, 195–241.

    Google Scholar 

  • Box, G. E. P. and Wilson, K. B. (1951). On the experimental attainment of optimum conditions,J. Roy. Statist. Soc. Ser. B,13, 1–45.

    Google Scholar 

  • Draper, N. R. and Guttman, I. (1988). An index of rotatability,Technometrics,30, 105–111.

    Google Scholar 

  • Draper, N. R. and Pukelsheim, F. (1990). Another look at rotatability.Technometrics,32, 195–202.

    Google Scholar 

  • Fleming, W. (1977).Functions of Several Variables, 2nd ed., Springer, New York.

    Google Scholar 

  • Hader, R. J. and Park, S. H. (1978). Slope-rotatable central composite designs,Technometrics,20, 413–417.

    Google Scholar 

  • Khuri, A. I. (1988). A measure of rotatability for response surface designs.Technometrics,30, 95–104.

    Google Scholar 

  • Khuri, A. I. and Cornell, J. A. (1987).Response Surfaces: Designs and Analyses, Marcel Dekker, New York.

    Google Scholar 

  • Myers, R. H. (1976).Response Surface Methodology, Edwards Brothers, Ann Arbor, Michigan.

    Google Scholar 

  • Park, S. H. (1987). A class of multifactor designs for estimating the slope of response surfaces,Technometrics,29, 449–453.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Statistics, Seoul National University, San 56-1, Shinrim-Dong, Kwanak-ku, 151-742, Seoul, Korea

    Sung H. Park & Jun H. Lim

  2. The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106, Tokyo, Japan

    Yasumasa Baba

Authors
  1. Sung H. Park
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  2. Jun H. Lim
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  3. Yasumasa Baba
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Cite this article

Park, S.H., Lim, J.H. & Baba, Y. A measure of rotatability for second order response surface designs. Ann Inst Stat Math 45, 655–664 (1993). https://doi.org/10.1007/BF00774779

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  • DOI: https://doi.org/10.1007/BF00774779

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