An approach to measuring rotatability in central composite designs

 
 
 
  • Abstract
  • Keywords
  • References
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  • Abstract


    An approach to measure design rotatability and a measure, that quantifies the percentage of rotatability (from 0 to 100) in the central composite designs are introduced. This new approach is quite different from the ones provided by previous authors which assessed design rotatability by the viewing of tediously obtained contour diagrams. This new approach has not practical limitations, and the measure is very easy to compute. Some examples were used to express this approach.


  • Keywords


    Central Composite Designs; Design Rotatability; Near Rotatable Designs; Perfectly Rotatable Designs; Second-Order Response-Surface Designs.

  • References


      [1] A.I. Khuri, A measure of rotatability for response surface designs. Technometrics, 30: 95–104, 1988. http://dx.doi.org/10.1080/00401706.1988.10488327.

      [2] A.I. Khuri, R.H. Myers, Modified ridge analysis. Technometrics, 21: 467–473, 1979. http://dx.doi.org/10.1080/00401706.1979.10489816.

      [3] A.I. Khuri, S. Mukhopadhyay, Response surface methodology, WIREs Computational Statistics, 2: 128–149, 2010. http://dx.doi.org/10.1002/wics.73.

      [4] D.C. Montgomery, Design and Analysis of Experiments. John Wiley and Sons, New York. 1991.

      [5] E.U. Ohaegbulem, P.E. Chigbu, On some elements of restrictions and replications on the central composite designs, International Journal of Statistics and Applications, 3(5): 188-197, 2013.

      [6] G.E.P. Box, J.S. Hunter, Multi-factor experimental designs for exploring response surfaces, The Annals of Mathematical Statistics, 28, 195–241, 1957. http://dx.doi.org/10.1214/aoms/1177707047.

      [7] N.R. Draper, F. Pukelsheim, Another look at rotatability, Technometrics, 32: 195–202, 1990. http://dx.doi.org/10.1080/00401706.1990.10484635.

      [8] N.R. Draper,I.Guttman, An index of rotatability. Technometrics, 30: 105–111, 1988. http://dx.doi.org/10.1080/00401706.1988.10488328.

      [9] R. H. Myers, Response Surface Methodology. Allyn and Bacon Inc., Boston. 1971.

      [10] T.L. Hebble, T.J. Mitchell, Repairing response surface designs. Technometrics, 14: 767–779, 1972.


 

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Article ID: 4657
 
DOI: 10.14419/ijasp.v3i2.4657




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