Advertisement

Optimal Central Composite Designs for Fitting Second Order Response Surface Linear Regression Models

  • Sung Hyun Park
  • Hyuk Joo Kim
  • Jae-Il Cho

The central composite design (CCD) is a design widely used for estimating second order response surfaces. It is perhaps the most popular class of second order designs. Since introduced by Box and Wilson (1951), the CCD has been studied and used by many researchers.

This paper deals with optimal CCDs under several design criteria for fitting second order response surface regression models. In Section 2, results on optimal CCDs under the criteria of orthogonality, rotatability and slope rotatability are reviewed. In Section 3, we discuss optimal CCDs under alphabetic design optimality criteria. The appropriate values of ? which minimize the squared bias when the true model is of third order are suggested in Section 4. Finally, in Section 5, considering all possible design criteria, suitable values of ? for the practical design purpose are recommended.

Keywords

Response Surface Response Surface Methodology Central Composite Design Factorial Point Order Design 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Box GEP, Draper, NR (1963) The choice of a second order rotatable design Biometrika. 50:335-352.MathSciNetGoogle Scholar
  2. Box GEP, Draper NR (1987) Empirical Model-Building and Response Surfaces. John Wiley.Google Scholar
  3. Box GEP, Hunter JS (1957) Multifactor experimental design for explor-ing response surfaces. Annals of Mathematical Statistics 28:195-241.MATHCrossRefMathSciNetGoogle Scholar
  4. Box GEP, Wilson KB (1951) On the experimental attainment of opti-mum conditions. Journal of Royal Statistical Society B13:1-38.MathSciNetGoogle Scholar
  5. Hader RJ, Park SH (1978) Slope-rotatable central composite designs. Technometrics 20:413-417.MATHCrossRefGoogle Scholar
  6. Khuri AI, Cornell JA (1996) Response Surfaces: Designs and Analyses (2nd edition). Marcel Dekker.Google Scholar
  7. Myers RH (1976) Response Surface Methodology. Blacksburg, VA.Google Scholar
  8. Myers RH, Montgomery DC (2002) Response Surface Methodology: Process and Product Optimization Using Designed Experiments (2nd edition). John Wiley.Google Scholar
  9. Park SH (1987) A class of multifactor designs for estimating the slope of response surfaces. Technometrics 29:449-453.MATHCrossRefMathSciNetGoogle Scholar
  10. Park SH, Kim HJ (1992) A measure of slope-rotatability for second order response surface experimental designs. Journal of Applied Statistics 19:391-404.CrossRefGoogle Scholar

Copyright information

© Physica-Verlag Heidelberg 2008

Authors and Affiliations

  • Sung Hyun Park
    • 1
  • Hyuk Joo Kim
    • 2
  • Jae-Il Cho
    • 3
  1. 1.Department of StatisticsSeoul National UniversitySeoulKorea
  2. 2.Division of Mathematics and Informational Statistics and Institute of Basic Natural SciencesWonkwang UniversityJeonbukKorea
  3. 3.Management Innovation PartDongbu ElectronicsGyeonggiKorea

Personalised recommendations