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Further Results on Optimal and Efficient Designs for Constrained Mixture Experiments

  • R. J. Martin
  • M. C. Bursnall
  • E. C. Stillman
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 51)

Abstract

Many practical experiments on mixtures (where the components sum to one) include additional lower or upper bounds on components. This paper gives some additional results on the form of the continuous D- and V-optimal designs for 3 and 4 components.

Keywords

mixture experiments optimal design 

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References

  1. Atkinson, A.C. and Donev, A.N.(1992). Optimum Experimental Designs. Oxford: University Press.zbMATHGoogle Scholar
  2. Hardin, R.H. and Sloane, N.J.A. (1993). A new approach to the construction of optimal designs. J. Statist. Plann. Inference 37, 339–369.MathSciNetzbMATHCrossRefGoogle Scholar
  3. Laake, P. (1975). On the optimal allocation of observations in experiments with mixtures. Scandinavian Journal of Statistics 2, 153–157.MathSciNetzbMATHGoogle Scholar
  4. Martin, R.J., Bursnall, M.C. and Stillman, E.C. (1999). Efficient designs for constrained mixture experiments. Statistics and Computing 9, 229–237.CrossRefGoogle Scholar
  5. Math Works (1992). Matlab version 3.5. Natick MA: The Math Works Inc.Google Scholar

Additional References

  1. Draper, N. R., Heiligers, B. and Pukelsheim, F. (2000). Kiefer ordering of simplex designs for second-degree mixture models with four and more ingredients. Annals of Statistics. (To appear).Google Scholar
  2. Draper, N. R. and Pukelsheim, F.(1999). Kiefer ordering of simplex designs for first- and second-degree mixture models. J. Statistical Planning Inf. 79, 325–348.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • R. J. Martin
    • 1
  • M. C. Bursnall
    • 2
  • E. C. Stillman
    • 1
  1. 1.Department of Probability and StatisticsUniversity of SheffieldSheffieldUK
  2. 2.Department of StatisticsUniversity of LeedsLeedsUK

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