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Optimum designs for optimum mixtures

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  • Pal, Manisha
  • Mandal, Nripes K.

Abstract

In a mixture experiment, the measured response is assumed to depend only on the relative proportion of ingredients or components present in the mixture. Scheffé [1958. Experiments with mixtures. J. Roy. Statist. Soc. B 20, 344-360; 1963. Simplex--centroid design for experiments with mixtures. J. Roy. Statist. Soc. B 25, 235-263] first systematically considered this problem and introduced different models and designs suitable in such situations. Optimum designs for the estimation of parameters of different mixture models are available in the literature. However, in a mixture experiment, often one is more interested in the optimum proportion of ingredients. In this paper, we try to find optimum designs for the estimation of optimum mixture combination on the assumption that the response function is quadratic concave over the simplex region.

Suggested Citation

  • Pal, Manisha & Mandal, Nripes K., 2006. "Optimum designs for optimum mixtures," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1369-1379, July.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:13:p:1369-1379
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    References listed on IDEAS

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    1. Valery Fedorov & Werner Müller, 1997. "Another view on optimal design for estimating the point of extremum in quadratic regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 46(1), pages 147-157, January.
    2. Viatcheslav Melas & Andrey Pepelyshev & Russell Cheng, 2003. "Designs for estimating an extremal point of quadratic regression models in a hyperball," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(2), pages 193-208, September.
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    Cited by:

    1. Mandal, N.K. & Pal, Manisha & Aggarwal, M.L., 2012. "Pseudo-Bayesian A-optimal designs for estimating the point of maximum in component-amount Darroch–Waller mixture model," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1088-1094.
    2. Pal, Manisha & Mandal, Nripes Kumar, 2008. "Minimax designs for optimum mixtures," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 608-615, April.
    3. Nripes Mandal & Manisha Pal & Bikas Sinha & Premadhis Das, 2015. "Optimum mixture designs in a restricted region," Statistical Papers, Springer, vol. 56(1), pages 105-119, February.
    4. Mandal, Nripes Kumar & Pal, Manisha, 2013. "Maximin designs for the detection of synergistic effects," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1632-1637.

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