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Optimal orthogonal block designs for a quadratic mixture model for three components

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  • L. Y. Chan

Abstract

In experiments with mixtures that involve process variables, if the response function is expressed as the sum of a function of mixture components and a function of process variables, then the parameters in the mixture part and in the process part can be estimated independently using orthogonal block designs. This paper is concerned with such a block design for parameter estimation in the mixture part of a quadratic mixture model for three mixture components. The behaviour of the eigenvalues of the moment matrix of the design is investigated in detail, the design is optimized according to E- and Aoptimality criteria, and the results are compared together with a known result on Doptimality. It is found that this block design is robust with respect to these diff erent optimality criteria against the shifting of experimental points. As a result, we recommend experimental points of the form (a, b, c) in the simplex S2, where c=0, b=1-a, and a can be any value in the range 0.17+/-0.02.

Suggested Citation

  • L. Y. Chan, 1999. "Optimal orthogonal block designs for a quadratic mixture model for three components," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(1), pages 19-34.
    • Handle: RePEc:taf:japsta:v:26:y:1999:i:1:p:19-34
    DOI: 10.1080/02664769922629
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    Cited by:

    1. Aggarwal, M. L. & Singh, Poonam & Gupta, Nidhi, 2004. "Orthogonal block designs in two blocks for second degree K-model," Statistics & Probability Letters, Elsevier, vol. 66(4), pages 423-434, March.
    2. Poonam Singh, 2003. "Optimal orthogonal designs in two blocks for Darroch and Waller’s quadratic mixture model in three and four components," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 419-430.
    3. Manohar L. Aggarwal & Poonam Singh, 2006. "D-optimal designs in two orthogonal blocks for Darroch and Waller's quadratic model in constrained mixture components," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 315-326.
    4. Aggarwal, M. L. & Sarin, V. & Singh, Poonam, 2002. "Optimal orthogonal designs in two blocks for Becker's mixture models in three and four components," Statistics & Probability Letters, Elsevier, vol. 59(4), pages 385-396, October.

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