Experimental Designs and Analysis of Data for Mixtures

  • George A.R. Taylor

    Student thesis: Master's ThesisMaster of Science (by Research)


    The problem of the design and analysis of experiments involving
    mixtures, where a restriction exists due to the fact that the sum of
    the proportions must be unity, was, as far as the writer is aware
    first mentioned in the literature by Claringbold*.

    Scheffe seems to have been the first to go into the problem in
    any great detail and he obtained equations for analysing such experiments
    and also considered some of the ramifications such as process
    variables, fractionation and restrictions on composition which make
    it necessary to use pseudocomponents. The equations which Scheffe
    derived are examined and criticised and their use illustrated by
    examples from experiments in which the writer has been involved. Scheffe's
    method of dealing with process variables is also illustrated by a
    synthetic example.

    Concentric shell designs recently developed by Doehlert are
    outlined and their relationship to balanced incomplete blocks, Scheffe's
    designs and Hadamard matrices is given.

    Draper and Lawrence have developed more sophisticated designs
    using techniques worked out by Box and Draper for Minimising variance
    and bias errors in regression equations. A critical comparison is
    made between their designs and Scheffe's,

    Following Box's method of Evolutionary Operation, equations
    have been derived to enable the technique to be applied to production
    processes where mixtures are involved. This is illustrated by a
    Simulated production process and some suggestions are made to overcome
    a difficulty encountered in this simulation which could easily occur
    in a real situation.

    The Appendix contains original tables to enable confidence
    limits to be calculated when using Scheffe's designs for the special,
    but usual, case when the replicates are of equal size.

    * Claringbold,P.J., "The Use of Simplex Designs in the Study of the Joint
    Action of Related Hormones", Biometrics, 1955, 11(2), 174.
    Date of Award1972
    Original languageEnglish


    • experimental designs
    • analysis of data
    • mixtures

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