In this paper sequential exploration of response surfaces for mixture experiments has been studied. The plan and the estimation and testing procedures for some of the well known models have been given.

Sequential Exploration in Mixture Experiments

Bibliography and Index of Authors

and the factor space is thus a simplex (Claringbold, 1955; Scheff6, 1958, 1963). Denote the expected response at x = (xl, ..., xq) by y(x). Various parametric forms for y(x) have been suggested; see, in particular, Scheff6 (1958, 1963) and Becker (1968). When polynomials are used, the constraint (1) introduces redundancy in the parameterizatioii; thus with first degree polynomials the expressions

A note on polynomial response functions for mixtures

In certain toxicological studies the term joint action has come to take a special meaning. If members of a group of related compounds all cause death of an organism when administered separately the simultaneous action of these substances is called their joint action. Bliss (1939) first discussed the analysis of data obtained in this manner. From this time the problem has been examined in terms of tolerance distribution theory and developed in relation to probit analysis (Finney, 1952). Plackett and Hewlett (1951) have extended the tolerance distribution theory to different theoretical forms of joint action and developed a set of mathematical models, each of which is based on many assumptions and is very difficult to fit to experimental data. Fisher (1954) has shown that parameters of the binomial distribution may be estimated without tolerance distribution assumptions. The aim of the present paper is to show that the study of joint action by means of an appropriate experimental design-the simplex designallows ready interpretation of experimental data with no reference to a joint tolerance distribution, and no further assumptions than normally required in quantal analysis. The method is also appropriate without modification to the study of joint action of substances eliciting a graded response simply by applying the standard estimation procedures. Examples will be drawn from the study of the action of oestrogens on the vagina of the ovariectomized mouse. The quantal response in this case is cornification of the vaginal epithelium.

http://www.jstor.org/stable/pdfplus/3001794.pdf

Use of the simplex design in the study of joint action of related hormones

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Design and Analysis of Experiments with Mixtures

/pdf/block-designs-for-mixture-experiments-1plti9su4i.pdf

Block Designs for Mixture Experiments

Extreme vertices designs were developed by McLean and Anderson [9] for situations where components are restricted by lower and upper bounds. We give here a transformation which provides alternative designs, construcked through symmetric-simplex designs [10], for restricted exploration. These designs can provide uniform exploration of the restricted factor-space (polyhedron) and avoid clusters of points.

Sequential Exploration in Mixture Experiments

Citations

Bibliography and Index of Authors

References

A note on polynomial response functions for mixtures

Use of the simplex design in the study of joint action of related hormones

Design and Analysis of Experiments with Mixtures

Block Designs for Mixture Experiments

Restricted Exploration of Mixtures by Symmetric-Simplex Design

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