The Simplex-Centroid Design for Experiments with Mixtures

Henry Scheffé

563 citations0/0 files storedJournal of the Royal Statistical Society Series B (Statistical Methodology)

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Optimal Experimental Design Methods Advanced Combinatorial Mathematics Bayesian Methods and Mixture Models

Abstract

SUMMARY A new design for experiments with mixtures of q components comprises the 2q − 1 points representing the mixtures consisting of all possible subsets of the q components, present in equal proportions. A suitable regression equation is proposed and fitted. Designs and regression equations permitting the introduction of n “process variables” in addition to the q “mixture variables” are considered, and fractional replication of the designs in the case where the process variables are all at two levels.

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References

1951On the Experimental Attainment of Optimum Conditions 1992On the Experimental Attainment of Optimum Conditions 1957Multi-Factor Experimental Designs for Exploring Response Surfaces 1958Experiments with Mixtures 1959Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments 1959Optimum Designs in Regression Problems 1959A Basis for the Selection of a Response Surface Design

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1984Experimental Design: Review and Comment 1966Extreme Vertices Design of Mixture Experiments 1998Mixture design—design generation, PLS analysis, and model usage 1984Log Contrast Models for Experiments with Mixtures 1996Experimental design II. Optimization 1971A Note on Polynomial Response Functions for Mixtures 2016I-Optimal Design of Mixture Experiments 1974Extreme Vertices Designs for Linear Mixture Models

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