## Experiments with Mixtures: Designs, Models, and the Analysis of Mixture DataThe most comprehensive, single-volume guide to conducting experiments with mixtures "If one is involved, or heavily interested, in experiments on mixtures of ingredients, one must obtain this book. It is, as was the first edition, the definitive work." -Short Book Reviews (Publication of the International Statistical Institute) "The text contains many examples with worked solutions and with its extensive coverage of the subject matter will prove invaluable to those in the industrial and educational sectors whose work involves the design and analysis of mixture experiments." -Journal of the Royal Statistical Society "The author has done a great job in presenting the vital information on experiments with mixtures in a lucid and readable style. . . . A very informative, interesting, and useful book on an important statistical topic." -Zentralblatt fur Mathematik und Ihre Grenzgebiete Experiments with Mixtures shows researchers and students how to design and set up mixture experiments, then analyze the data and draw inferences from the results. Virtually every technique that has appeared in the literature of mixtures can be found here, and computing formulas for each method are provided with completely worked examples. Almost all of the numerical examples are taken from real experiments. Coverage begins with Scheffe lattice designs, introducing the use of independent variables, and ends with the most current methods. New material includes: * Multiple response cases * Residuals and least-squares estimates * Categories of components: Mixtures of mixtures * Fixed as well as variable values for the major component proportions * Leverage and the Hat Matrix * Fitting a slack-variable model * Estimating components of variances in a mixed model using ANOVA table entries * Clarification of blocking mates and choice of mates * Optimizing several responses simultaneously * Biplots for multiple responses |

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### Contents

1 | |

Designs Models and the Analysis of Mixture Data 2 The Original Mixture Problem Designs and Models for Exploring the Entire Simplex Factor Space | 22 |

Designs Models and the Analysis of Mixture Data 3 The Use of Independent Variables | 96 |

Designs Models and the Analysis of Mixture Data 4 Multiple Constraints on the Component Proportions | 132 |

Designs Models and the Analysis of Mixture Data 5 The Analysis of Mixture Data | 223 |

Designs Models and the Analysis of Mixture Data 6 Other Mixture Model Forms | 286 |

Designs Models and the Analysis of Mixture Data 7 The Inclusion of Process Variables in Mixture Experiments | 354 |

Designs Models and the Analysis of Mixture Data 8 Additional Topics | 438 |

Designs Models and the Analysis of Mixture Data 9 Matrix Algebra Least Squares and the Analysis of Variance | 521 |

Designs Models and the Analysis of Mixture Data 10 Data Sets from Mixture Experiments with Partial Solutions | 538 |

Designs Models and the Analysis of Mixture Data Bibliography and Index of Authors | 589 |

Designs Models and the Analysis of Mixture Data Answers to Selected Questions | 604 |

Designs Models and the Analysis of Mixture Data Appendix | 637 |

643 | |

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### Common terms and phrases

algorithm Analysis analysis of variance average blending properties block calculated centroid coefﬁcient estimates component proportions constrained region constraints coordinates Cornell corresponding data values deﬁned Deﬁnition denoted design points effects equation error variance estimated standard errors example experimental region experiments with mixtures extreme vertices F-ratio F-test factor space ﬁnal ﬁrst ﬁrst-degree model ﬁt ﬁtted model ﬁtting ﬁve formulas fraction L-pseudocomponent lack of ﬁt lattice linear blending listed in Table lower bounds M-component matrix minor resins mixture blends mixture components mixture experiments mixture model mixture-amount model form model of Eq nonlinear blending observations parameter estimates patties Piepel plots polynomial prediction process variables propylene glycol quadratic model regression replicate residual response surface response values Scheffé-type second-degree model Section signiﬁcance signiﬁcantly simplex simplex-centroid design simplex-lattice Snee special cubic model speciﬁc standard errors Statistical studentized residuals sum of squares Technometrics three-component triangle variance-covariance matrix vector vertex zero