A Primer on Experiments with Mixtures

John A. Cornell 지음

Wiley 2011년 09월 26일 출간

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The concise yet authoritative presentation of key techniques for basic mixtures experimentsInspired by the author's bestselling advanced book on the topic, A Primer on Experiments with Mixtures provides an introductory presentation of the key principles behind experimenting with mixtures. Outlining useful techniques through an applied approach with examples from real research situations, the book supplies a comprehensive discussion of how to design and set up basic mixture experiments, then analyze the data and draw inferences from results.Drawing from his extensive experience teaching the topic at various levels, the author presents the mixture experiments in an easy-to-follow manner that is void of unnecessary formulas and theory. Succinct presentations explore key methods and techniques for carrying out basic mixture experiments, including:Designs and models for exploring the entire simplex factor space, with coverage of simplex-lattice and simplex-centroid designs, canonical polynomials, the plotting of individual residuals, and axial designsMultiple constraints on the component proportions in the form of lower and/or upper bounds, introducing L-Pseudocomponents, multicomponent constraints, and multiple lattice designs for major and minor component classificationsTechniques for analyzing mixture data such as model reduction and screening components, as well as additional topics such as measuring the leverage of certain design pointsModels containing ratios of the components, Cox's mixture polynomials, and the fitting of a slack variable modelA review of least squares and the analysis of variance for fitting dataEach chapter concludes with a summary and appendices with details on the technical aspects of the material. Throughout the book, exercise sets with selected answers allow readers to test their comprehension of the material, and References a

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Preface ix1. Introduction 11.1 The Original Mixture Problem, 21.2 A Pesticide Example Involving Two Chemicals, 21.3 General Remarks About Response Surface Methods, 91.4 An Historical Perspective, 13References and Recommended Reading, 17Questions, 17Appendix 1A: Testing for Nonlinear Blending of the Two Chemicals Vendex and Kelthane While Measuring the Average Percent Mortality (APM) of Mites, 202. The Original Mixture Problem: Designs and Models for Exploring the Entire Simplex Factor Space 232.1 The Simplex-Lattice Designs, 232.2 The Canonical Polynomials, 262.3 The Polynomial Coefficients As Functions of the Responses at the Points of the Lattices, 312.4 Estimating The Parameters in the {q,m} Polynomials, 342.5 Properties of the Estimate of the Response, y(x), 372.6 A Three-Component Yarn Example Using A {3, 2} Simplex-Lattice Design, 382.7 The Analysis of Variance Table, 422.8 Analysis of Variance Calculations of the Yarn Elongation Data, 452.9 The Plotting of Individual Residuals, 482.10 Testing the Degree of the Fitted Model: A Quadratic Model or Planar Model?, 492.11 Testing Model Lack of Fit Using Extra Points and Replicated Observations, 552.12 The Simplex-Centroid Design and Associated Polynomial Model, 582.13 An Application of a Four-Component Simplex-Centroid Design: Blending Chemical Pesticides for Control of Mites, 602.14 Axial Designs, 622.15 Comments on a Comparison Made Between An Augmented Simplex-Centroid Design and a Full Cubic Lattice for Three Components Where Each Design Contains Ten Points, 662.16 Reparameterizing Scheffe's Mixture Models to Contain A Constant (β0) Term: A Numerical Example, 692.17 Questions to Consider at the Planning Stages of a Mixture Experiment, 772.18 Summary, 78References and Recommended Reading, 78Questions, 80Appendix 2A: Least-Squares Estimation Formula for the Polynom

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저자(글) John A. Cornell

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JOHN A. CORNELL, PhD, is Professor Emeritus of Statistics at the University of Florida. A recognized authority on the topic of experimental design, he has more than forty years of experience in both academia and industrial consulting and was awarded the Shewhart Medal by the American Society of Quality (ASQ) in 2001. A Fellow of both the ASQ and American Statistical Association, Dr. Cornell is the author of Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data, Third Edition, also published by Wiley.