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.

• 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, ŷ(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 Scheffé’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 Polynomial Coefficients and Their Variances: Matrix Notation 85Appendix 2B: Cubic and Quartic Polynomials and Formulas for the Estimates of the Coefficients 90Appendix 2C: The Partitioning of the Sources in the Analysis of Variance Table When Fitting the Scheffé Mixture Models 913. Multiple Constraints on the Component Proportions 953.1 Lower-Bound Restrictions on Some or All of the Component Proportions 953.2 Introducing L-Pseudocomponents 973.3 A Numerical Example of Fitting an L-Pseudocomponent Model 993.4 Upper-Bound Restrictions on Some or All Component Proportions 1013.5 An Example of the Placing of an Upper Bound on a Single Component: The Formulation of a Tropical Beverage 1033.6 Introducing U-Pseudocomponents 1073.7 The Placing of Both Upper and Lower Bounds on the Component Proportions 1123.8 Formulas for Enumerating the Number of Extreme Vertices, Edges, and Two-Dimensional Faces of the Constrained Region 1193.9 McLean and Anderson’s Algorithm for Calculating the Coordinates of the Extreme Vertices of a Constrained Region 1233.10 Multicomponent Constraints 1283.11 Some Examples of Designs for Constrained Mixture Regions: CONVRT and CONAEV Programs 1313.12 Multiple Lattices for Major and Minor Component Classifications 138Summary 154References and Recommended Reading 155Questions 1574. The Analysis of Mixture Data 1594.1 Techniques Used in the Analysis of Mixture Data 1604.2 Test Statistics for Testing the Usefulness of the Terms in the Scheffé Polynomials 1634.3 Model Reduction 1704.4 An Example of Reducing the System from Three to Two Components 1734.5 Screening Components 1754.6 Other Techniques Used to Measure Component Effects 1794.7 Leverage and the Hat Matrix 1904.8 A Three-Component Propellant Example 1924.9 Summary 195References and Recommended Reading 196Questions 1975. Other Mixture Model Forms 2015.1 The Inclusion of Inverse Terms in the Scheffé Polynomials 2015.2 Fitting Gasoline Octane Numbers Using Inverse Terms in the Model 2045.3 An Alternative Model Form for Modeling the Additive Blending Effect of One Component in a Multicomponent System 2055.4 A Biological Example on the Linear Effect of a Powder Pesticide in Combination with Two Liquid Pesticides Used for Suppressing Mite Population Numbers 2125.5 The Use of Ratios of Components 2155.6 Cox’s Mixture Polynomials: Measuring Component Effects 2195.7 An Example Illustrating the Fits of Cox’s Model and Scheffé’s Polynomial 2245.8 Fitting a Slack-Variable Model 2295.9 A Numerical Example Illustrating the Fits of Different Reduced Slack-Variable Models: Tint Strength of a House Paint 2335.10 Summary 239References and Recommended Reading 240Questions 2426. The Inclusion of Process Variables in Mixture Experiments 2476.1 Designs Consisting of Simplex-Lattices and Factorial Arrangements 2496.2 Measuring the Effects of Cooking Temperature and Cooking Time on the Texture of Patties Made from Two Types of Fish 2516.3 Mixture-Amount Experiments 2566.4 Determining the Optimal Fertilizer Blend and Rate for Young Citrus Trees 2626.5 A Numerical Example of the Fit of a Combined Model to Data Collected on Fractions of the Fish Patty Experimental Design 2696.6 Questions Raised and Recommendations Made When Fitting a Combined Model Containing Mixture Components and Other Variables 2726.7 Summary 277References and Recommended Reading 278Questions 280Appendix 6A: Calculating the Estimated Combined Mixture Component–Process Variable Model of Eq. (6.10) Without the Computer 2827. A Review of Least Squares and the Analysis of Variance 2857.1 A Review of Least Squares 2857.2 The Analysis of Variance 2887.3 A Numerical Example: Modeling the Texture of Fish Patties 2897.4 The Adjusted Multiple Correlation Coefficient 2937.5 The Press Statistic and Studentized Residuals 2937.6 Testing Hypotheses About the Form of the Model: Tests of Significance 295References and Recommended Reading 298Bibliography 299Answers to Selected Questions 317Appendix 337Index 347