Experimental Design for Formulation (ASA-SIAM Series on Statistics and Applied Probability, Series Number 15)

Many products, such as foods, personal-care products, beverages, and cleaning agents, are made by mixing ingredients together. This book describes a systematic methodology for formulating such products so that they perform according to one's goals, providing scientists and engineers with a fast track to the implementation of the methodology. Experimental Design for Formulation contains examples from a wide variety of fields and includes a discussion of how to design experiments for a mixture setting and how to fit and interpret models in a mixture setting. It also introduces process variables, the combining of mixture and nonmixture variables in a designed experiment, and the concept of collinearity and the possible problems that can result from its presence. Experimental Design for Formulation is a useful manual for the formulator and can also be used by a resident statistician to teach an in-house short course. Statistical proofs are largely absent, and the formulas that are presented are included to explain how the various software packages carry out the analysis. Many examples are given of output from statistical software packages, and the proper interpretation of computer output is emphasized. Other topics presented include a discussion of an effect in a mixture setting, the presentation of elementary optimization methods, and multiple-response optimization wherein one seeks to optimize more than one response. Annotation This book describes a systematic methodology for formulating mixed-ingredient products so that they perform to particular standards, providing scientists and engineers with a fast track to the implementation of the methodology. Examples from a wide variety of fields are included, as well as a discussion of how to design experiments for a mixture setting and how to fit and interpret models in a mixture setting. It also introduces process variables, the combining of mixture and nonmixture variables in a designed experiment, and the concept of collinearity and the possible problems that can result from its presence. The book is a useful manual for the formulator and can also be used by a resident statistician to teach an in-house short course. Statistical proofs are largely absent, and the formulas that are presented are included to explain how the various software packages carry out the analysis Experimental Design for Formulation 2 ASA-SIAM Series on Statistics and Applied Probability 3 ISBN 0-89871-580-6 5 Contents 6 List of Figures 10 List of Tables 14 Preface 18 Part I Preliminaries 22 Chapter 1 Introduction 24 Chapter 2 Mixture Space 30 Chapter 3 Models for a Mixture Setting 36 Part II Design 54 Chapter 4 Designs for Simplex-Shaped Regions 56 Chapter 5 Designs for Non-Simplex-Shaped Regions 82 Chapter 6 Design Evaluation 116 Chapter 7 Blocking Mixture Experiments 140 Part III Analysis 172 Chapter 8 Building Models in a Mixture Setting 174 Chapter 9 Model Evaluation 204 Chapter 10 Model Revision 226 Chapter 11 Effects 278 Chapter 12 Optimization 298 Part IV Special Topics 318 Chapter 13 Including Process Variables 320 Chapter 14 Collinearity 346 Bibliography 372 Index 384 Many scientific experiments can be broken down into three stages: the planning of the experiment, the implementation of the experiment, and the analysis and interpretation of the data that are collected. Gender-Structured Population Modeling: Mathematical Methods, Numerics, and Simulations gives a unified presentation of and mathematical framework for modeling population growth by couple formation