Optimal Design Of Experiments

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Optimal Design Of Experiments

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Author : Peter Goos
language : en
Publisher: John Wiley & Sons
Release Date : 2011-06-28

Optimal Design Of Experiments written by Peter Goos and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Science categories.

"This is an engaging and informative book on the modern practice of experimental design. The authors' writing style is entertaining, the consulting dialogs are extremely enjoyable, and the technical material is presented brilliantly but not overwhelmingly. The book is a joy to read. Everyone who practices or teaches DOE should read this book." - Douglas C. Montgomery, Regents Professor, Department of Industrial Engineering, Arizona State University "It's been said: 'Design for the experiment, don't experiment for the design.' This book ably demonstrates this notion by showing how tailor-made, optimal designs can be effectively employed to meet a client's actual needs. It should be required reading for anyone interested in using the design of experiments in industrial settings." —Christopher J. Nachtsheim, Frank A Donaldson Chair in Operations Management, Carlson School of Management, University of Minnesota This book demonstrates the utility of the computer-aided optimal design approach using real industrial examples. These examples address questions such as the following: How can I do screening inexpensively if I have dozens of factors to investigate? What can I do if I have day-to-day variability and I can only perform 3 runs a day? How can I do RSM cost effectively if I have categorical factors? How can I design and analyze experiments when there is a factor that can only be changed a few times over the study? How can I include both ingredients in a mixture and processing factors in the same study? How can I design an experiment if there are many factor combinations that are impossible to run? How can I make sure that a time trend due to warming up of equipment does not affect the conclusions from a study? How can I take into account batch information in when designing experiments involving multiple batches? How can I add runs to a botched experiment to resolve ambiguities? While answering these questions the book also shows how to evaluate and compare designs. This allows researchers to make sensible trade-offs between the cost of experimentation and the amount of information they obtain.

Optimal Design Of Experiments

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Author : Friedrich Pukelsheim
language : en
Publisher: SIAM
Release Date : 1993-01-01

Optimal Design Of Experiments written by Friedrich Pukelsheim and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Mathematics categories.

Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. The optimal design for statistical experiments is first formulated as a concave matrix optimization problem. Using tools from convex analysis, the problem is solved generally for a wide class of optimality criteria such as D-, A-, or E-optimality. The book then offers a complementary approach that calls for the study of the symmetry properties of the design problem, exploiting such notions as matrix majorization and the Kiefer information matrix ordering. The results are illustrated with optimal designs for polynomial fit models, Bayes designs, balanced incomplete block designs, exchangeable designs on the cube, rotatable designs on the sphere, and many other examples. Since the book's initial publication in 1993, readers have used its methods to derive optimal designs on the circle, optimal mixture designs, and optimal designs in other statistical models. Using local linearization techniques, the methods described in the book prove useful even for nonlinear cases, in identifying practical designs of experiments. Audience: anyone involved in planning statistical experiments, including mathematical statisticians, applied statisticians, and mathematicians interested in matrix optimization problems.

Model Oriented Design Of Experiments

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Author : Valerii V. Fedorov
language : en
Publisher: Springer Nature
Release Date : 2024-12-26

Model Oriented Design Of Experiments written by Valerii V. Fedorov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-26 with Medical categories.

This book presents the basic ideas of statistical methods in the design of optimal experiments. This new edition now includes sections on design techniques based on the elemental Fisher information matrices (as opposed to Pearson information/moment matrices), allowing a seamless extension of the design techniques to inferential problems where the shape of distributions is essential for optimal design construction. Topics include designs for nonlinear models, models with random parameters and models with correlated observations, designs for model discrimination and misspecified (contaminated) models, and designs in functional spaces. The authors avoid technical details, assuming a moderate background in calculus, matrix algebra, and statistics. In many places, however, suggestions are made as to how the ideas presented in this book can be extended and elaborated for use in real scientific research and practical engineering problems.

Sequential Analysis And Optimal Design

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Author : Herman Chernoff
language : en
Publisher: SIAM
Release Date : 1972-01-31

Sequential Analysis And Optimal Design written by Herman Chernoff and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-01-31 with Technology & Engineering categories.

An exploration of the interrelated fields of design of experiments and sequential analysis with emphasis on the nature of theoretical statistics and how this relates to the philosophy and practice of statistics.

Optimal Mixture Experiments

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Author : B.K. Sinha
language : en
Publisher: Springer
Release Date : 2014-05-24

Optimal Mixture Experiments written by B.K. Sinha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-24 with Mathematics categories.

​The book dwells mainly on the optimality aspects of mixture designs. As mixture models are a special case of regression models, a general discussion on regression designs has been presented, which includes topics like continuous designs, de la Garza phenomenon, Loewner order domination, Equivalence theorems for different optimality criteria and standard optimality results for single variable polynomial regression and multivariate linear and quadratic regression models. This is followed by a review of the available literature on estimation of parameters in mixture models. Based on recent research findings, the volume also introduces optimal mixture designs for estimation of optimum mixing proportions in different mixture models, which include Scheffé’s quadratic model, Darroch-Waller model, log- contrast model, mixture-amount models, random coefficient models and multi-response model. Robust mixture designs and mixture designs in blocks have been also reviewed. Moreover, some applications of mixture designs in areas like agriculture, pharmaceutics and food and beverages have been presented. Familiarity with the basic concepts of design and analysis of experiments, along with the concept of optimality criteria are desirable prerequisites for a clear understanding of the book. It is likely to be helpful to both theoreticians and practitioners working in the area of mixture experiments.

Handbook Of Design And Analysis Of Experiments

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Author : Angela Dean
language : en
Publisher: CRC Press
Release Date : 2015-06-26

Handbook Of Design And Analysis Of Experiments written by Angela Dean and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-26 with Mathematics categories.

This carefully edited collection synthesizes the state of the art in the theory and applications of designed experiments and their analyses. It provides a detailed overview of the tools required for the optimal design of experiments and their analyses. The handbook covers many recent advances in the field, including designs for nonlinear models and algorithms applicable to a wide variety of design problems. It also explores the extensive use of experimental designs in marketing, the pharmaceutical industry, engineering and other areas.

Optimal Design Of Experiments

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Author : Friedrich Pukelsheim
language : en
Publisher: SIAM
Release Date : 2006-04-01

Optimal Design Of Experiments written by Friedrich Pukelsheim and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-01 with Mathematics categories.

Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. The optimal design for statistical experiments is first formulated as a concave matrix optimization problem. Using tools from convex analysis, the problem is solved generally for a wide class of optimality criteria such as D-, A-, or E-optimality. The book then offers a complementary approach that calls for the study of the symmetry properties of the design problem, exploiting such notions as matrix majorization and the Kiefer matrix ordering. The results are illustrated with optimal designs for polynomial fit models, Bayes designs, balanced incomplete block designs, exchangeable designs on the cube, rotatable designs on the sphere, and many other examples.

The Construction Of Optimal Stated Choice Experiments

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Author : Deborah J. Street
language : en
Publisher: John Wiley & Sons
Release Date : 2007-07-20

The Construction Of Optimal Stated Choice Experiments written by Deborah J. Street and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-20 with Mathematics categories.

The most comprehensive and applied discussion of stated choice experiment constructions available The Construction of Optimal Stated Choice Experiments provides an accessible introduction to the construction methods needed to create the best possible designs for use in modeling decision-making. Many aspects of the design of a generic stated choice experiment are independent of its area of application, and until now there has been no single book describing these constructions. This book begins with a brief description of the various areas where stated choice experiments are applicable, including marketing and health economics, transportation, environmental resource economics, and public welfare analysis. The authors focus on recent research results on the construction of optimal and near-optimal choice experiments and conclude with guidelines and insight on how to properly implement these results. Features of the book include: Construction of generic stated choice experiments for the estimation of main effects only, as well as experiments for the estimation of main effects plus two-factor interactions Constructions for choice sets of any size and for attributes with any number of levels A discussion of designs that contain a none option or a common base option Practical techniques for the implementation of the constructions Class-tested material that presents theoretical discussion of optimal design Complete and extensive references to the mathematical and statistical literature for the constructions Exercise sets in most chapters, which reinforce the understanding of the presented material The Construction of Optimal Stated Choice Experiments serves as an invaluable reference guide for applied statisticians and practitioners in the areas of marketing, health economics, transport, and environmental evaluation. It is also ideal as a supplemental text for courses in the design of experiments, decision support systems, and choice models. A companion web site is available for readers to access web-based software that can be used to implement the constructions described in the book.

The Theory Of The Design Of Experiments

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Author : D.R. Cox
language : en
Publisher: CRC Press
Release Date : 2000-06-06

The Theory Of The Design Of Experiments written by D.R. Cox and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-06 with Mathematics categories.

Why study the theory of experiment design? Although it can be useful to know about special designs for specific purposes, experience suggests that a particular design can rarely be used directly. It needs adaptation to accommodate the circumstances of the experiment. Successful designs depend upon adapting general theoretical principles to the spec