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Optimal Design for Nonlinear Response Models

Optimal Design for Nonlinear Response Models
Author: Valerii V. Fedorov
Publisher: CRC Press
Total Pages: 402
Release: 2013-07-15
Genre: Mathematics
ISBN: 1439821526

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Optimal Design for Nonlinear Response Models discusses the theory and applications of model-based experimental design with a strong emphasis on biopharmaceutical studies. The book draws on the authors' many years of experience in academia and the pharmaceutical industry. While the focus is on nonlinear models, the book begins with an explanation of


Optimal Design of Experiments

Optimal Design of Experiments
Author: Friedrich Pukelsheim
Publisher: SIAM
Total Pages: 527
Release: 2006-04-01
Genre: Mathematics
ISBN: 0898716047

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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.


Non-Linear Theory of Elasticity and Optimal Design

Non-Linear Theory of Elasticity and Optimal Design
Author: L.W. Ratner
Publisher: Elsevier
Total Pages: 281
Release: 2003-11-12
Genre: Science
ISBN: 008053760X

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In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it can be done only with a destructive test for each structure. For building and explaining the theory, a new logical structure was introduced as the basis of the theory. One of the important physical implications of this logic is that it describes mathematically the universal domain of the possible stable physical relations.


Optimal Design of Experiments

Optimal Design of Experiments
Author: Peter Goos
Publisher: John Wiley & Sons
Total Pages: 249
Release: 2011-06-28
Genre: Science
ISBN: 1119976162

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"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.


Response Surfaces: Designs and Analyses

Response Surfaces: Designs and Analyses
Author: Andre I. Khuri
Publisher: CRC Press
Total Pages: 544
Release: 1996-08-08
Genre: Mathematics
ISBN: 9780824797416

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Response Surfaces: Designs and Analyses; Second Edition presents techniques for designing experiments that yield adequate and reliable measurements of one or several responses of interest, fitting and testing the suitability of empirical models used for acquiring information from the experiments, and for utilizing the experimental results to make decisions concerning the system under investigation. This edition contains chapters on response surface models with block effects and on Taguchi's robust parameter design, additional details on transformation of response variable, more material on modified ridge analysis, and new design criteria, including rotatability for multiresponse experiments. It also presents an innovative technique for displaying correlation among several response. Numerical examples throughout the book plus exercises--with worked solutions to selected problems--complement the text.


Applied Optimal Designs

Applied Optimal Designs
Author: Martijn P.F. Berger
Publisher: John Wiley & Sons
Total Pages: 320
Release: 2005-03-11
Genre: Mathematics
ISBN: 9780470856970

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There is an increasing need to rein in the cost of scientific study without sacrificing accuracy in statistical inference. Optimal design is the judicious allocation of resources to achieve the objectives of studies using minimal cost via careful statistical planning. Researchers and practitioners in various fields of applied science are now beginning to recognize the advantages and potential of optimal experimental design. Applied Optimal Designs is the first book to catalogue the application of optimal design to real problems, documenting its widespread use across disciplines as diverse as drug development, education and ground water modelling. Includes contributions covering: Bayesian design for measuring cerebral blood-flow Optimal designs for biological models Computer adaptive testing Ground water modelling Epidemiological studies and pharmacological models Applied Optimal Designs bridges the gap between theory and practice, drawing together a selection of incisive articles from reputed collaborators. Broad in scope and inter-disciplinary in appeal, this book highlights the variety of opportunities available through the use of optimal design. The wide range of applications presented here should appeal to statisticians working with optimal designs, and to practitioners new to the theory and concepts involved.


Model-Oriented Design of Experiments

Model-Oriented Design of Experiments
Author: Valerii V. Fedorov
Publisher: Springer Science & Business Media
Total Pages: 120
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461207037

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Here, the authors explain the basic ideas so as to generate interest in modern problems of experimental design. The topics discussed include designs for inference based on nonlinear models, designs for models with random parameters and stochastic processes, designs for model discrimination and incorrectly specified (contaminated) models, as well as examples of designs in functional spaces. Since the authors avoid technical details, the book assumes only a moderate background in calculus, matrix algebra, and statistics. However, at many places, hints are given as to how readers may enhance and adopt the basic ideas for advanced problems or applications. This allows the book to be used for courses at different levels, as well as serving as a useful reference for graduate students and researchers in statistics and engineering.


Response Surface Methodology

Response Surface Methodology
Author: Raymond H. Myers
Publisher: Wiley
Total Pages: 856
Release: 2016-02-01
Genre: Mathematics
ISBN: 9781118916018

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Praise for the Third Edition: “This new third edition has been substantially rewritten and updated with new topics and material, new examples and exercises, and to more fully illustrate modern applications of RSM.” - Zentralblatt Math Featuring a substantial revision, the Fourth Edition of Response Surface Methodology: Process and Product Optimization Using Designed Experiments presents updated coverage on the underlying theory and applications of response surface methodology (RSM). Providing the assumptions and conditions necessary to successfully apply RSM in modern applications, the new edition covers classical and modern response surface designs in order to present a clear connection between the designs and analyses in RSM. With multiple revised sections with new topics and expanded coverage, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Fourth Edition includes: Many updates on topics such as optimal designs, optimization techniques, robust parameter design, methods for design evaluation, computer-generated designs, multiple response optimization, and non-normal responses Additional coverage on topics such as experiments with computer models, definitive screening designs, and data measured with error Expanded integration of examples and experiments, which present up-to-date software applications, such as JMP®, SAS, and Design-Expert®, throughout An extensive references section to help readers stay up-to-date with leading research in the field of RSM An ideal textbook for upper-undergraduate and graduate-level courses in statistics, engineering, and chemical/physical sciences, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Fourth Edition is also a useful reference for applied statisticians and engineers in disciplines such as quality, process, and chemistry.


Statistica Sinica

Statistica Sinica
Author:
Publisher:
Total Pages: 704
Release: 1998
Genre: Mathematical statistics
ISBN:

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