Robust A Optimal Designs For Mixture Experiments In Scheffe Models
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Author | : B.K. Sinha |
Publisher | : Springer |
Total Pages | : 213 |
Release | : 2014-05-24 |
Genre | : Mathematics |
ISBN | : 8132217861 |
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.
Author | : John A. Cornell |
Publisher | : John Wiley & Sons |
Total Pages | : 682 |
Release | : 2011-09-20 |
Genre | : Mathematics |
ISBN | : 111815049X |
The most comprehensive, single-volume guide to conductingexperiments with mixtures "If one is involved, or heavily interested, in experiments onmixtures of ingredients, one must obtain this book. It is, as wasthe first edition, the definitive work." -Short Book Reviews (Publication of the International StatisticalInstitute) "The text contains many examples with worked solutions and with itsextensive coverage of the subject matter will prove invaluable tothose in the industrial and educational sectors whose work involvesthe design and analysis of mixture experiments." -Journal of the Royal Statistical Society "The author has done a great job in presenting the vitalinformation on experiments with mixtures in a lucid and readablestyle. . . . A very informative, interesting, and useful book on animportant statistical topic." -Zentralblatt fur Mathematik und Ihre Grenzgebiete Experiments with Mixtures shows researchers and students how todesign and set up mixture experiments, then analyze the data anddraw inferences from the results. Virtually every technique thathas appeared in the literature of mixtures can be found here, andcomputing formulas for each method are provided with completelyworked examples. Almost all of the numerical examples are takenfrom real experiments. Coverage begins with Scheffe latticedesigns, introducing the use of independent variables, and endswith the most current methods. New material includes: * Multiple response cases * Residuals and least-squares estimates * Categories of components: Mixtures of mixtures * Fixed as well as variable values for the major componentproportions * Leverage and the Hat Matrix * Fitting a slack-variable model * Estimating components of variances in a mixed model using ANOVAtable entries * Clarification of blocking mates and choice of mates * Optimizing several responses simultaneously * Biplots for multiple responses
Author | : |
Publisher | : John Wiley & Sons |
Total Pages | : 690 |
Release | : |
Genre | : |
ISBN | : 111963542X |
Author | : Chetan Verma |
Publisher | : Authors' Ink Publications |
Total Pages | : 305 |
Release | : |
Genre | : |
ISBN | : 9385137999 |
The book contains selected published research papers present in the literature since late fifties. The authors of the papers are eminent academicians, planners and scientists of repute in their respective areas. In the section on Introduction to Design of Experiments, the short overview is given on design of experiment, its optimality & efficiency criteria. Introduction to Mixture Problem: Design and its Construction, this section contains the basic concept and models for mixture problem, and also contains the construction of designs and its test criteria for mixture problems. Mixture experiments are generally conducted in different branches of agricultural and industrial research where it is not feasible to have the components of the mixture in full range but in some restricted space. Papers giving exhaustive reviews of such situation have been included in Constraints on the Component Proportions and Process Variable in Mixture Experiments. In the section on Optimal Mixture Design contains the papers related with optimality criteria of mixture experiments. In the section on Mixture Model Forms and Additional Topics contain the papers based on the different studies related with the mixture experiments. This is perhaps one of the few attempts to bring together papers on Mixture Experiments with emphasis on agricultural and industrial sectors for promoting mixture methodology.
Author | : Bovas Abraham |
Publisher | : Springer Science & Business Media |
Total Pages | : 450 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461217768 |
This book is based on the papers presented at the International Conference 'Quality Improvement through Statistical Methods' in Cochin, India during December 28-31, 1996. The Conference was hosted by the Cochin University of Science and Technology, Cochin, India; and sponsored by the Institute for Improvement in Quality and Productivity (IIQP) at the University of Waterloo, Canada, the Statistics in Industry Committee of the International Statistical Institute (lSI) and by the Indian Statistical Institute. There has been an increased interest in Quality Improvement (QI) activities in many organizations during the last several years since the airing of the NBC television program, "If Japan can ... why can't we?" Implementation of QI meth ods requires statistical thinking and the utilization of statistical tools, thus there has been a renewed interest in statistical methods applicable to industry and technology. This revitalized enthusiasm has created worldwide discussions on Industrial Statistics Research and QI ideas at several international conferences in recent years. The purpose of this conference was to provide a forum for presenting and ex changing ideas in Statistical Methods and for enhancing the transference of such technologies to quality improvement efforts in various sectors. It also provided an opportunity for interaction between industrial practitioners and academia. It was intended that the exchange of experiences and ideas would foster new international collaborations in research and other technology transfers.
Author | : Marlos A. G. Viana |
Publisher | : American Mathematical Soc. |
Total Pages | : 358 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0821848917 |
A decade after the publication of Contemporary Mathematics Vol. 287, the present volume demonstrates the consolidation of important areas, such as algebraic statistics, computational commutative algebra, and deeper aspects of graphical models. --
Author | : Wendell F. Smith |
Publisher | : SIAM |
Total Pages | : 386 |
Release | : 2005-01-01 |
Genre | : Science |
ISBN | : 9780898718393 |
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.
Author | : John A. Cornell |
Publisher | : John Wiley & Sons |
Total Pages | : 376 |
Release | : 2011-09-26 |
Genre | : Mathematics |
ISBN | : 0470907428 |
The concise yet authoritative presentation of key techniques for basic mixtures experiments Inspired 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 designs Multiple 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 classifications Techniques for analyzing mixture data such as model reduction and screening components, as well as additional topics such as measuring the leverage of certain design points Models containing ratios of the components, Cox's mixture polynomials, and the fitting of a slack variable model A review of least squares and the analysis of variance for fitting data Each 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 and Recommended Reading sections outline further resources for study of the presented topics. A Primer on Experiments with Mixtures is an excellent book for one-semester courses on mixture designs and can also serve as a supplement for design of experiments courses at the upper-undergraduate and graduate levels. It is also a suitable reference for practitioners and researchers who have an interest in experiments with mixtures and would like to learn more about the related mixture designs and models.
Author | : Wendell F. Smith |
Publisher | : SIAM |
Total Pages | : 372 |
Release | : 2005-04-01 |
Genre | : Science |
ISBN | : 0898715806 |
Gender-Structured Population Modeling: Mathematical Methods, Numerics, and Simulations gives a unified presentation of and mathematical framework for modeling population growth by couple formation.
Author | : Douglas C. Montgomery |
Publisher | : John Wiley & Sons |
Total Pages | : 690 |
Release | : 2020-06-23 |
Genre | : Technology & Engineering |
ISBN | : 1119722101 |
Design and Analysis of Experiments provides a rigorous introduction to product and process design improvement through quality and performance optimization. Clear demonstration of widely practiced techniques and procedures allows readers to master fundamental concepts, develop design and analysis skills, and use experimental models and results in real-world applications. Detailed coverage of factorial and fractional factorial design, response surface techniques, regression analysis, biochemistry and biotechnology, single factor experiments, and other critical topics offer highly-relevant guidance through the complexities of the field. Stressing the importance of both conceptual knowledge and practical skills, this text adopts a balanced approach to theory and application. Extensive discussion of modern software tools integrate data from real-world studies, while examples illustrate the efficacy of designed experiments across industry lines, from service and transactional organizations to heavy industry and biotechnology. Broad in scope yet deep in detail, this text is both an essential student resource and an invaluable reference for professionals in engineering, science, manufacturing, statistics, and business management.