An innovative discussion of building empirical models and the fitting of surfaces to data. Introduces the general philosophy of response surface methodology, and details least squares for response surface work, factorial designs at two levels, fitting second-order models, adequacy of estimation and the use of transformation, occurrence and elucidation of ridge systems, and more. Some results are presented for the first time. Includes real-life exercises, nearly all with solutions.
The authority on building empirical models and the fitting of such surfaces to data—completely updated and revised Revising and updating a volume that represents the essential source on building empirical models, George Box and Norman Draper—renowned authorities in this field—continue to set the standard with the Second Edition of Response Surfaces, Mixtures, and Ridge Analyses, providing timely new techniques, new exercises, and expanded material. A comprehensive introduction to building empirical models, this book presents the general philosophy and computational details of a number of important topics, including factorial designs at two levels; fitting first and second-order models; adequacy of estimation and the use of transformation; and occurrence and elucidation of ridge systems. Substantially rewritten, the Second Edition reflects the emergence of ridge analysis of second-order response surfaces as a very practical tool that can be easily applied in a variety of circumstances. This unique, fully developed coverage of ridge analysis—a technique for exploring quadratic response surfaces including surfaces in the space of mixture ingredients and/or subject to linear restrictions—includes MINITAB® routines for performing the calculations for any number of dimensions. Many additional figures are included in the new edition, and new exercises (many based on data from published papers) offer insight into the methods used. The exercises and their solutions provide a variety of supplementary examples of response surface use, forming an extremely important component of the text. Response Surfaces, Mixtures, and Ridge Analyses, Second Edition presents material in a logical and understandable arrangement and includes six new chapters covering an up-to-date presentation of standard ridge analysis (without restrictions); design and analysis of mixtures experiments; ridge analysis methods when there are linear restrictions in the experimental space including the mixtures experiments case, with or without further linear restrictions; and canonical reduction of second-order response surfaces in the foregoing general case. Additional features in the new edition include: New exercises with worked answers added throughout An extensive revision of Chapter 5: Blocking and Fractionating 2k Designs Additional discussion on the projection of two-level designs into lower dimensional spaces This is an ideal reference for researchers as well as a primary text for Response Surface Methodology graduate-level courses and a supplementary text for Design of Experiments courses at the upper-undergraduate and beginning-graduate levels.
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.
A hands-on approach to the basic principles of empirical model building. Includes a series of real-world statistical problems illustrating modeling skills and techniques. Covers models of growth and decay, systems where competition and interaction add to the complexity of the model, and discusses both classical and nonclassical data analysis methods.
Lean production, has long been regarded as critical to business success in many industries. Over the last ten years, instruction in six sigma has been increasingly linked with learning about the elements of lean production. Introduction to Engineering Statistics and Lean Sigma builds on the success of its first edition (Introduction to Engineering Statistics and Six Sigma) to reflect the growing importance of the "lean sigma" hybrid. As well as providing detailed definitions and case studies of all six sigma methods, Introduction to Engineering Statistics and Lean Sigma forms one of few sources on the relationship between operations research techniques and lean sigma. Readers will be given the information necessary to determine which sigma methods to apply in which situation, and to predict why and when a particular method may not be effective. Methods covered include: • control charts and advanced control charts, • failure mode and effects analysis, • Taguchi methods, • gauge R&R, and • genetic algorithms. The second edition also greatly expands the discussion of Design For Six Sigma (DFSS), which is critical for many organizations that seek to deliver desirable products that work first time. It incorporates recently emerging formulations of DFSS from industry leaders and offers more introductory material on the design of experiments, and on two level and full factorial experiments, to help improve student intuition-building and retention. The emphasis on lean production, combined with recent methods relating to Design for Six Sigma (DFSS), makes Introduction to Engineering Statistics and Lean Sigma a practical, up-to-date resource for advanced students, educators, and practitioners.
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.
A hands-on approach to the basic principles of empirical model building. Includes a series of real-world statistical problems illustrating modeling skills and techniques. Covers models of growth and decay, systems where competition and interaction add to the complexity of the model, and discusses both classical and nonclassical data analysis methods.
This book describes methods for designing and analyzing experiments that are conducted using a computer code, a computer experiment, and, when possible, a physical experiment. Computer experiments continue to increase in popularity as surrogates for and adjuncts to physical experiments. Since the publication of the first edition, there have been many methodological advances and software developments to implement these new methodologies. The computer experiments literature has emphasized the construction of algorithms for various data analysis tasks (design construction, prediction, sensitivity analysis, calibration among others), and the development of web-based repositories of designs for immediate application. While it is written at a level that is accessible to readers with Masters-level training in Statistics, the book is written in sufficient detail to be useful for practitioners and researchers. New to this revised and expanded edition: • An expanded presentation of basic material on computer experiments and Gaussian processes with additional simulations and examples • A new comparison of plug-in prediction methodologies for real-valued simulator output • An enlarged discussion of space-filling designs including Latin Hypercube designs (LHDs), near-orthogonal designs, and nonrectangular regions • A chapter length description of process-based designs for optimization, to improve good overall fit, quantile estimation, and Pareto optimization • A new chapter describing graphical and numerical sensitivity analysis tools • Substantial new material on calibration-based prediction and inference for calibration parameters • Lists of software that can be used to fit models discussed in the book to aid practitioners
This is the first edited volume on response surface methodology (RSM). It contains 17 chapters written by leading experts in the field and covers a wide variety of topics ranging from areas in classical RSM to more recent modeling approaches within the framework of RSM, including the use of generalized linear models. Topics covering particular aspects of robust parameter design, response surface optimization, mixture experiments, and a variety of new graphical approaches in RSM are also included. The main purpose of this volume is to provide an overview of the key ideas that have shaped RSM, and to bring attention to recent research directions and developments in RSM, which can have many useful applications in a variety of fields. The volume will be very helpful to researchers as well as practitioners interested in RSM''s theory and potential applications. It will be particularly useful to individuals who have used RSM methods in the past, but have not kept up with its recent developments, both in theory and applications. Sample Chapter(s). Chapter 1: Two-Level Factorial and Fractional Factorial Designs in Blocks of Size Two. Part 2 (560 KB). Contents: Two-Level Factorial and Fractional Factorial Designs in Blocks of Size Two. Part 2 (Y J Yang & N R Draper); Response Surface Experiments on Processes with High Variation (S G Gilmour & L A Trinca); Random Run Order, Randomization and Inadvertent Split-Plots in Response Surface Experiments (J Ganju & J M Lucas); Statistical Inference for Response Surface Optima (D K J Lin & J J Peterson); A Search Method for the Exploration of New Regions in Robust Parameter Design (G Mer-Quesada & E del Castillo); Response Surface Approaches to Robust Parameter Design (T J Robinson & S S Wulff); Response Surface Methods and Their Application in the Treatment of Cancer with Drug Combinations: Some Reflections (K S Dawson et al.); Generalized Linear Models and Response Transformation (A C Atkinson); GLM Designs: The Dependence on Unknown Parameters Dilemma (A I Khuri & S Mukhopadhyay); Design for a Trinomial Response to Dose (S K Fan & K Chaloner); Evaluating the Performance of Non-Standard Designs: The San Cristobal Design (L M Haines); 50 Years of Mixture Experiment Research: 1955OCo2004 (G F Piepel); Graphical Methods for Comparing Response Surface Designs for Experiments with Mixture Components (H B Goldfarb & D C Montgomery); Graphical Methods for Assessing the Prediction Capability of Response Surface Designs (J J Borkowski); Using Fraction of Design Space Plots for Informative Comparisons between Designs (C M Anderson-Cook & A Ozol-Godfrey); Concepts of Slope-Rotatability for Second Order Response Surface Designs (S H Park); Design of Experiments for Estimating Differences between Responses and Slopes of the Response (S Huda). Readership: Researchers in academia and industry interested in response surface methodology and its applications; engineers interested in improving quality and productivity in industry."
Food process modelling provides an authoritative review of one of the most exciting and influential developments in the food industry. The modelling of food processes allows analysts not only to understand such processes more clearly but also to control them more closely and make predictions about them. Modelling thus aids the search for greater and more consistent food quality. Written by a distinguished international team of experts, Food process modelling covers both the range of modelling techniques and their practical applications across the food chain.
