Split-plot designs often arise in agriculture and industrial experimentation when some factors are harder to vary than others, leading to randomization restrictions. This has an effect on both the run order and analysis of the experiment. Response surface methodology (RSM) split-plot designs for experiments with quantitative factors have received a lot of coverage in the literature. These designs are not appropriate, however, if categorical factors are also present. Draper and John (1988) and Wu and Ding (1998) explore techniques for adding categorical factors to non-split-plot RSM designs. Building on their initial idea of adding the categorical factor sequentially after taking an initial base design in the quantitative factors, this thesis explores how to add a two-level categorical factor in the split-plot RSM setting. Due to the randomization restrictions, adding a categorical factor in the split-plot setting requires considerably more care, in order to meet basic feasibility requirements and to maintain the structure. We explore four techniques for adding categorical factors and present results on requirements for the feasibility of proposed assignments of the categorical factor. We find that not all methods are appropriate for every base design. Throughout the thesis, we expand upon an example of an RSM split-plot experiment in quantitative factors for a ceramic pipe experiment from Vining and Kowalski (2008), by introducing a hypothetical additional categorical factor at either the whole-plot (hard-to-vary) or split-plot (easy-to-vary) level. We discuss optimal strategies for assigning a factor, conduct some initial exploration of the different response surfaces after perturbations to the data using contour plots, and suggest further avenues for analysis. The thesis culminates in tables of D-optimal designs for the various assignment methods based on an algorithm and computer code written for the various assignment methods.

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.

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.

"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.

This book provides a comprehensive treatment of the design of blocked and split-plot experiments. The optimal design approach advocated in the book will help applied statisticians from industry, medicine, agriculture, chemistry and many other fields of study in setting up tailor-made experiments. The book also contains a theoretical background, a thorough review of the recent work in the area of blocked and split-plot experiments, and a number of interesting theoretical results.

"Comprising more than 500 entries, the Encyclopedia of Research Design explains how to make decisions about research design, undertake research projects in an ethical manner, interpret and draw valid inferences from data, and evaluate experiment design strategies and results. Two additional features carry this encyclopedia far above other works in the field: bibliographic entries devoted to significant articles in the history of research design and reviews of contemporary tools, such as software and statistical procedures, used to analyze results. It covers the spectrum of research design strategies, from material presented in introductory classes to topics necessary in graduate research; it addresses cross- and multidisciplinary research needs, with many examples drawn from the social and behavioral sciences, neurosciences, and biomedical and life sciences; it provides summaries of advantages and disadvantages of often-used strategies; and it uses hundreds of sample tables, figures, and equations based on real-life cases."--Publisher's description.

Based on deep theoretical as well as practical experience in Reliability and Quality Sciences, Robust Design Methodology for Reliability constructively addresses practical reliability problems. It offers a comprehensive design theory for reliability, utilizing robust design methodology and six sigma frameworks. In particular, the relation between un-reliability and variation and uncertainty is explored and reliability improvement measures in early product development stages are suggested. Many companies today utilise design for Six Sigma (DfSS) for strategic improvement of the design process, but often without explicitly describing the reliability perspective; this book explains how reliability design can relate to and work with DfSS and illustrates this with real–world problems. The contributors advocate designing for robustness, i.e. insensitivity to variation in the early stages of product design development. Methods for rational treatment of uncertainties in model assumptions are also presented. This book promotes a new approach to reliability thinking that addresses the design process and proneness to failure in the design phase via sensitivity to variation and uncertainty; includes contributions from both academics and industry practitioners with a broad scope of expertise, including quality science, mathematical statistics and reliability engineering; takes the innovative approach of promoting the study of variation and uncertainty as a basis for reliability work; includes case studies and illustrative examples that translate the theory into practice. Robust Design Methodology for Reliability provides a starting point for new thinking in practical reliability improvement work that will appeal to advanced designers and reliability specialists in academia and industry including fatigue engineers, product development and process/ quality professionals, especially those interested in and/ or using the DfSS framework.