G. Geoffrey Vining

Data Analysis: A Model-Comparison Approach

1. Introduction to Data Analysis. 2. Simple Models: Definitions of Error and Parameter Estimates. 3. Simple Models: Models of Error and Sampling Distributions. 4. Simple Models: Statistical Inferences about Parameter Values. 5. Simple Regression: Estimating Models with a Single Continuous Predictor. 6. Multiple Regression: Models with Multiple Continuous Predictors. 7. Moderated and Nonlinear Regression Models. 8. One-Way ANOVA: Models with a Single Categorical Predictor. 9. Factorial ANOVA: Models with Multiple Categorical Predictors and Product Terms. 10. Models with Continuous and Categorical Predictors: ANCOVA. 11.Repeated-Measures ANOVA: Models with Nonindependent Errors. 12. Continuous Predictors with Nonindependent Observations. 13. Outliers and Ill-Mannered Error.

Taguchi's parameter design: a panel discussion

It is more than a decade since Genichi Taguchis ideas on quality improvement were inrroduced in the United States. His parameter-design approach for reducing variation in products and processes has generated a great deal of interest among both quality practitioners and statisticians. The statistical techniques used by Taguchi to implement parameter design have been the subject of much debate, however, and there has been considerable research aimed at integrating the parameter-design principles with well-established statistical techniques. On the other hand, Taguchi and his colleagues feel that these research efforts by statisticians are misguided and reflect a lack of understanding of the engineering principles underlying Taguchis methodology. This panel discussion provides a forum for a technical discussion of these diverse views. A group of practitioners and researchers discuss the role of parameter design and Taguchis methodology for implementing it. The topics covered include the importance of vari...

Combining Taguchi and Response Surface Philosophies: A Dual Response Approach

G. Taguchi and his school have made significant advances in the use of experimental design and analysis in industry. Of particular significance is their promotion of the use of statistical methods ...

Response Surface Methodology: A Retrospective and Literature Survey

Response surface methodology (RSM) is a collection of statistical design and numerical optimization techniques used to optimize processes and product designs. The original work in this area dates from the 1950s and has been widely used, especially in the chemical and process industries. The last 15 years have seen the widespread application of RSM and many new developments. In this review paper we focus on RSM activities since 1989. We discuss current areas of research and mention some areas for future research.

Response surface designs within a split-plot structure

In many industrial experiments, time and/or cost constraints often force certain factors in a designed experiment to be much harder to change than others. An appropriate approach to such an experiment restricts the randomization, which leads to a split-plot structure. This paper first establishes how one can modify the common central-composite design to efficiently accommodate a split-plot structure. The proposed designs allow pure-error estimates of the two variance components. We next discuss the conditions on the design that make ordinary least squares and weighted least squares estimates equivalent. These conditions are easy to obtain in practice. An important consequence is that people can use standard experimental design software to analyze second-order response surfaces. We give examples of central composite and Box-Behnken designs that meet the conditions. We conclude with an example.

Split-Plot Designs and Estimation Methods for Mixture Experiments With Process Variables

In mixture experiments with process variables, the response depends not only on the proportions of the mixture components, but also on the effects of the process variables. In many such mixture-process variable experiments, constraints such as time or cost prohibit the selection of treatments completely at random. In these situations, restrictions on the randomization force the level combinations of one group of factors to be fixed and the combinations of the other group of factors are run. Then a new level of the first factor group is fixed and combinations of the other group of factors are run. Earlier work referred to this restriction on randomization as a split-plot approach where several factor-level combinations among one or more groups of process variables defined the whole-plot treatments while a group of mixture blends defined the subplot treatments. New split-plot designs are presented for mixture experiments with process variables while considering a new model form. Three methods of estimation are considered for the terms in the model.

Variance dispersion properties of second-order response surface designs

Often, second-order response surface designs are chosen on the basis of a single-valued criterion such as D- or G-optimality. While such criteria provide a useful basis for selecting designs, they often fail to convey the true nature of the designs sup..

Construction of Balanced Equivalent Estimation Second-Order Split-Plot Designs

Practical restrictions on randomization are commonplace in industrial experiments due to the presence of hard-to-change or costly-to-change factors. Using a split-plot design (SPD) structure reduces the number of times that these hard-to-change factors are reset during the experiment. A class of second-order response surface SPDs has been proposed in which the ordinary least squares estimates of the model are equivalent to the generalized least squares estimates. Equivalent estimation designs provide best linear unbiased estimates that are independent of the variance components and can be obtained with standard statistical software. Moreover, design selection is robust to model misspecification and does not require previous knowledge of the variance components. This article expands the conditions to obtain equivalent estimation designs and outlines two systematic design construction techniques for building balanced versions of the central composite design. In addition, it presents an approach to generating equivalent estimation D-optimal designs. By applying these design construction techniques, a catalog of designs is generated. These methods provide practitioners with the necessary tools to build equivalent estimation SPDs for a wide variety of applications.

Tutorial: Industrial Split-plot Experiments

ABSTRACT Many industrial experiments involve two types of factors: those that are hard-to-change and those that are easy-to-change (ETC). Hard-to-change (HTC) factors have levels that are difficult and/or expensive to change. As a result, the experimenter would prefer to run the experiment in such a manner as to minimize the number of times that he/she must change the levels of these factors. Unfortunately, it is precisely the changing of these levels that provides the information about the effects of the HTC factors. Consequently, when we minimize the number of times we change the levels of these factors, we also minimize the relevant information about their effects. This paper summarizes the structure and the analysis of industrial split-plot experiments. The purpose of this article is to teach practitioners how to identify split-plot experimental conditions, how to run the experiment efficiently, and then how to analyze the results. The article illustrates both first-order and second-order experiments. The first four sections provide a basic background on experimental design and an introduction to first-order split-plot experiments. The remainder of this article contains more advanced topics dealing with second-order, split-plot experiments.

A new model and class of designs for mixture experiments with process variables

Experiments that involve the blending of several components are known as mixture experiments. In some mixture experiments, the response depends not only on the proportion of the mixture components, but also on the processing conditions, A new combined model is proposed which is based on Taylor series approximation and is intended to be a compromise between standard mixture models and standard response surface models. Cost and/or time constraints often limit the size of industrial experiments. With this in mind, we present a new class of designs that will accommodate the fitting of the new combined model.