Design and Analysis of Experiments

Abstract

Since writing the first edition of Design and Analysis of Experiments, there have been a number of additions to the research investigator’s toolbox. In this second edition, we have incorporated a few of these modern topics. Small screening designs are now becoming prevalent in industry for aiding the search for a few influential factors from amongst a large pool of factors of potential interest. In Chap. 15, we have expanded the material on saturated designs and introduced the topic of supersaturated designs which have fewer observations than the number of factors being investigated. We have illustrated that useful information can be gleaned about influential factors through the use of supersaturated designs even though their contrast estimators are correlated. When curvature is of interest, we have described definitive screening designs which have only recently been introduced in the literature, and which allow second order effects to be measured while retaining independence of linear main effects and requiring barely more than twice as many observations as factors. Another modern set of tools, now used widely in areas such as biomedical and materials engineering, the physical sciences, and the life sciences, is that of computer experiments. To give a flavor of this topic, a new Chap. 20 has been added. Computer experiments are typically used when a mathematical description of a physical process is available, but a physical experiment cannot be run for ethical or cost reasons. We have discussed the major issues in both the design and analysis of computer experiments. While the complete treatment of the theoretical background for the analysis is beyond the scope of this book, we have provided enough technical details of the statistical model, as well as an intuitive explanation, to make the analysis accessible to the intended reader. We have also provided computer code needed for both design and analysis. Chapter 19 has been expanded to include two new experiments involving split-plot designs from the discipline of human factors engineering. In one case, imbalance due to lost data, coupled with a mixed model, motivates introduction of restricted-maximum-likelihood-based methods implemented in the computer software sections, including a comparison of these methods to those based on least squares estimation