Design of Experiments
This chapter presents the framework for the design and analysis of experiments. First, the general principles of design, including confounding, signal-to-noise ratio, randomisation, and blocking, are considered. Next, the commonly encountered factorial and fractional factorial designs are analysed in detail. Both analysis and design of such experiments, including the topics of model determination, replicates, confounding patterns, and resolution, are explored. Appropriate methods, including the development of orthogonal and orthonormal bases, for the analysis of such experiments using computers are presented. Although the results focus on 2-factorial design, higher-order design experiments are also considered, and the procedure for their analysis is explained. Detailed examples and cases are given. Third, methods for analysis of curvature, or quadratic terms, in a model are examined using factorial design with centre point replicates. Finally, the idea behind response surface methodologies, such as central composite design and optimal design, is briefly explored. Examples drawn from a wide range of different examples are considered. By the end of this chapter, the reader should be able to design and analyse factorial and fractional factorial experiments and curvature experiments and perform basic response surface methodologies using appropriate computational assistance.
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