Strategies to analyse unreplicated fractional factorial split-plot designs Seminar

Abstract
Split-plot designs have been playing a crucial role in industrial settings since Taguchi cross-product experiments received acknowledgment in the west. As a consequence, much discussion was generated in the statistical community, especially in the 1980s and in the 1990s, which led to more efficient ways to run similar types of industrial experiments. A good discussion on the various features of robust design problems can be found in Box, Bisgaard, and Fung (1988). Examples of robust designs involving the use of split-plot designs also appear in Box and Jones (1992), Box (1996), and Bisgaard (2000). However, to investigate dispersion effects we need first to have residuals, and no attention in the literature has been given in the estimation and analysis of residuals in split-plot plans. This problem is more difficult in unreplicated split-plot designs, where first we have to identify and sort out the active effects from the non-active ones to have some degrees of freedom left to make any residual analysis. We provide a framework to study the residuals of unreplicated (2k-p x 2q-r) split-plot designs. Special consideration is given to the investigation and analysis of dispersion effects. We apply the results for the unreplicated split-plot model in a real experiment conducted at the Engineering Research Center for Plasma at the Univeristy of Wisconsin-Madison with the intention of improving the plasma treatment on paper. References: Bisgaard, S. (2000). ?The Design and Analysis of 2k-p × 2q-r Split Plot Experiments,? Journal of Quality Technology, 32, 1, 39-56. Box, G. E. P. (1996). ?Split Plot Experiments,? Quality Engineering, 8, 3, 515-520. Box, G. E. P., Bisgaard, S. and Fung, C. (1988). ?An Explanation and Critique of Taguchi?s Contribution to Quality Engineering,? Quality Reliability Engineering International, 4, 123-131. Box, G. E. P. and Jones, S. (1992). ?Split-Plot Designs for Robust Product Experimentation,? Journal of Applied Statistics, 19(1), 3-26.