Componentwise Variance Dispersion Graphs for Mixture Experiments

• Activity Number: 222
• Type: Invited
• Date/Time: Tuesday, July 31, 2007 : 8:30 AM to 10:20 AM
• Sponsor: Section on Quality and Productivity
• Author(s): John J. Borkowski*+ and Boonorm Chomtee and Kamolchanok Choochaow
• Companies: Montana State University and Kasetsart University and Silpakorn University
• Keywords: mixture experiment ; variance dispersion graph ; prediction variance trace ; G-efficiency

Abstract

Consider a q-component mixture experiment with constraints defined by lower and upper bounds for each component proportion. Whether the design region is a simplex or some irregularly shaped subregion, the problem of interest is the extension of variance dispersion graphs (VDGs) to experiments involving mixtures. As an alternative to studying the prediction variance on shrunken polyhedral spaces (Piepel and Anderson 1993) or to the prediction variance trace (PVT) plots involving Cox directions (Vining, Cornell, and Myers 1993), a new graphical tool, called the componentwise variance dispersion graph (CVDG), will be proposed. A CVDG contains componentwise plots of the variability throughout the entire polyhedral design space. A CVDG also provides the mixture yielding the maximum prediction variance which in turn provides the design's G-efficiency. Examples of CVDGs will be presented.