Methods for Assessing Curvature and Interaction in Mixture Experiments

• Published in: Technometrics Vol. 44; no. 2; pp. 161 - 172
• Main Authors: Piepel, Greg F, Hicks, Ruel D, Szychowski, Jeff M, Loeppky, Jason L
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 01.05.2002; The American Society for Quality and The American Statistical Association
• Subjects: Chemical composition; Curvature; Decimals; Factorial design; Geometric lines; Glass; Mixture component effects; Mixture component interactions; Mixture interaction plot; Modeling; Nuclear waste; Nuclear waste glass examples; Parallel lines; Spinel
• ISSN: 0040-1706; 1537-2723
• DOI: 10.1198/004017002317375118

The terms curvature and interaction traditionally are not defined or used in the context of mixture experiments because curvature and interaction effects are partially confounded due to the mixture constraint that the component proportions sum to 1. Instead, the term nonlinear blending traditionally is defined and used. However, just as the concept of a component effect is defined specifically for mixture experiments, the concepts of curvature and interaction can be also. These special definitions lead to special sets of points for assessing the curvature and interaction of mixture components. An interaction plot for mixture components is obtained by plotting measured or predicted response values at the special points for assessing interaction. Together with response trace (component effects) plots, the new mixture component interaction plots provide for graphically assessing the linear, curvature, and interaction effects of mixture components. These methods provide a more complete picture of how mixture components affect a response, which is useful in formulating mixtures and confirming or extending subject matter knowledge. The special sets of points and the graphical techniques used to assess linear, curvature, and interaction effects are illustrated using two nuclear waste glass examples.