Understanding interactions between mixture components and process variables

• Published in: Quality engineering 2023-01, Vol.35 (1), p.1-19
• Main Authors: Snee, Ronald D., Hoerl, Roger W.
• Format: Article
• Language: English
• Subjects: Contours; Cox effects; graphical display; interaction visualization; mixture-process interaction; Mixtures; process variable effects; Process variables; Variables
• ISSN: 0898-2112; 1532-4222
• DOI: 10.1080/08982112.2022.2083516

The study of mixture component effects in the presence of process variables has been of interest since the work of Scheffé. A key advantage of designed experiments in general is the ability to estimate and interpret interactions. A unique feature of mixture-process experiments is the potential presence of interactions between the mixture components and the process variables. The classic approach to interpret these has been to use contour plots and evaluate individual interaction coefficients in Scheffé mixture-process models. It is proposed to study the interactions along the Cox component axes, which greatly enhances the insight into the nature of these interactions that can be obtained from contour plots. Further, we propose an alternative analysis that produces estimates of the process variable main effects in mixture-process models. Both graphical and analytical methods are presented. This approach provides an overall view of the main effects and interactions that is consistent with how these terms are evaluated in factorial and response surface experiments with only process variables. Limitations of the classic approach are identified and discussed. Three examples are included to illustrate the approach.