Understanding interactions between mixture components and process variables

Abstract

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.

Keywords:

• Cox effects
• graphical display
• interaction visualization
• mixture-process interaction
• process variable effects

Additional information

Notes on contributors

Ronald D. Snee

Ronald D. Snee is founder and president of Snee Associates LLC in Newark, DE. He earned a doctorate in applied and mathematical statistics from Rutgers University in New Brunswick, NJ. He worked at DuPont for 24 years in a variety of assignments prior to pursuing his consulting career. Snee is an Honorary Member of ASQ, has received the ASQ Shewhart, Grant and Distinguished Service medals, and is an ASQ fellow and an Academician in the International Academy for Quality.

Roger W. Hoerl

Roger W. Hoerl is a Brate-Peschel associate professor of statistics at Union College in Schenectady, NY. He has a doctorate in applied statistics from the University of Delaware in Newark, DE. He worked at General Electric for 17 years prior to pursuing his academic career. Hoerl is an ASQ fellow, a recipient of the ASQ’s Shewhart Medal and Brumbaugh Award, and an Academician in the International Academy for Quality.