QPRC 2016

Comparing the Slack-Variable Mixture Model with Other Alternatives

William A. Brenneman

Procter & Gamble Company

There have been many linear regression models proposed to analyze mixture experiments including the Scheffé model, the slack-variable model, and the Kronecker model. The use of the slack-variable model is somewhat controversial within the mixture experiment research community. However, in situations that the slack-variable ingredient is used to fill in the formulation and the remaining ingredients have constraints such that they can be chosen independently of one another, the slack-variable model is extremely popular by practitioners mainly due to the ease of interpretation. In this paper, we advocate that for some mixture experiments the slack-variable model has appealing properties including numerical stability and better prediction accuracy when model-term selection is performed. We also explain how the effects of the slack-variable model components should be interpreted and how easy it is for practitioners to understand the components effects. We also investigate how to choose the slackvariable component, what transformation should be used to reduce collinearity, and under what circumstances the slack-variable model should be preferred. Both simulation and practical examples are provided to support the conclusions.

Biographical Sketch:  William Brenneman is a Research Fellow at Procter & Gamble in the Quantitative Sciences Department and an Adjunct Professor at Georgia Tech in the Industrial and Systems Engineering Department.  Since joining P&G in 2000, he has worked on a wide range of projects that deal with statistics applications in his areas of expertise: design and analysis of experiments, robust parameter design, reliability engineering, statistical process control, computer experiments, and general statistical thinking.  He was also instrumental in the development of an in-house statistics curriculum. He received a Ph.D. degree in Statistics from the University of Michigan, an MS in Mathematics from the University of Iowa and a BA in Mathematics and Secondary Education from Tabor College.  William is a Fellow of the American Statistical Association (ASA), a Fellow of the American Society for Quality (ASQ), and a member of the Institute of Mathematical Statistics and the Institute for Operations Research and Management Sciences.  He has served as ASQ Statistics Division Chair and is currently the Chair for the Quality and Productivity Section of ASA and an Associate Editor of Technometrics. William also has seven years of experience as an educator at the high school and college level.