A Component Slope Linear Model for Mixture Experiments

Abstract

The Scheffé linear model and the Cox linear model are two first-order model forms commonly used for analyzing mixture experiment data. In a fitted Scheffé linear model, the coefficient for a mixture component is the predicted response at that pure component (i.e., single-component mixture). In a fitted Cox linear model, the coefficient for a mixture component is the predicted difference in response at that pure component and at a pre-specified reference mixture. An alternative first-order model for mixture experiments, the component slope linear mixture (CSLM) model, is proposed in this article. In a fitted CSLM model, the coefficient for a mixture component is the predicted slope of the linear response surface along the Cox effect direction for that component (where the direction is determined by a pre-specified reference mixture). The CSLM model and methods for fitting it are presented. The advantages and disadvantages of the CSLM model, Scheffé linear model, and Cox linear model are discussed. The three models are illustrated and interpreted for an example involving the liquidus temperature of spinel crystals in simulated nuclear waste glass.

Key Words:

• Cox linear mixture model
• mixture component effects
• nuclear waste glass example
• Scheffé linear mixture model

Additional information

Notes on contributors

Greg F. Piepel

Greg F. Piepel Laboratory Fellow in the Statistical Sciences group at Battelle-Pacific Northwest Division in Richland, Washington, USA. He is also the developer of the MIXSOFT software and presents short courses on the design and analysis of mixture experiments (http://members.aol.com/mixsoft). His research interests are in the design and analysis of mixture and other constrained region experiments, optimal experimental design, statistical methods development, and solving applied problems in the physical and engineering sciences. Dr. Piepel is a Fellow of the American Statistical Association and is on the Editorial Review Board of the Journal of Quality Technology. He has numerous publications in the statistics and engineering literature.