Abstract
In a mixture experiment, q ≥ 2 components are mixed in various proportions, and one or more responses are measured for each mixture. Scheffé quadratic models are often used to model responses as functions of the component proportions. A complete Scheffé quadratic model contains q linear terms βixi and Q = q(q – 1)/2 quadratic crossproduct terms βijxixj (i < j). Because Q increases rapidly as q increases, alternative models containing fewer quadratic terms than the complete Scheffé quadratic model are of interest. Traditionally, reduced Scheffé quadratic models, formed by augmenting linear terms with selected quadratic crossproduct terms, are used. We propose generating partial quadratic mixture (PQM) models by augmenting linear terms with selected quadratic crossproduct terms and/or squared terms βiixi2. The interpretations and potential advantages of PQM models compared to equivalent restricted Scheffé quadratic models and to reduced Scheffé quadratic models are discussed. The methods are illustrated using data from two constrained mixture experiments involving simulated waste glass.
Additional information
Notes on contributors
Greg F. Piepel
Dr. Piepel is a Staff Scientist at PNNL and is a Senior Member of ASQ. His e-mail address is [email protected].
Jeff M. Szychowski
Mr. Szychowski is an M.S. student in the Department of Statistics.
Jason L. Loeppky
Mr. Loeppky is a Ph.D. student in the Department of Statistics and Actuarial Science. He is a Member of ASQ.