Journal ArticleDOI
A Note on Model Reduction for Experiments With Both Mixture Components and Process Variables
John W. Gorman,John A. Cornell +1 more
TLDR
In this paper, a reparametrized model form is presented that enables the effects of the process variables to be separated from the blending effects of mixture components using a subset-selection procedure.Abstract:
In mixture experiments containing process variables, the traditional Scheffe-type model contains terms in the mixture components and crossproducts between the mixture components and the process variables. The crossproduct coefficients estimate the effects of the process variables on the blending properties of the mixture components only and do not provide any overall measure of the main effects and interactions of the process variables by themselves. In this note a reparametrized model form is presented that enables the effects of the process variables to be separated from the blending effects of the mixture components. Reduced model forms are obtained using a subset-selection procedure. The model-reduction technique is illustrated using data from a six-factor fish-patty experiment.read more
Citations
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Journal ArticleDOI
Mixture Experiment Approaches: Examples, Discussion, and Recommendations
TL;DR: A mixture experiment involves varying the proportions of two or more ingredients, called components of the mixture, and studying the changes that occur in the measured properties (responses) of the components as mentioned in this paper.
Journal ArticleDOI
Models for Mixture Experiments When the Response Depends on the Total Amount
TL;DR: In this article, the authors consider mixture experiments in which the response also depends on the total amount, and develop mixture-amount models appropriate for such situations, where models in the component amounts are also considered and are shown to be reduced forms of the mixture-factor models.
Journal ArticleDOI
Optimal designs for experiments with mixtures: a survey
TL;DR: In this article, a survey article on known results about analytic solutions and numerical solutions of optimal designs for various regression models for experiments with mixtures is presented, including polynomial models, models with homogeneous functions, models containing inverse terms and ratios, log contrast models, and models with quantitative variables, and mod els containing the amount of mixture.
Journal ArticleDOI
Fractional Design Plans for Process Variables in Mixture Experiments
John A. Cornell,John W. Gorman +1 more
TL;DR: In this article, the authors describe how to experiment with industrial processes involving the blending of ingredients to form end products, and experiment with these processes consists of varying the proportions of the individual ingredients (i.e., varying the blends) as well as varying the conditions at whic..
Journal ArticleDOI
Mixture experiments with process variables: D-optimal orthogonal experimental designs
TL;DR: In this paper, an experimental design for quadratic (or linear) blending in the presence of process variables is presented, where the number of design points needed when different orthogonal blocks are used is usually smaller than when a single block is repeated at the various process variables levels.
References
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Journal ArticleDOI
Some Comments on Cp
TL;DR: In this article, the typical configuration of a Cp plot when the number of variables in the regression problem is large and there are many weak effects is studied, and a particular configuration that is very commonly seen can arise in a simple way.
Journal ArticleDOI
Fitting Equations to Data.
Book
Experiments with Mixtures: Designs, Models and the Analysis of Mixture Data
TL;DR: In this paper, the original Mixture Problem is described and models for exploring the Entire Simplex Factor Space are presented, including matrix algebra, least squares, and the analysis of variance.
Journal ArticleDOI
The Simplex-Centroid Design for Experiments with Mixtures
Henry Scheffé,Henry Scheffé +1 more