The Geometry of Constrained Mixture Experiments

In mixture experiments, the proportions of the components are often constrained by upper and lower bounds. The resulting experimental region is usually an irregular polyhedron. The experimental region, however, can be obtained from a regular simplex by truncation. This technique allows derivation of...

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Bibliographic Details
Published in:Technometrics 1986-05, Vol.28 (2), p.95-102
Main Author: Crosier, Ronald B.
Format: Article
Language:English
Subjects:
Applications
Centroids
Exact sciences and technology
Experiment design
Gasoline
H I regions
Hyperplanes
Mathematics
Polyhedrons
Probability and statistics
Pseudocomponents
Sciences and techniques of general use
Statistics
Vertices
Vertices algorithm
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Summary:In mixture experiments, the proportions of the components are often constrained by upper and lower bounds. The resulting experimental region is usually an irregular polyhedron. The experimental region, however, can be obtained from a regular simplex by truncation. This technique allows derivation of formulas for the number of boundaries, and the volume, of the experimental region. The formulas for the number of boundaries provide guidance for designing mixture experiments. The formula for volume may be used to determine if small changes in the constraints have a small effect on the experimental region. The volume formula is also used, along with the truncation procedure, to calculate center-of-mass centroids. A new algorithm is given for generation of the vertices of mixture regions constrained by upper and lower bounds.
ISSN:0040-1706
1537-2723
DOI:10.1080/00401706.1986.10488110