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Fractional simplex designs for interaction screening in complex mixtures.

Authors
  • McConkey, B J
  • Mezey, P G
  • Dixon, D G
  • Greenberg, B M
Type
Published Article
Journal
Biometrics
Publication Date
Sep 01, 2000
Volume
56
Issue
3
Pages
824–832
Identifiers
PMID: 10985222
Source
Medline
License
Unknown

Abstract

In mixture experiments, one may be interested in estimating not only main effects but also some interactions. Main effects and significant interactions in a mixture may be estimated through appropriate mixture experiments, such as simplex-centroid designs. However, for mixtures with a large number of factors, the run size for these designs becomes impractically large. A subset of a full simplex-centroid design may be used, but the problem remains regarding which factor-level settings should be selected. In this paper, we propose a solution that considers design points with either one or p individual nonzero factor-level settings. These fractional simplex designs provide a means of screening for interactions and of investigating the behavior of many-component mixtures as a whole while greatly reducing the run size compared with full simplex-centroid designs. The means of construction of the design arrays is described, and designs for < or = 31 factors are presented. Some of the proposed methodology is illustrated using generated data.

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