Efficient Visual Mixture Design of Experiments using Property Clustering Techniques

Abstract

Mixture design is a design of experiments (DOE) tool used to determine the optimum combination of chemical constituents that deliver a desired response (or property) using a minimum number of experimental runs. While the approach is sufficient for most experimental designs, it suffers from combinatorial explosion and visualization difficulties when dealing with multicomponent mixtures. To circumvent these problems, a recently developed design technique called property clustering is applied. In this type of design the properties are transformed to conserved surrogate property clusters described by property operators, which have linear mixing rules even if the operators themselves are nonlinear. Product and process property targets are then used to describe a feasibility target region. To solve the mixture design, components are mixed according to property operator models in a reverse problem format until the mixture falls within the feasibility target region. Once candidate solutions are found, they can be screened with additional criteria per the experimenter's preference. The degree of accuracy of this modeling technique depends heavily on the ability of the property operator models to adequately describe the property within the studied design space. This work utilizes linear Scheffe and Cox models as property operators of a mixture design to demonstrate the benefits of applying property clustering to chemometric techniques.

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