Advancements in Mixture Design
Organizers: Mark J. Anderson and Pat Whitcomb, Stat-Ease Inc.Session Chair: Mark J. Anderson, Stat-Ease, Inc.
State-of-the-Art Tools for Designing Mixture Experiments
Pat Whitcomb and Mark J. Anderson
Stat-Ease Inc.
Due to the nature of mixture experiments, canned designs are usually too restrictive for actual experimentation. In such cases an algorithmic design is required. We explore various mathematical tools useful for building and evaluating alternative algorithmic designs. To assess “goodness of design” such evaluations must consider the model choice, specific optimality criteria (e.g. D, IV, etc), precision of estimation (fraction of design space), the number of runs (required precision), testing for lack of fit, the choice of metric for components, and so forth. All of these issues are considered at practical level – keeping the actual experimenter in mind. This brings to the forefront such considerations as subject matter knowledge (first principles and experience), component choice, and the feasibility of the experiment design.
Model-Robust Mixture Experiment Designs
Greg F. Piepel
Pacific Northwest National Laboratory
The most commonly used experimental designs for mixture experiments are comprised primarily of points on the boundary of the applicable experimental region. These include simplex-lattice and simplex-centroid designs for simplex mixture regions, as well as extreme-vertices and optimal designs for constrained mixture regions. These mixture designs generally have good variance properties for the corresponding mixture model forms assumed to be adequate. However, because mixture experiment models only approximate the true unknown relationships, they are subject to bias errors as well as variance errors. Methods for developing mixture and mixture-process variable (MPV) experiment designs that are robust for a potential model form versus the assumed model form, or robust for several model forms, have been presented in the literature. However, the literature for model-robust mixture and MPV designs is limited compared to that for non-mixture response surface designs. Also, these model-robust methods are generally unknown, not implemented in software, and hence are seldom used to design mixture and MPV experiments. Brief synopses of model-robust methods for mixture and MPV experiments are presented with illustrative examples. Recommendations are given for implementing these methods with existing software. Future needs are also presented.
Mining Mixture Data to Find the Most Reliable Prediction Model
Dean V. Neubauer
Corning Inc./RIT
Glass researchers perform numerous experimental melts over time in an effort to optimize compositions to achieve desired physical properties. These databases are often generated over several years and are rarely “mined” to extract useful predictive models. This talk will cover how a glass researcher (user) would typically analyze such data (brute force regression) and then compare these results to models created by data mining techniques, such as partial least squares (PLS), neural net analysis (artificial neural net), and pseudocomponent transformations (via the Design-Expert® software’s historical analysis feature). It will be shown that a user can obtain an excellent prediction model using Design-Expert’s historical analysis feature without the need for more sophisticated data mining approaches. Design-Expert is a registered trademark of Stat-Ease, Inc.