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N. CHANTARAT and T. T. Allen. Dept. of Industrial, Welding & Systems Engineering, Ohio State Univ., 1971 Neil Ave., 210 Baker Systems Bldg., Columbus, OH 43210 In some food science-related mixture experiments, factors of interest are qualitative in nature, e.g., the “presence or absence” of a tiny, fixed amount of a food additive or the categorical type of food processes used. In addition, some researchers have treated the total amount of ingredients as a qualitative factor. To date, the inclusion of qualitative factors in mixture experiments has received comparatively little attention. This research proposes a method based on the “combined array approach” to construct mixture designs involving qualitative factors. The proposed method uses the Expected Integrated Mean Squared Error (EIMSE) criterion, which takes into account both bias and variance errors. The proposed method can further reduce expected prediction errors compared to D-optimal alternatives whose performance is sensitive to model misspecification. The objectives are to analyze the prediction errors of existing design methodologies from the literature and to create new procedures that generate relatively accurate prediction models and that require substantially fewer experimental runs than existing methods. Our proposed procedures involve generating exhaustive set of candidate points. Next, the EIMSE criterion is minimized as a function of both mixture and qualitative factors, assuming the models of order d and (d + 1) for fit and true models respectively and using a genetic algorithm for optimization. The proposed methodology was compared with alternatives from the literature. Results included that, with the same or even lower number of experimental runs, our proposed designs achieves substantially reduced expected prediction errors compares with alternatives. Our method is apparently the only available approach that directly addresses both bias and variance errors and thus can be trusted to provide accurate prediction models in the context of mixture experiments involving qualitative factors. Also, using a combined array approach permits dramatic reductions in the number of experimental runs needed for a given prediction accuracy target.
Session 113, Product Development: General
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