15F-37 |
New procedures for mixture experiments with process variables that address bias related prediction errors |
N. CHANTARAT1, T. Allen1, and P. Ratanatriwong2. (1) Industrial, Welding, & Systems Engineering, Ohio State Univ., 1971 Neil Ave., Rm. 210, Columbus, OH 43210, (2) Food Science & Technology, Ohio State Univ., 2121 Fyffe Rd., Columbus, OH 43210 In a mixture experiment, the system responses (e.g., taste ratings) are assumed to be functions of the relative proportions of the recipe components and, potentially, process variables (e.g., pressure and temperature). The application of formal statistical approaches to structure mixture experimental planning and analysis has become increasingly common in the food industry. Yet, as we demonstrate, existing formal procedures result in unnecessarily inaccurate response predictions and require unnecessarily large numbers of experimental runs. This follows because existing approaches are based on objectives such as D-optimality that ignore bias errors and product array structures. The objectives are: (1) to analyze the prediction errors of existing methodologies using models from the literature, (2) to create new procedures that generate relatively accurate prediction models and that require substantially fewer runs than existing methods, and (3) to demonstrate the usefulness of the proposed methods with a case study. Our proposed procedures involve generating candidate points on the simplex that satisfy all constraints. Next, the expected integrated mean squared error criterion is minimized as a function of both mixture and process variables combined, assuming Scheffe’ product models of order d and (d + 1) for fit and true models respectively and using a genetic algorithm. The proposed methodology was compared with alternatives from the literature using a standard accuracy related criterion and a well-studied example also from the literature. Results included that, with the same number of runs, our proposed design has two to three times lower prediction errors than alternatives. Our method is apparently the only available approach that directly addresses bias errors and thus can be trusted to provide accurate prediction models. Also, using a combined array for the process and recipe variables potentially permits dramatic reductions in the number of experimental runs needed for a given prediction accuracy target.
Session 15F, Product Development
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