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Prediction-Interval Constrained Programming

Summary: It is important in a production process to select the levels of the process variables so that the quality variables are produced within specifications. Regression analysis can be used for modeling imperfectly understood process relationships, but this does not always give optimal solutions. Use of optimization techniques, such as linear programming, provide optimal solutions for deterministic situations but are often not directly applicable to process control problems. Use of optimization techniques based on a regression model can be inaccurate because the variability of the regression model is ignored resulting in a high risk of the "optimal solution" not meeting the specifications. This paper develops and explains a prediction-interval constrained programming approach which is an extension of the general approach of chance constrained programming. The formulation yielded by prediction-interval constrained programming includes the variability inherent in the regression approach and yields an optimal solution for a specified level of risk.

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  • Topics: Statistics
  • Keywords: Statistics,Statistical methods,Optimization,Regression
  • Author: Olson, David L.; Wei, Jerry C.; White, Edna M.
  • Journal: Journal of Quality Technology