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Efficient Optimality Criterion for the Response Surface Designs

Serpil Aktaş

Abstract


Response Surface method uses a set of designed experiments to obtain an optimal response in the experimental design studies. The two most common designs generally used in response surface modeling are central composite and Box-Behnken designs. The optimal design is to select design points according to some criteria, two of those are D-optimality and the distance based optimality. D-optimality design minimizes the volume of the confidence ellipsoid of the regression estimates of the linear model parameters. The design spreads the design points uniformly over the design space in the distance based optimality. In this case, this method provides one solution for selecting the design points and the distance-based optimality algorithm selects design points from the candidate set, such that the points are spread evenly over the design space. Distance based-optimality selects the candidate point with the largest Euclidean distance from the origin or the point that is closest to a pure component as the starting point. The aim of the selection process is to reduce the number of experimental runs. In this study the optimality criteria are studied and which is the more efficient approach for achieving a robust design compared with original design approach is investigated for both central composite and Box-Behnken designs.

Keywords


response surface design, optimal design, experimental design

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