A Class of Optimal Three-Level Response Surface Designs

• Activity Number: 422
• Type: Contributed
• Date/Time: Wednesday, August 1, 2007 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): William Li*+ and Xuan Lu
• Companies: The University of Minnesota and Tsinghua University
• Keywords: augmented pairs design ; central composite design ; optimal design ; orthogonal design ; response surface design ; sequential experiment

Abstract

Three-level experimental designs are popular choices for fitting response surface models. Morris (2000) proposed a class of three-level composite designs, which are constructed sequentially. At stage 1, a two-level orthogonal design is selected; and at Stage 2, augmented points resulting from pairs of points of the two-level designs are added. The resulting designs are called augmented pairs (AP) designs. We consider optimal AP designs by finding the best two-level orthogonal such that the resulting three-level AP designs have optimal criteria values. Both orthogonal and non-orthogonal two-level designs are considered. In the second part of the research we construct minimal AP designs, for which the two-level designs used in Stage 1 are restricted to be saturated designs.