On Some Two- and Three-dimensional D-minimax Designs for Estimating Slopes of a Third-order Response Surface

Abstract

Design of experiments is considered for the situation where estimation of the slopes of a response surface is the main interest. Under the D-minimax criterion, the objective is to minimize the generalized variance of the estimated axial slopes at a point maximized over all points in the region of interest in the factor space. For the third-order model over spherical regions, the D-minimax designs are derived in two and three dimensions. The efficiencies of some two- and three-dimensional designs available in the literature are also investigated.

Keywords:

• D-minimax designs
• Optimal designs
• Response surface designs

Mathematical Subject Classification:

• Primary 62K05
• Secondary 62K20