On D-minimax optimal second-order designs for estimating slopes of second-order response surfaces

Minimization of determinant of the covariance matrix of the estimated axial slopes at a point, maximized over all points in the region of interest, is taken as the design criterion. Optimal designs under this D-minimax criterion are considered for four different second-order models over hypercubic regions. Relative performances of the optimal designs are investigated. Optimal designs from the classes of product designs, central composite designs and Kono designs are also derived. Some efficient exact designs are obtained.