Slope-Rotatable Central Composite Designs

Publisher Website
Google Scholar
Abstract
An analogue of the Box-Hunter rotatability property for second order response surface designs in k independent variables is presented. When such designs are used to estimate the first derivatives with respect to each independent variable the variance of the estimated derivative is a function of the coordinates of the point at which the derivative is evaluated and is also a function of the design. By choice of design it is possible to make this variance constant for all points equidistant from the design origin. This property is called slope-rotatability by analogy with the corresponding property for the variance of the estimated response, ŷ. For central composite designs slope-rotatability can be achieved simply by adjusting the axial point distances (α), so that the variance of the pure quadratic coefficients is one-fourth the variance of the mixed second order coefficients. Tables giving appropriate values of α have been constructed for 2 ≤ k ≤ 8. For 5 ≤ k ≤ 8 central composite designs involving fractional factorials are used. It is also shown that appreciable advantage is gained by replicating axial points rather than confining replication to the center point only.

This publication has 0 references indexed in Scilit: