A Class of Multi-Factor Designs for Estimating the Slope of Response Surfaces

Journal of Korean Society for Quality Management > Volume 14(1); 1986 > Article

Journal of Korean Society for Quality Management 1986;14(1): 26-.

ABSTRACT

A class of multi-factor designs for estimating the slope of second order response surfaces is presented. For multi-factor designs the variance of the estimated slope at a point is a function of the direction of measurement of the slope and the design. If we average the variance over all possible directions, the averaged variance is only a function of the point and 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 over all directions", and the necessary and sufficient conditions for a design to have this property are given and proved. The class of design with this property is mainly discussed.

Key Words: Response surface designs;Slope estimation;Rotatability;Slope-rotatability;