Rotatability is a Sufficient Condition for A- and D-Rotatability

Abstract

Designs for estimating axial slopes of a response surface are considered. A design is said to be A- (D-) rotatable if the trace (determinant) of variance–covariance matrix of the estimated slopes at a point in the factor space is a function of the distance of the point from the center of the design. It is shown that for any order d and any dimension k, a design which is rotatable in the Box and Hunter (1957) sense is automatically A- and D-rotatable. Some specific examples illustrating the validity of this general result are provided.

Keywords:

• A-rotatability
• D-rotatability
• dth order designs
• Response surface designs
• Rotatable designs

Mathematics Subject Classification:

• 62K99

Acknowledgment

This research was supported by Project No. SS 06/06 of Kuwait University.