Measure of rotatability of modified five-level second-order rotatable design using supplementary difference sets

Abstract

Rotatability is a desirable quality of fitting response surface experimental designs. The property states that the variance of the estimated response made from the Taylor’s series expansion are constant on circles, spheres and hyper-spheres about the centre of the design. In this article, a measure of rotatability of modified second-order rotatable design is presented. The variance function of a second-order response design and an infinite class of supplementary difference sets is used in coming up with the design.

Keywords

• response surface
• rotatable designs
• second-order designs
• five level
• supplementary difference sets