Response Surface Methodology (RSM) is a collection of mathematical and statistical techniques useful for analyzing
experiments where the yield is believed to be influenced by one or more controllable factors. Box and Hunter (1957) introduced
rotatable designs in order to explore the response surfaces. The analogue of Box-Hunter rotatability criterion is a requirement
that the variance of i
yˆ(x)/ x be constant on circles (v=2), spheres (v=3) or hyper spheres (v 4) at the design origin. These
estimates of the derivatives would then be equally reliable for all points (x , x ,...,x ) 1 2 v
equidistant from the design origin.
This property is called as slope rotatability (Hader and Park (1978)). Anjaneyulu et al (1997) established that SOSRD (OAD) has
the additional interesting property that the sum of the variance of estimates of slopes in all axial directions at any point is a
function of the distance of the point from the design origin.
