A New Construction of Variance-Sum Third Order Slope Rotatable Designs

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 ∂ŷ(x)/∂x_i be constant on circles (v=2), spheres (v=3) or hyperspheres (v ≥ 4) at the design origin. These estimates of the derivatives would then be equally reliable for all points (x₁,x₂,...,x_v) equidistant from the design origin. This property is called as slope rotatability (Hader and Park (1978)). Anjaneyulu et al (1995-2000) introduced Third Order Slope Rotatable Designs. Anjaneyulu et al(2004) introduced and established that TOSRD(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. In this paper we made an attempt to construct Variance-Sum Third Order Slope Rotatable in four levels.