ON VARIANCE-SUM SECOND AND THIRD ORDER SLOPE ROTATABLE DESIGNS: RESPONSE SURFACE METHODOLOGY

Response Surface Methodology is a collection of mathematical and statistical techniques useful for analyzing problems where severalindependent variables influence a dependent variable or response and the goal is to find the product mix to optimize this response.As the estimation of slope of response surface occurs frequently in practica situations,the authors established that Second Order Slope Rotatable Designs Over All Directions (SOSRD(OAD))has he 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. They have constructed v dimensional Variance-Sum SOSRD from a known (v-1)dimensional Variance-Sum SOSRD using embedding techniques.Group- Divisibility in Variance-Sum SOSRD is also ntroduced and constructed various designs in view of its practical applicability.They also introduced and constructed the Variance-Sum Third Order Slope Rotatable Designs over an axial direction using Doubly Balanced Incomplete Block Designs and established several interesting relations among TOSRD,Variance-Sum TOSRD and TOSRD(OAD).