On the Efficiencies of Second Order Response Surface Designs for the Estimation of Responses and Slopes Using Symmetrical Unequal Block Arrangements with Two Unequal Block Sizes

Abstract

In this paper, the efficiencies of various second order response surface designs, like second order rotatable designs (SORD), second order slope rotatable designs (SOSRD), SORDs with an equi-spaced doses design, and SOSRDs with an equi-spaced doses design using symmetrical unequal block arrangements (SUBA) with two unequal block sizes, are studied for the estimation of responses and slopes at different points (central, axial, cube corner points) on second order response surface designs. The study is done because in some cases a SORD, and SOSRD constructed by using a SUBA with two unequal block sizes have fewer design points compared to those constructed by other methods.