Slope-Rotatability of Second Order Response Surface Regression Models with Correlated Error

Abstract

In Das [8], a study of slope rotatable designs with correlated error was initiated and second order slope-rotatability conditions over axial directions were derived for a general correlated error structure. In this article a class of multifactor designs for estimating the slope of a second order response surface regression model with correlated error is considered. Second order slope-rotatability over all directions and also with equal maximum directional variance in the case of two factors have been derived for a general correlated error structure. In the process, some measures have been proposed for robust slope-rotatability over axial directions, over all directions and with equal maximum directional variance, and are illustrated with examples.