ABSTRACT
CORRELATED ERRORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 6.5 ROBUST SECOND-ORDER SLOPE ROTATABLE AND MODIFIED
SLOPE ROTATABLE DESIGNS UNDER INTRA-CLASS STRUCTURE . . . 117 6.6 ILLUSTRATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 6.7 CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Slope-rotatability is also a natural and highly desirable property as rotatability in response surface methodology. The present chapter considers a class of multifactor designs for estimating the slope of second-order response surfaces with correlated errors. The concepts of robust slope-rotatability and modified robust slope-rotatability along axial directions are introduced. For robust slope-rotatability along axial directions, it requires that the variance of the estimated slope at a point to be only a function of the distance of the point from the design origin, and independent of correlation parameter or parameters involved in the errors variance-covariance matrix. General conditions of robust second-order slope-rotatability and modified slope-rotatability along axial directions are derived for a general correlated error structure. These conditions are simplified for intra-class correlation structure. Some optimal robust second-order slope-rotatable designs (over all directions or A-optimal,D-optimal and with equal maximum directional variance in Chapter 7) are examined with respect to modified slope-rotatability. It is observed that robust second-order slope-rotatable designs over all directions, or with equal maximum directional variance slope, or D-optimal slope are not generally modified robust second-order slope-rotatable designs. An example of modified robust second-order slope-rotatable design under tri-diagonal correlation structure is displayed.
