ABSTRACT
DIRECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7.4 ROBUST SECOND-ORDER SYMMETRIC BALANCED DESIGN . . . . . . . . . 131 7.5 ROBUST SLOPE-ROTATABILITY WITH EQUAL MAXIMUM
DIRECTIONAL VARIANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 7.6 D-OPTIMAL ROBUST SECOND-ORDER SLOPE-ROTATABLE
DESIGNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 7.7 ROBUST SLOPE ROTATABLE DESIGNS OVER ALL DIRECTIONS,
WITH EQUAL MAXIMUM DIRECTIONAL VARIANCE AND D-OPTIMAL SLOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.8 CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Second-order slope-rotatability and modified slope-rotatability conditions along axial directions are derived in Chapter 6 for a general variance-covariance structure of errors. The present chapter introduces some concepts of optimal robust second-order slope-rotatable designs (over all directions (or A-optimal slope), with equal maximum directional variance and D-optimal slope) for correlated errors. Second-order slope-rotatability conditions over all directions, with equal maximum directional variance and D-optimal slope are derived for a general correlated error structure. It is examined that robust second-order rotatable designs are also robust slope-rotatable over all directions, with equal maximum directional variances and D-optimal slope. Equal maximum directional variance slope-rotatable design requires that the maximum variance of the estimated slope over all possible directions 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 variance-covariance matrix of errors. In the process, robust second-order symmetric balanced designs are introduced. A class of robust second-order slope-rotatable designs over all directions, with equal maximum directional variance and D-optimal slope-rotatable designs is investigated for some special correlation structures of errors, i.e., intra-class, inter-class, compound symmetry, tri-diagonal and autocorrelated structures.
