ABSTRACT
Optimality or at least rotatability is a highly desirable criterion for fitting a response surface design. This chapter confines to first-order linear regression models with correlated errors. The concept of robust first-order rotatability and optimality are examined for different well-known error variance-covariance structures. Generally, it is very difficult to derive optimal or at least efficient designs for even linear models with correlated errors, and for some correlation structures, D-optimal design does not exist. It is shown that D-optimal robust first-order designs are always robust first-order rotatable but the converse is not true. For compound symmetry, inter-class, intra-class and tri-diagonal correlation error structures, some construction methods of D-optimal robust first-order designs are discussed. For autocorrelated error structure, efficient robust rotatable designs are presented.
