The use of third-order response surface designs suggests experimental situations involving second-order lack-of-fits. New sequential third-order response surface designs are proposed for use in modeling third-order effects using very simple mathematical principles. The experimental runs admitted into the designs are hat matrix aided and the new designs show high design efficiencies. Grid formation is adopted as a principle of discretizing a continuous design space. For a cuboidal region in k dimensions, five grid levels are utilized and the associated 5^k grid points form the candidate set for consideration in design construction. The new sequential designs are augmentations of the standard central composite designs and are generated using block of points corresponding to some diagonal elements of the hat matrix. All designs studied in two and three variables have very good optimality properties
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