Choosing a suitable experimental design is an important step in the investigations of the factors that may influence one or more response variables. There are several criteria to keep in mind when the choice is made, one of which is rotatability. When a design is rotatable, it will produce information that predicts ŷ with the same precision at all points equidistant from the coded origin of the design. Another way of saying this is that the contours of V(ŷ), the variance of the predicted value, will be spherical about the design origin. In experimental practice, exact rotatability is not essential, but the knowledge of how to obtain it is useful in producing approximate rotatability while perhaps attaining other desirable design characteristics.
Keywords:
center points;
central composite designs;
experimental designs;
first-order designs;
response surfaces;
rotatability;
second-order designs;
two-level factorial designs;
variance contours
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