Multiresponse Rotatability

Since its introduction by Box and Hunter, rotatability of a response surface design has always been associated with single-response models. This article extends this design concept to multiresponse models. For these models, rotatability means constant prediction variances and covariances, and hence correlations, among the predicted responses at points that are equidistant from the design center. It is shown that multiresponse rotatability can be achieved if and only if the design is rotatable in the usual sense for a single-response model whose order, or degree, is the highest among all the response models under consideration. This property does not depend on the form of the variance-covariance matrix of the responses.