SEQUENTIAL DESIGNS FOR SPHERICAL WEIGHT FUNCTIONS.
WISCONSIN UNIV MADISON DEPT OF STATISTICS
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Two papers by Box and Draper 1959, 1963 discussed the selection of first and second order rotatable designs when a spherical region of interest was defined and account had to be taken of possible biases due to the fact that the polynomial model under consideration was inadequate by one order. Here we consider a different but related problem. Suppose the intensity of interest in the factor space is represented, not by a spherical region of interest, but by a symmetric multivariate distribution weight function. Previously it was assumed that total interest lay uniformly over a spherical region and there was no interest outside it. We wish to specify the runs of a second order design which can be performed sequentially so that both the first order portion and the full second order design provide protection against biases of one order higher. In particular, we shall consider designs which are either the basic central composite type and consist of a cube plus star plus center points, or designs which contain an extra star. The extra star is required in some cases to allow certain conditions to be met. Author
- Operations Research