Two-strata rotatability in split-plot central composite designs

Abstract

A rotatable design (Ann. Math. Stat. 1957; 28:195–241) for k factors is one such that the prediction variance is purely a function of distance from the design center. Of special interest in this paper is the rotatable central composite design (CCD), which most software packages use as the typical default choice for a second-order design. In many cases some factors are hard to change while others are easy to change, which creates a split-plot experiment. This paper establishes that the split-plot structure precludes the possibility of any second-order design being rotatable in the traditional sense. As an alternative this paper proposes the two-strata rotatable split-plot CCD, where the resulting prediction variance is a function of the whole plot (WP) distance and the subplot (SP) distance separately instead of the sum of them. The resulting design is rotatable in the WP space when the SP factors are held fixed, and vice versa. In the special case where the WP variance component is zero, the two-strata rotatable split-plot CCD becomes the standard rotatable CCD. Copyright © 2009 John Wiley & Sons, Ltd.