On Robustness of Response Surface Designs

One of the important properties of a 'good' response surface design is that the design should be insensitive to wild observations. In this note, a measure of sensitivity to wild observations is studied. It is shown that designs are made robust to wild observations by making $Tr[X'X)^{-1}M]$ small where M is a moment matrix over some region of interest. The proposed criterion is compared with that suggested by Box and Draper. Some about robust two-variable response surface designs are given.