On the minimum bias response surface designs of Box and Draper

The minimum bias design criterion is an important part of response surface methodology. In this paper, necessary and sufficient conditions for minimum bias designs are derived in terms of the design moments. It is shown that the sufficient conditions of Box and Draper (J. Amer. Statist. Assoc. 54 (1959) 622) are sometimes, but not always, necessary depending on the order of the polynomial model and the number of factors.