Optimal Central Composite Designs for Fitting Second Order Response Surface Linear Regression Models

The central composite design (CCD) is a design widely used for estimating second order response surfaces. It is perhaps the most popular class of second order designs. Since introduced by Box and Wilson (1951), the CCD has been studied and used by many researchers.

This paper deals with optimal CCDs under several design criteria for fitting second order response surface regression models. In Section 2, results on optimal CCDs under the criteria of orthogonality, rotatability and slope rotatability are reviewed. In Section 3, we discuss optimal CCDs under alphabetic design optimality criteria. The appropriate values of ? which minimize the squared bias when the true model is of third order are suggested in Section 4. Finally, in Section 5, considering all possible design criteria, suitable values of ? for the practical design purpose are recommended.