Constructing response surface designs with orthogonal quadratic effects using cyclic generators

摘要

The central composite designs (CCDs [1]) and small composite designs (SCDs [2,3]) are designs for sequential experimentation for response surface optimization. The CCDs for fitting the second-order response surface require a 2-level factorial or a resolution V fraction at the first stage (screening stage). The SCDs developed for fitting the same model require many fewer runs at the first stage as they only require a resolution III* fraction. This paper introduces an algorithm which can augment a 2-level first-order design with additional 3-level runs to form a second-order design. This algorithm does not require the 2-level first-order design in stage I to be a resolution V or resolution III* fraction. These augmented runs are made up of circulant matrices. Since CCDs and SCDs are special cases of the designs constructed this way, we call the new designs generalized composite designs or GCDs. Like CCDs and SCDs, GCDs have orthogonal quadratic effects. GCDs can often be found with numbers of runs between those of SCDs and CCDs. This is useful because SCDs often have poorly estimated parameters and CCDs often require substantially more runs than required to fit a full quadratic model.