A note on small composite designs for sequential experimentation

The recommended approach to experiments using the response surface methodology is sequential, i.e., experiments should be conducted iteratively. Al the first stage, a first-order design, usually an orthogonal two-level design (with a few center points) is used to find out whether the current region is appropriate and to allow the estimation of main effects (and possibly some interactions). The design at the first stage is then augmented with more runs in the second stage. The combined design allows the estimation of the remaining interaction and quadratic effects. Some well-known classes of designs which allow such a sequential experimentation are the central composite designs, the small composite designs and the augmented-pair designs. This paper reviews these designs and introduces a new algorithm which is able to augment any first order design with additional design points to form a good design for a second-order model.