Response Surface Designs

Experimenters may wonder why they should choose one design over another. Below is a summary of the purpose for each response surface design type. Experimenters will generally use Central Composite, Box-Behnken, or Optimal designs.

Randomized

Central Composite designs (CCD) are based on 2-level factorial designs, augmented with center and axial points to fit quadratic models. Regular CCD’s have 5 levels for each factor. This can be modified by choosing an axial distance of 1.0 creating a Face-Centered, Central Composite design which has only 3 levels per factor. The center points are replicated to provide excellent prediction capability near the center of the factor space. A central composite design is a common augment from the two-level factorial design. Categoric factors can be added to these designs, however, the design is duplicated for every categoric treatment combination.

Box-Behnken designs always have three levels for each factor and are purpose built to fit a quadratic model. The Box-Behnken design does not have runs at the extreme combinations of all the factors, but compensates by having better prediction precision in the center of the factor space. While a run or two can be botched in these designs the accuracy of the observations in the remaining runs is critical to the dependability of the model. Categoric factors can be added to these designs, however, the design is duplicated for every categoric treatment combination.

One Factor designs are used when there is only one continuous factor in the experiment. They create evenly spaced runs across the factor range. Categoric factors can be added to these designs, however, the design is duplicated for every categoric treatment combination.

Miscellaneous contains a collection of designs are not recommended but available for use. These designs include the 3-level Factorial, Hybrid, Pentagonal, and Hexagonal designs. These designs have limitations and/or inferior properties to Central Composite, Box-Behnken and Optimal designs.

Supersaturated

Supersaturated designs have fewer rows in the design than terms in the design model. The extra step of choosing a subset of the full model must be taken before analysis. Terms in any subset model may be partially or completely aliased.

Definitive Screen (5 to 30 factors) – These screening designs allow for three-level numeric factors and two-level categoric factors. This structure allows clean estimates of the main effects and detection of second-order effects.

Split-Plot

Split-plot designs allow some of the factors to be hard to change (HTC). This restricts the randomization for these factors; they will be held constant for a group of runs during the experiment. The cost for restricting the randomization is lower precision for estimates coming from HTC factors. Only restrict the randomization if it is absolutely necessary.

Split-Plot Central Composite designs are similar to their randomized cousins in that they are purpose built to fit and test quadratic models. The HTC factors require modifications to the basic structure of a CCD, but the resulting designs provide robust tests for the quadratic model and very good statistical properties. However, maintaining the central composite structure while restricting the randomization requires many runs. If the number of runs is too large, consider split-plot optimal designs.

See also: Custom Designs for both randomized and split-plot type designs.