A response surface design is a set of advanced design of experiments (DOE) techniques that help you better understand and optimize your response. Response surface design methodology is often used to refine models after you have determined important factors using screening designs or factorial designs; especially if you suspect curvature in the response surface.
For example, you would like to determine the best conditions for injection-molding a plastic part. You first used a screening or factorial experiment to determine the significant factors (temperature, pressure, cooling rate). You can use a response surface designed experiment to determine the optimal settings for each factor.
Central composite designs are especially useful in sequential experiments because you can often build on previous factorial experiments by adding axial and center points.
For example, you would like to determine the best conditions for injection-molding a plastic part. You first run a factorial experiment and determine the significant factors: temperature (levels set at 190° and 210°) and pressure (levels set at 50MPa and 100MPa). If the factorial design detects curvature, you can use a response surface designed experiment to determine the optimal settings for each factor. The design points for this experiment are below.
|210°, 50MPa||214.1°, 75MPa (axial point)||210°, 100MPa|
|200°, 39.6MPa (axial point)||200°, 110.4MPa (axial point)|
|190°, 50MPa||185.9°, 75MPa (axial point)||190°, 100MPa|
Face centered designs are a type of central composite design with an alpha of 1. In this design the axial points are at the center of each face of the factorial space, so levels = + 1. This variety of design requires 3 levels of each factor. Augmenting an existing factorial or resolution V design with appropriate axial points can also produce this design.
A Box-Behnken design is a type of response surface design that does not contain an embedded factorial or fractional factorial design.
Box-Behnken designs have treatment combinations that are at the midpoints of the edges of the experimental space and require at least three continuous factors. The following figure shows a three-factor Box-Behnken design. Points on the diagram represent the experimental runs that are done:
These designs allow efficient estimation of the first- and second-order coefficients. Because Box-Behnken designs often have fewer design points, they can be less expensive to do than central composite designs with the same number of factors. However, because they do not have an embedded factorial design, they are not suited for sequential experiments.
Box-Behnken designs can also prove useful if you know the safe operating zone for your process. Central composite designs usually have axial points outside the "cube." These points may not be in the region of interest, or may be impossible to conduct because they are beyond safe operating limits. Box-Behnken designs do not have axial points, thus, you can be sure that all design points fall within your safe operating zone. Box-Behnken designs also ensure that all factors are not set at their high levels at the same time.