# Choosing the Best Design for Process Optimization

Shari on Aug. 29, 2017

Ever wonder what the difference is between the various response surface method (RSM) optimization design options? To help you choose the best design for your experiment, I’ve put together a list of things you should know about each of the three primary response surface designs—Central Composite, Box-Behnken, and Optimal.

Central Composite Design (CCD)

• Developed for estimating a quadratic model
• Created from a two-level factorial design, and augmented with center points and axial points
• Relatively insensitive to missing data
• Features five levels for each factor (Note: The number of levels can be reduced by choosing alpha=1.0, a face-centered CCD which has only three levels for each factor.)
• Provides excellent prediction capability near the center (bullseye) of the design space

Box-Behnken Design (BBD)

• Created for estimating a quadratic model
• Requires only three levels for each factor
• Requires specific positioning of design points
• Provides strong coefficient estimates near the center of the design space, but falls short at the corners of the cube (no design points there)
• BBD vs CCD: If you end up missing any runs, the accuracy of the remaining runs in the BBD becomes critical to the dependability of the model, so go with the more robust CCD if you often lose runs or mismeasure responses.

Optimal Design

• Customize for fitting a linear, quadratic or cubic model (Note: In Design-Expert® software you can change the user preferences to get up to a 6th order model.)
• Produce many levels when augmented as suggested by Design-Expert, but these can be limited by choosing the discrete factor option
• Design points are positioned mathematically according to the number of factors and the desired model, therefore the points are not at any specific positions—they are simply spread out in the design space to meet the optimality criteria, particularly when using the coordinate exchange algorithm
• The default optimality for “I” chooses points to minimize the integral of the prediction variance across the design space, thus providing good response estimation throughout the experimental region.
• Other comments: If you have knowledge of the subject matter, you can edit the desired model by removing the terms that you know are not significant or can't exist. This will decrease the required number of runs. Also, you can also add constraints to your design space, for instance to exclude particular factor combinations that must be avoided, e.g., high-temperature and high time for cooking.

For an in-depth exploration of both factorial and response surface methods, attend Stat-Ease’s Modern DOE for Process Optimization workshop.

Shari Kraber
shari@statease.com