Create Response Surface Design

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.

The difference between a response surface equation and the equation for a factorial design is the addition of the squared (or quadratic) terms that lets you model curvature in the response, making them useful for:

Understanding or mapping a region of a response surface. Response surface equations model how changes in variables affect a response of interest.
Finding the levels of variables that optimize a response.
Selecting the operating conditions to meet specifications.

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.

Perform the analysis

Complete the following steps to specify the design.

Enter the name of your response variable: The worksheet includes a column with this name where you enter the data from the experiment.
Table of factors: Under Name, enter a descriptive name for each factor.; Specify whether each factor is continuous or categorical. For continuous factors, enter numbers. Enter the lower number for the study in the Low column. For example, to study the temperatures 30 and 40, enter 30 in the Low column and 40 in the High column.; For any categorical factors, enter labels for the levels. Labels can be numbers or text. If you have a text factor and the levels have no natural order, you can specify the levels in any order.
Number of replicates: Enter how many times to perform each experimental run that is in the base design. Usually, you consider the available resources and the purpose of your design when you select the number of replicates. You can add replicates to your design later with Stat > DOE > Modify Design. For more information on replicates, go to Replicates and repeats in designed experiments.

Example

A scientist wants to conduct an experiment to maximize crystal growth. Previous research has determined that catalyst exposure time, catalyst percentage, and temperature explain much of the variability in crystal growth.

Choose Stat > DOE > Quick Designs.
Select Select a Three-Factor Design.
Select Create an experiment with two or three continuous factors. Select OK.
Select Estimate main, interaction and quadratic effects. Select OK.
In the new dialog, in Enter the name of your response variable, enter Growth.

Complete the table with the following settings:

Name	Type	Low	High
Catalyst exposure time	Continuous	12	36
Catalyst percentage	Continuous	2	10
Temperature	Continuous	20	45

In Number of replicates, select None. Select OK.

The design summary table shows that the design has 20 base runs. The worksheet contains the 20 runs in run order, which is random.