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Response Surface Methodology (RSM)

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Setting up a RSM
RSM Array
Center point

Design of experiments (DOE)

Full version of Develve
For commercial use

Response Surface Methodology is a statistical test setup with more factors on different levels combined in one experiment. It is used when analyzing complex problems with a multiple of influence factors in once including interactions. This is done by using test arrays. A RSM is DOE with specially designed arrays for calculating interactions and quadratic responses.

This document is an introduction of the RSM functionality of Develve for more information how to conduct a RSM see Setting up a Response surface test (RSM).

Select DOE in the statistical mode drop-down menu to start a Design of experiment. The data of the input table is sorted according the factorial table (see example). With this option it is possible to conduct a RSM with various arrays.

For calculating the statistical properties of a data set the data must entered in the input table 1. The data will sorted according the Factorial table 9. and the result will be displayed in the result array 3. and Graph image 2.

9) Factorial table
In this table the coded array is visible. This must be coded and may not be renamed like in a DOE, a RSM always works with coded arrays!


First select a array (DOE => Factorial Array).
Mostly used for the RSM are Box-Behnken and Central Composite (CCD) arrays.

Box-Behnken design Central Composite design
Extreme combinations No Yes
Size of matrix Smaller Bigger
Amount of levels 3 5
No Circumscribed points The Circumscribed point especially
for the bigger arrays are far from
the normal setting

Select array

Add data

The test array will be added in the Factorial table.
Now the test results put in the input table

See Data file.

Select the Response surface box (DOE => Response surface) for the statistical analysis.

In this window you can select the factors to include in the Response surface. Develve will calculate the coefficient of the selected factors and if it is significant. See here for the formula of the calculation.

Colors of the cells

Response Surface Graph

Display the Response Surface Graph by clicking on Graph.

By clicking on the graph the calculated result will pop-up with coded input value.
single response 2D graph 3D response graph
By right click on the graph one of the responses can be displayed in 2 or 3D.

Extrapolation of the result

Without extrapolation With a extrapolation of 2
Be careful with extrapolation of data!