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 advanced DOE with specially designed arrays for calculating interactions and quadratic responses.
When comparing a standard DOE with a RSM the DOE gives a 2D image of the output of 1 factor, a RSM produces a 3D image of the output of 2 factors in one image.
Standard DOE 2D
Why use a RSM test setup
To find optimal settings
To find more robust settings
Understand how factors interact with each other
What is a Factor
A factor is a input for a experiment that can change the output when variating. Its like a dimmer (a factor) of a lamp when turning the knob the brightness of the lamp changes.
What is important for a successful RSM?
The output can be measured, in continuous a scale (Ratio or Interval)!
The influencing factors are known
Important Factors can be controlled (variated on a desired level or fixed on a constant level)
Keep the RSM simple as possible
DO the Confirmation Run!
The Level of the factor
The level of a factor is the input setting of test. For the lamp dimmer the setting of the dimmer is the level (0%, 25%, 50% ect).
But the bigness of a lamp can have more influences from different factors with it own levels:
A Full Factorial Array can be used for a RSM but compared with a CCC more test runs are needed (Full 27 , CCC 20, BB 15) and the quadratic fitting is poor.
As you can see in a Box-Behnken design there are less data point needed compared with a Central Composite design.
With a Box-Behnken design every factor is having 3 levels compared to Central Composite 5 with 2 circumscribed points with a bigger distance.
Box-Behnken compared with Central Composite design is missing the corner points, it will never occur that all the factors are high or low at the same time (No extreme combinations).
Central Composite design
Modifications of the Central Composite Array
There are 2 modifications of the standard CCC array to eliminate the
Always build and test the complete array.
When adding repetitions it is preferred is not to test replicates on a row (samples with the same setting) but first finish the first replicate then the next. This is to randomize the order to prevent drift over time in the result.
When testing try not to test all factors on the first level than on the second level but try to randomize.
Do not add an extra test in the array except Center points this will create an unbalanced array, and can lead to wrong results.
The test array will be added in the Factorial table.
Now the test results put in the input table
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
Select all the factors with Check All.
De select all insignificant factors.
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.
After defining the optimum settings build samples according these settings to confirm the result.