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Setting up a Response surface test (RSM)

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Setting up a Response surface test (RSM)

Full version of Develve
For commercial use
Main Help

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 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 RSM 3D

Why use a RSM test setup

  1. To find optimal settings
  2. To find more robust settings
  3. 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?

  1. The output can be measured, in continuous a scale (Ratio or Interval)!
  2. The influencing factors are known
  3. Important Factors can be controlled (variated on a desired level or fixed on a constant level)
  4. Keep the RSM simple as possible
  5. 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:
Factor Levels Scale
Power1, 2, 9, 30, 40 60 100WattRatio
Setting on the dimmer0%…100%Ratio
Input current0...230VRatio
Color of glassClear, White, Silver, Green, RedOrdinal
Type of lampLight bulb, LED, TLOrdinal
ArmatureSilver reflector, White reflector, No reflectorOrdinal
Shape of lampBall, Cone, CandleNominal

Settings of levels

  1. Try to chose realistic values for the levels (not impractical high or low)
  2. Avoid impossible combinations of the levels with other factors in the experiment
  3. The Factor must have a continuous scale
    • Color of glass , Type of lamp, Armature, Shape of lamp are not suitable!
  4. The
    point is the average of the min and max value of the levels
Good distribution of the Levels Wrong distribution of the levels

The test Arrays

For a RSM there are various types of Arrays each with its own pros and cons. See table below.
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

RMS Arrays compared with Full factorial and Orthogonal

The arrays designed for RSM are Rotatable around their Center point and symmetrical, this is not the case with Orthogonal Array and Factorial Array. Rotatable is desired for the quadratic fitting of the model.
Full Factorial Array Orthogonal Array
Rotatable No No
Symmetrical Yes No
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.

Array selection

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.
Factors Box-Behnken Central Composite
Test runs Test runs Distance
2 13 1.414
3 15 20 1.682
4 26 30 2.000
5 45 52 2.378
6 54 91 2.828

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).
Box-Behnken design Central Composite design
No extreme

Modifications of the Central Composite Array

There are 2 modifications of the standard CCC array to eliminate the
point outside
the maximum setting.
Standard CCC CCI CCF
Circumscribed Inscribed Face centered
Best fitting The extreme settings are extrapolated Poor Quadratic fitting
• 5 Levels
• 2 Levels outside the investigated limits
• 5 Levels
• All levels are within the investigated limits
• 3 Levels
• All levels are within the investigated limits
Not Rotatable

Select array

Use coded array!

Use the coded array and don't change the coded values for the actual levels!
Coded array Do not use a uncoded array!
To see the not coded axles put the actual data in the Response Surface table
Example Coded and not Coded
As visible in the below graphs in the non coded result influence of the quadratic factors is gone. For this a zero crossing is needed and the minimum and maximum of all the factors must be the same.
Coded result Data file Not coded result Data file Coded result with Non coded in table

Building and testing the samples

Now build the samples according the array.

Some important points

Add data

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

See Data file.

Analyzing the result

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.

Confirmation Run

After defining the optimum settings build samples according these settings to confirm the result.