Measuring and data collection

Choosing a statistical test

Minimum sample size

Not normally distributed

Statistical process control (SPC)

How to conduct a DOE

Setting up a Response surface test (RSM)

For commercial use

75 EURO

RSM Array

• Rotatable

• Center point

Formula

Design of experiments (DOE)

For commercial use

75 EURO

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 |

- To find optimal settings
- To find more robust settings
- Understand how factors interact with each other

- 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!

But the bigness of a lamp can have more influences from different factors with it own levels:

Factor | Levels | Scale |

Power | 1, 2, 9, 30, 40 60 100Watt | Ratio |

Setting on the dimmer | 0%…100% | Ratio |

Input current | 0...230V | Ratio |

Color of glass | Clear, White, Silver, Green, Red | Ordinal |

Type of lamp | Light bulb, LED, TL | Ordinal |

Armature | Silver reflector, White reflector, No reflector | Ordinal |

Shape of lamp | Ball, Cone, Candle | Nominal |

- Try to chose realistic values for the levels (not impractical high or low)
- Avoid impossible combinations of the levels with other factors in the experiment
- The Factor must have a continuous scale
- Color of glass , Type of lamp, Armature, Shape of lamp are
**not**suitable!

- Color of glass , Type of lamp, Armature, Shape of lamp are
- The Centerpoint is the average of the min and max value of the levels

Good distribution of the Levels | Wrong distribution of the levels |

Compared | ||

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 |

Compared | ||

Full Factorial Array | Orthogonal Array | |

Rotatable | No | No |

Symmetrical | Yes | No |

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 Circumscribed | |

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 points | Extreme points |

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 • Rotatable | • 5 Levels • All levels are within the investigated limits • Rotatable | • 3 Levels • All levels are within the investigated limits • Not Rotatable |

Coded array | Do not use a uncoded array! |

To see the not coded axles put the actual data in the Response Surface table |

Coded result Data file | Not coded result Data file | Coded result with Non coded in table |

Some important points

- 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.

Now the test results put in the input table

See Data file.

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.

- GreenNot significant
- YellowSignificant

De select all insignificant factors.

By clicking on the graph the calculated result will pop-up with coded input value.

single response 2D graph | 3D response graph |