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How to conduct a DOE

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Measuring and data collection
Choosing a statistical test
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Not normally distributed
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How to conduct a DOE
Setting up a Response surface test (RSM)


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Design of experiments (DOE)
How to conduct a DOE
Factorial Array
Edit factorial array
Rename Levels of DOE Factors
Interactions
Adding repetitions
Block Levels
Sort data in subgroups
Anova DOE
Confirmation run
Response graphs
Response surface methodology


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A DOE (Design Of Experiments) is structured, planned method, which is used to find the relationship between different factors that affect a tested subject and the different outputs. This is done with multiple factors on various levels combined in one experiment. Instead of testing each factor individually in a DOE multiple factors are variated at once to reduce the amount of test with the possibility to analyze interactions between factors.

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.

Why use a complex DOE instead of the standard approach?

With the classical approach only one input factor is changed to determine the influence of it on the output with a DOE more than one input is changed to see the influence of multiple factors on the output.

So the answer is to reduce the amount of experiments.
In other words reduce cost and time.

As visible in the below table with a classical approach with 16 tests 1 factor is examined and with a DOE approach 4. With an other matrix this could be even more!
Classical DOE
Test Factor 1 Factor 2 Factor 3 Factor 4
1HighHighHighHighHigh
2HighHighHighHighLow
3HighHighHighLowHigh
4HighHighHighLowLow
5HighHighLowHighHigh
6HighHighLowHighLow
7HighHighLowLowHigh
8HighHighLowLowLow
9LowLowHighHighHigh
10LowLowHighHighLow
11LowLowHighLowHigh
12LowLowHighLowLow
13LowLowLowHighHigh
14LowLowLowHighLow
15LowLowLowLowHigh
16LowLowLowLowLow
But this is not all, with a DOE it is possible to investigate interactions and create response surface graphs. About these later more.

Of course it is possible to do the classical test with only 1 High and 1 Low test but then the statistical power is lower as with the DOE approach.

With more than 2 factors it is wise to use a DOE approach.

What is important for a successful DOE?

  1. The output can be measured, preferable in continuous scale!!
  2. The influencing factors are known
  3. Important Factors can be controlled (variated on a desired level or fixed on a constant level)
  4. Try to control Noise (uncontrollable factors) or record them (Environment temperature, Air pressure, different operators, ect)
  5. Keep the DOE simple as possible
  6. 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
Shape of lampBall, Cone, Candle
Power1, 2, 9, 30, 40 60 100Watt
Setting on the dimmer0%…100%
Input current0...230V
Color of glassClear, White, Silver, Green, Red
Type of lampLight bulb, LED, TL
ArmatureSilver reflector, White reflector, No reflector

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

The test Arrays

For a DOE there are various types of Arrays each with it own pros and cons. See table below.
Name Full factorial Response surface Orthogonal
TypeFull Factorial ArrayBox-Behnken designOrthogonal Array
Central Composite designPlackett–Burman Array
Amount of testsHigh (all combinations)MediumSmall
No interactions
UsageSimpleMore complexSimple no interactions
Complex with interactions
InteractionsAll interactionsFirst level interactionsYes possible
Response Surface designNoYesNo
When starting for the first time with a DOE start with a simple and small DOE

Amount of test with different arrays

There are various types of arrays the simple one is the Full Factorial array, this array consisted of all the combinations of the levels. The amount of test with a Full Factorial is high, therefor there are arrays designed to reduce this.
Test Full Factorial Array Box-Behnken design BB3 Orthogonal Array L9
Factor 1Factor 2Factor 3Factor 1Factor 2Factor 3Factor 1Factor 2Factor 3Factor 4
1-1-1-1000-1-1-1-1
20-1-1-1-10-1000
31-1-11-10-1111
4-10-1-1100-101
500-1110001-1
610-10-1-101-10
7-11-10001-110
801-10-1110-11
911-101-1110-1
10-1-10011
110-10-10-1
121-10-101
13-10010-1
14000101
15100000
16-110
17010
18110
19-1-11
200-11
211-11
22-101
23001
24101
25-111
26011
27111
As visible for the orthogonal array the smallest amount of test is needed. With this small amount of test even 4 factors can be tested on 3 levels (-1,0 and 1) for the other arrays types only 3 factors can be tested on 3 levels!
Of course this small amount of test is not for free.... With the L9 orthogonal array interactions and Response Surface can't be calculated and the power is lower. The power can easily increased by adding repetitions.

Array selection

The choice between arrays for a DOE is between Full Factorial and a Fractional array (Orthogonal) if you not want to draw a Response surface. Looking to the table below it is clear that quite fast a Full Factorial array is not economical.
2 Levels 3 Levels
Factors Full Factorial Orthogonal Full Factorial Orthogonal Box-Behnken
Test Runs Test Runs Test Runs Test Runs Test Runs
2 4 4 9 9
3 8 4 27 9 16
4 16 8 81 9 26
5 32 8 243 18 45
6 64 8 729 18 54
7 128 8 2187 18
8 256 12 6561 27

Above 4 factors with 2 levels go for a Orthogonal array, and above 3 factors with 3 levels the advise is to go for an Orthogonal array. If interactions are needed a Box-Behnken design or Central Composite design. When building the samples for an Orthogonal array a reduced amount of different samples need to be build. If the power is to low the array can easily be replicated to increase the sample size.

Interactions

A interaction is when the result is not the sum of two factors. With an interaction it can occur that the result of the to factors is lower or higher as the sum of the result.
When using an Orthogonal array interactions are not included. The interactions have to be included in the array this can be calculated with Develve see.
Be careful with adding interactions in a design:
Interaction
with the typical crossing line
No interaction

2 or 3 level design

2 Levels 3 Levels
Amount of testsLowHigher
Non linear response
No

Yes
There are Orthogonal arrays with 2 or 3 levels and even with different amount of levels in one array. With Orthogonal Arrays it is possible to combining columns to get factors with more levels. When generating Full Factorial array for each factor an dedicated amount of levels can be chosen.

Example without interactions

We want to create a DOE with the following factors
Factor Level 1 Level 2
Size10mm20mm
Weight1kg10kg
ColorWhiteBlack
There are 3 factors and in a L4 is space for 3 factors.

Example with interactions

We want to create a DOE with the following factors
Factor Level 1 Level 2
Size10mm20mm
Weight1kg10kg
ColorWhiteBlack
Interaction 1SizeWeight
Interaction 2SizeColor
Interaction 3WeightColor
There are 3 factors, in a L4 array is space for 3 Factors on 2 levels but we also want to include interactions so a bigger array is needed L8 is space for 7 factors.
Open this array.

Now add the first interaction. Column C is now used for the interaction calculation.The second interaction. Column E is also used for an interaction calculation.
The third interaction. Column F is now also used for a interaction calculation.The name of the factors and levels are added.
With this array all the factors and first order interaction can be tested. The not used columns can be removed (C, E, F and G).
As you can see the result is the same as a Full factorial array this is because all the interactions between the factors are tested.

Building and testing the samples

Now build the samples according the array.
Fist sample 10mm, 1kg and white etc.

Some important points

Analyzing the result

Put the measurement data in the input table. In this case there is one replicate. See sort data in subgroups for how it is calculated.

Data file
Looking to the data

Anova DOE

To check on significance influence of each factor in the DOE. If a factor is not significant it can bee pooled, and the influence of the non pooled factors is getting bigger.

Weight and color are not significant.

After pooling Color (the least significant factor) and Weight are still not significant.

Confirmation Run

In the Anova Dialog the optimal setting can selected in the column Level confirmation run. To confirm output (14.43) of the DOE build samples according these settings!

When a interaction is significant only set the level of the interaction do not set them individual. If you do both you set the influence of the factor twice!