Dummy treatments for Taguchi designs

A useful technique for customizing Taguchi designs is the use of "dummy treatments". You can create a dummy treatment in Minitab by repeating levels for a factor if there are at least two different levels.

Run A B C D
1 1 1 1 1
2 1 2 2 2
3 1 3 3 3
4 2 1 2 3
5 2 2 3 1
6 2 3 1 2
7 3 1 3 2
8 3 2 1 3
9 3 3 2 1
L9 (34) array
Run A B C D
1 1 1 1 1
2 1 2 2 2
3 1 3 3 3
4 2 1 2 3
5 2 2 3 1
6 2 3 1 2
7 1 1 3 2
8 1 2 1 3
9 1 3 2 1
L9 (34) array, with dummy treatment

For example, if you want to use an L9 (34) array, which has four three-level factors, but you have one factor with only two levels, you can use a dummy treatment.

Factor A has repeated level 1, instead of level 3. This results in an L9 (34) array with one factor at 2 levels and three factors at 3 levels. The array is still orthogonal, although it is not balanced.

L9 (34) array

Run A B C D
1 1 1 1 1
2 1 2 2 2
3 1 3 3 3
4 2 1 2 3
5 2 2 3 1
6 2 3 1 2
7 3 1 3 2
8 3 2 1 3
9 3 3 2 1

L9 (34) array, with dummy treatment

Factor A has repeated level 1, instead of level 3. This results in an L9 (34) array with one factor at 2 levels and three factors at 3 levels. The array is still orthogonal, although it is not balanced.
Run A B C D
1 1 1 1 1
2 1 2 2 2
3 1 3 3 3
4 2 1 2 3
5 2 2 3 1
6 2 3 1 2
7 1 1 3 2
8 1 2 1 3
9 1 3 2 1

When you choose which factor level to use as the dummy treatment, consider the amount of information about the factor level and the availability of experimental resources. For example, if you know more about level 1 than level 2, you may want to choose level 2 as your dummy treatment. Similarly, if level 2 is more expensive than level 1, requiring more resources or time to test, you may want to choose level 1 as your dummy treatment.

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