Estimating selected interactions
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Taguchi designs are primarily intended to study main effects of factors. Occasionally, you may want to study some of the two-way interactions. Some of the Taguchi designs (orthogonal arrays) allow the study of a limited number of two-way interactions. This usually requires that you leave some columns out of the array by not assigning factors to them. Some of the array columns are confounded with interactions between other array columns. Confounding means that the factor effect is blended with the interaction effect, thus they cannot be evaluated separately.

You can ask Minitab to automatically assign factors to array columns in a way that avoids confounding. Or, if you know exactly what design you want and know the columns of the full array that correspond to the design, you can assign factors to array columns yourself. Assigning factors to columns of the array does not change how the design appears in the worksheet. For example, if you assigned Factor A to Column 3 of the array and Factor B to Column 2 of the array, Factor A would still appear in Column 1 in the worksheet and Factor B would still appear in Column 2 in the worksheet.

Interaction tables show confounded columns, which can help you to assign factors to array columns. For interaction tables for Minitab's catalog of Taguchi designs (orthogonal arrays), see Interaction tables. The interaction table for the L8 (2**7) array is shown below.

 

1

2

3

4

5

6

7

1

 

3

2

5

4

7

6

2

 

 

1

6

7

4

5

3

 

 

 

7

6

5

4

4

 

 

 

 

1

2

3

5

 

 

 

 

 

3

2

6

 

 

 

 

 

 

1

The columns and rows represent the column numbers of the Taguchi design (orthogonal array). Each table cell contains the interactions confounded for the two columns of the orthogonal array.

For example, the entry in cell (1, 2) is 3. This means that the interaction between columns 1 and 2 is confounded with column 3. Thus, if you assigned factors A, B, and C to columns 1, 2, and 3, you could not study the AB interaction independently of factor C. If you suspect that there is a substantial interaction between A and B, you should not assign any factors to column 3. Similarly, the column 1 and 3 interaction is confounded with column 2, and the column 2 and 3 interaction is confounded with column 1.