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The design generators determine how the fraction (or subset of runs) is selected from the full set of runs in a fractional factorial design.
| A | B | C |
|---|---|---|
| –1 | –1 | –1 |
| +1 | –1 | –1 |
| –1 | +1 | –1 |
| +1 | +1 | –1 |
| –1 | –1 | +1 |
| +1 | –1 | +1 |
| –1 | +1 | +1 |
| +1 | +1 | +1 |
| A | B | C | D=ABC |
|---|---|---|---|
| –1 | –1 | –1 | –1 |
| +1 | –1 | –1 | +1 |
| –1 | +1 | –1 | +1 |
| +1 | +1 | –1 | –1 |
| –1 | –1 | +1 | +1 |
| +1 | –1 | +1 | –1 |
| –1 | +1 | +1 | –1 |
| +1 | +1 | +1 | +1 |
Because the settings for factor D are equal to the settings for factor A times the settings for factor B times the settings for factor C, factor D is confounded with the ABC interaction. Because effects that are confounded cannot be estimated separately from each other, design generators should be carefully chosen.
By default, Minitab uses the design generators that create the design with the highest resolution for the number of factors in the design.
You can use different design generators by choosing 2-level factorial (specify generators). To open 2-level factorial (specify generators), choose .
When you use a non-default design generator to create a design, you must start with a base design that has the same number of runs but fewer factors.
For example, say you create a 2^(5-2) design with five factors and eight runs, but change Minitab's default design generators of D=AB and E=AC. To get the correct design, calculate the number of factors in the base design by subtracting the number of design generators from the total number of factors that you want. Then determine which design has the correct number of runs.
For the previous example, five factors minus two generators equals three factors in the base design. A 2^3 full factorial design has the eight runs needed, so that is the design that you can start with.
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