# What is a design generator?

The design generators determine how the fraction (or subset of runs) is selected from the full set of runs in a fractional factorial design.

For example, to construct a 1/2 fraction, 4-factor design using the design generator D=ABC, Minitab does the following:
1. Construct the full 3-factor design where –1 and +1 represent the low and high factor levels, respectively.
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
2. Generate the runs for factor D by multiplying the settings for factors A, B, and C together. For example, the setting for factor D for the first run is –1 * –1 * –1 = –1 (the low setting).
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.

## Choose a different design generator

You can use different design generators by choosing 2-level factorial (specify generators). To open 2-level factorial (specify generators), choose Stat > DOE > Factorial > Create Factorial Design.

### To determine which design to 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.

### Example of using a different design generator

Suppose you want a 2^(5-2) design that uses design generators D = AB and E = BC (instead of D = AB and E = AC).
1. Choose Stat > DOE > Factorial > Create Factorial Design.
2. Choose 2-level factorial (specify generators).
3. From Number of factors, choose 3.
4. Click Designs. In the field at the top, choose Full factorial.
5. Click Generators. In Add factors to the base design by listing their generators (e.g. F=ABC), enter D = AB E = BC.
6. Click OK in each dialog box.