# Example of creating a 2-level fractional factorial design with blocks

A scientist studies the effects of 5 input variables on the impurity of a vaccine. Each batch of vaccine contains the raw material for 4 tubes of the vaccine to use in the experiment. The scientist plans to use a 16-run experiment, thus the scientist needs 4 batches of vaccine. To account for differences in the 4 batches, the scientist uses 4 blocks. Each factor has 2 levels, so the scientist uses Create 2-Level Factorial Design (Default Generators) to create a 5-factor, 16-run experiment, with 4 blocks.

1. Choose Stat > DOE > Factorial > Create Factorial Design.
2. From Number of factors, select 5.
3. Click Designs.
4. Select the 1/2 fraction design.
5. In Number of blocks, choose 4.
6. Click OK in each dialog box.

## Interpret the results

The first table gives a summary of the design. After blocking, this is a resolution III design because the design aliases blocks with 2-way interactions.

The Minitab worksheet below shows the settings for each factor for only the first 6 of the 16 experimental runs. The design was created using the default settings of −1 for low and 1 for high, although it is recommended that you enter actual settings for each level. The scientist uses the order that is shown to determine the settings for each run. The first four runs of the experiment use raw material from the same batch (Block 1). In the first run of the experiment, Factor A is high, Factor B is high, Factor C is high, Factor D is low, and Factor E is low.

###### Note

Minitab randomizes the design by default, so if you replicate this example your run order will not match the order in the example output.

### Fractional Factorial Design

Design Summary Factors: 5 Base Design: 5, 16 Resolution with blocks: III Runs: 16 Replicates: 1 Fraction: 1/2 Blocks: 4 Center pts (total): 0
* NOTE * Blocks are confounded with two-way interactions. Design Generators: E = ABCD Block Generators: AB, AC Alias Structure I + ABCDE Blk1 = AB + CDE Blk2 = AC + BDE Blk3 = BC + ADE A + BCDE B + ACDE C + ABDE D + ABCE E + ABCD AD + BCE AE + BCD BD + ACE BE + ACD CD + ABE CE + ABD DE + ABC
C1 C2 C3 C4 C5 C6 C7 C8 C9
StdOrder RunOrder CenterPt Blocks A B C D E
4 1 1 1 1 1 1 −1 −1
2 2 1 1 −1 −1 1 −1 −1
8 3 1 1 1 1 −1 1 −1
1 4 1 1 −1 −1 −1 −1 1
7 5 1 2 1 1 1 1 1
12 6 1 2 −1 −1 1 1 1
... ... ... ... ... ... ... ... ...
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