# Plackett-Burman designs

## What is a Plackett-Burman design?

Plackett-Burman designs are usually resolution III, 2-level designs. In a resolution III design, main effects are aliased with 2-way interactions. Therefore, you should only use these designs when you are willing to assume that 2-way interactions are negligible.

Use Plackett-Burman designs to identify the most important factors early in the experimentation phase. Minitab generates designs for up to 47 factors. Each design is based on the number of runs, from 12 to 48, and is always a multiple of 4. The number of factors must be less than the number of runs. For example, a design with 20 runs lets you estimate the main effects for up to 19 factors.

For example, say you are examining the various factors that affect ice cream texture: fat content, pasteurization temperature, homogenization process, mixing speed, draw temperature, emulsifier, stabilizer, and cooling speed. You can use a Plackett-Burman experiment to identify the most important main effects, use fractional or full factorial designs to study them more, then use response surface designs to optimize your process.

After you create the design, conduct the experiment to obtain the response data, and enter the data in the worksheet, you can analyze the design with Stat > DOE > Factorial > Analyze Factorial Design.

## Summary of Plackett-Burman designs

These are the designs up through n = 48, where n is the number of runs. In all cases except n = 28, the design can be specified by a single column. The table below displays the columns that specify the designs. In the table below, only the first column is displayed (written as a row to save space). This column is permuted cyclically to get an (n - 1) x (n - 1) matrix. Then a last row of all minus signs is added. For n = 28, the design starts with the first 9 rows. These are then split into 3 blocks of 9 columns each. Then the 3 blocks are permuted (rowwise) cyclically and a last column of all minus signs is added to get the full design.

For 12, 20, and 24-run designs, each main effect gets partially confounded with more than one 2-way interaction.

Each design can have up to k = (n - 1) factors. If you specify a k that is less than (n - 1), only the first k columns are used.

###### Note

Plackett-Burman designs with 8 or 16 runs are not available in Create Factorial Design because each has a corresponding 2-level factorial design with an equal or better resolution. To open Create Factorial Design, go to Stat > DOE > Factorial > Create Factorial Design.

12 Runs
+ + - + + + - - - + -
20 Runs
+ + - - + + + + - + - + - - - - + + -
24 Runs
+ + + + + - + - + + - - + + - - + - + - - - -
28 Runs

+ - + + + + - - - - + - - - + - - + + + - + - + + - +

+ + - + + + - - - - - + + - - + - - - + + + + - + + -

- + + + + + - - - + - - - + - - + - + - + - + + - + +

- - - + - + + + + - - + - + - - - + + - + + + - + - +

- - - + + - + + + + - - - - + + - - + + - - + + + + -

- - - - + + + + + - + - + - - - + - - + + + - + - + +

+ + + - - - + - + - - + - - + - + - + - + + - + + + -

+ + + - - - + + - + - - + - - - - + + + - + + - - + +

+ + + - - - - + + - + - - + - + - - - + + - + + + - +

32 Runs
- - - - + - + - + + + - + + - - - + + + + + - - + + - + - - +
36 Runs
- + - + + + - - - + + + + + - + + + - - + - - - - + - + - + + - - + -
40 Runs (derived by duplicating the 20 run design)
+ + - - + + + + - + - + - - - - + + - + + - - + + + + - + - + - - - - + + -
44 Runs
+ + - - + - + - - + + + - + + + + + - - - + - + + + - - - - - + - - - + +- + - + + -
48 Runs
+ + + + + - + + + + - - + - + - + + + - - + - - + + - + + - - - + - + - + + - - - - + - - - -
By using this site you agree to the use of cookies for analytics and personalized content.  Read our policy