Plackett-Burman Design

Plackett-Burman designs are fractional factorial designs used primarily for screening a large number of factors to identify the most significant ones. They allow efficient experimentation with fewer runs than full factorial designs.

• Resolution III: Main effects are confounded with two-factor interactions.
• Assumption: Interaction effects are negligible compared to main effects.
• Runs: The number of runs is a multiple of four (e.g., 8, 12, 16, 20).

Structure of the Design Matrix

A Plackett-Burman matrix for 12 runs (screening 11 factors + dummy) looks like:

Run  F1  F2  F3  F4  F5  F6  F7  F8  F9  F10 F11  Dummy
1     +   +   +   -   +   -   -   -   +    -   -    +
2     -   +   +   +   -   +   -   -   -    +   -    +
...   ...
12    +   -   +   +   +   -   +   -   -    -   +    -

‘+’ indicates the high level of a factor and ‘-’ indicates the low level.

4. Steps to Construct a Plackett-Burman Design

1. Decide on the number of factors (k) to screen.
2. Select the smallest Plackett-Burman matrix with ≥ k + 1 columns (include one dummy column if necessary).
3. Assign factors to columns randomly.
4. Set factor levels: high (+1) and low (−1).
5. Conduct experiments in the order of runs.
6. Analyze main effects: calculate the difference in mean response between high and low levels for each factor.

When to Use a Plackett–Burman Design

Early-stage experimentation, when you have many potential factors but need to quickly identify the few that matter most.

Many Factors, Limited Runs

If you have, for example, 11 or 19 factors but still want to keep the total number of runs under 25, a Plackett–Burman design offers an efficient solution.

Desire for a Nonregular Aliasing Structure

Through partial aliasing, the influence of any two‐factor interaction is distributed across multiple main‐effect estimates. This spreading of interaction effects can, on average, reduce the bias in individual main‐effect estimates.

One‐Time Screening

If you don’t plan to add more factors later or to expand the design to higher resolutions, note that Plackett–Burman plans are static: you cannot turn a 12‐run plan into a 24‐run plan without completely re‐planning the experiment.

Limitations

Because of resolution III, any non-negligible two-factor interactions will bias your main-effect estimates.

Only two levels per factor—no ability to detect curvature.

Do not use for definitive optimization; follow-up with a higher-resolution design (e.g.\ a Central-Composite or Box–Behnken) once key factors are known.