Plackett-Burman Screening Design
Also known as: PB design, PB screening, Plackett-Burman Tarama Deseni
The Plackett-Burman design is a two-level orthogonal screening design introduced by R.L. Plackett and J.P. Burman in 1946 that allows researchers to estimate the main effect of each factor independently using the smallest possible number of experimental runs. Run counts are always multiples of four, making it exceptionally economical for studies with many candidate factors.
Key highlights
- Highly economical: N runs screen up to N−1 factors, so a 12-run design handles up to 11 factors.
- Fully orthogonal main-effect estimates mean no collinearity and no ambiguity in attributing effects.
- Run counts scale in multiples of four, giving flexibility to match practical experimental constraints.
- Backed by the original 1946 paper and decades of application in pharmaceutical, chemical, and manufacturing research.
Intuition
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How it works
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When to use it
Use a Plackett-Burman design when you need to screen a large number of factors — typically five or more — and you want to identify the few that are truly influential while using the minimum number of experimental runs. Three conditions should hold: the response is approximately normally distributed for a given set of conditions, two-factor and higher-order interactions can be assumed negligible relative to main effects at this early screening stage, and the factors can each be set reliably at two discrete levels. If strong interactions are suspected, a full or fractional factorial design is more appropriate. After screening, significant factors should be studied further with a response-surface methodology such as the central composite design.
Strengths & limitations
- Highly economical: N runs screen up to N−1 factors, so a 12-run design handles up to 11 factors.
- Fully orthogonal main-effect estimates mean no collinearity and no ambiguity in attributing effects.
- Run counts scale in multiples of four, giving flexibility to match practical experimental constraints.
- Backed by the original 1946 paper and decades of application in pharmaceutical, chemical, and manufacturing research.
- Main effects are partially aliased with two-factor interactions in non-regular Plackett-Burman designs, so interactions cannot be estimated or cleanly separated.
- The design supports main-effect screening only; curvature and interaction modelling require a follow-up design.
- With very few runs, the residual degrees of freedom can be small, reducing the power to detect modest effects.
- Factors must be controllable at exactly two levels, ruling out naturally continuous or ordered multi-level factors without discretisation.
Common pitfalls
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Applications
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Frequently asked
How many factors can a 12-run Plackett-Burman design screen?
A 12-run Plackett-Burman design can screen up to 11 factors. In general, a design with N runs screens up to N−1 factors, because one degree of freedom is used for the overall mean. Common sizes are 8-run (7 factors), 12-run (11 factors), 16-run (15 factors), and 20-run (19 factors).
Why can't two-factor interactions be estimated?
In non-regular Plackett-Burman designs, every main effect is partially aliased with every two-factor interaction — no pair of columns is completely independent of any cross-product column. This 'complex aliasing' means that if a large interaction exists, the estimate for the corresponding main effect will be biased. For this reason, the design is appropriate only when interactions can be assumed small at the screening stage.
What should I do after identifying the important factors?
Plackett-Burman screening is explicitly the first phase of a two-phase strategy. Once you know which two to five factors are active, run a follow-up experiment — such as a central composite design or Box-Behnken design — to model curvature and interactions among those important factors and find the optimal operating conditions.
Is the Plackett-Burman design the same as a fractional factorial?
They are related but different. Fractional factorials are subsets of full 2^k factorials and produce regular designs with clearly defined aliasing patterns. Plackett-Burman designs include non-regular designs (e.g. the 12-run design) where aliasing is more complex and spread across many terms. When N is a power of 2, the Plackett-Burman design coincides with a resolution-III fractional factorial.
Sources
- 1.Plackett, R.L. & Burman, J.P. (1946). The Design of Optimum Multifactorial Experiments. Biometrika, 33(4), 305–325.
- 2.Montgomery, D.C. (2017). Design and Analysis of Experiments (9th ed.). Wiley.ISBN 978-1119492443
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Cite this page
ScholarGate. (2026, June 1). Plackett-Burman Design. ScholarGate. https://scholargate.app/experimental-design/plackett-burman