What is a Plackett-Burman design?
A Plackett-Burman design is a two-level screening design that estimates the main effects of up to N−1 factors in only N experimental runs, where N is a multiple of 4. Introduced by Plackett and Burman in 1946, it is the most run-efficient way to ask one question of many factors at once: which of these actually matter? The famous 12-run design screens as many as 11 factors, each at a low (−) and high (+) level.
A screening design is one built to separate the vital few factors from the trivial many before any optimization begins. Plackett-Burman achieves this by being orthogonal — every factor column is perfectly balanced, with the high and low levels appearing equally often and independently of every other factor. That orthogonality lets each main effect be calculated cleanly, even though many factors share the same handful of runs.
These plackett-burman doe designs sit at the front of the design-of-experiments workflow. They are deliberately economical: by assuming interactions are negligible during screening, they spend every run learning about main effects. For the underlying screening logic and how it connects to fractional designs, see our fractional factorial design guide, which shares the same resolution III foundation.
When to screen (main effects only)
Use a Plackett-Burman design at the very start of a project, when you have a long list of factors and no idea which ones matter. The single goal of screening is to rank factors by main effect and discard the inert ones — not to find the optimum and not to study interactions. That narrowed focus is exactly what buys the run economy.
Screening is the right move when three conditions hold: you have 5 or more factors, you can reasonably assume two-factor interactions are small relative to main effects, and your run budget is tight. If you only have 2–4 factors, skip screening and run a full factorial design instead — it costs little more and gives you every interaction. The trade-off between the two is laid out in our broader DOE for bioprocess optimization guide.
A useful mental model: screening answers "which knobs are connected to the machine?" and optimization answers "where should those knobs be set?" Plackett-Burman is purpose-built for the first question and intentionally bad at the second.
Run counts (multiples of 4)
Plackett-Burman run counts are always multiples of 4, because the designs are constructed from Hadamard matrices that exist only at those orders. A design with N runs handles up to N−1 factors; any columns you do not assign to a real factor become dummy columns that measure pure noise — a free estimate of your error.
| Runs (N) | Max factors (N−1) | Typical use | Spare/dummy columns at k factors |
|---|---|---|---|
| 8 | 7 | Small screen (= a 2⁷⁻⁴ fraction) | 7 − k |
| 12 | 11 | The workhorse screen | 11 − k |
| 16 | 15 | Many factors, more power | 15 − k |
| 20 | 19 | Large factor lists | 19 − k |
| 24 | 23 | Very large screens | 23 − k |
A practical rule of thumb: choose the smallest design whose factor capacity exceeds your factor count by at least 3–4 columns. Those spare columns give you dummy estimates of error, which you need to judge significance. Screening 7 real factors? The 12-run design leaves 4 dummy columns — a comfortable noise estimate.
Lay out a Plackett-Burman screen in seconds
Pick your factors and the free DOE generator builds the balanced screening matrix and randomizes the run order for you.
Plackett-Burman software for media optimization
The single most common application of these designs is media development, and "plackett burman software for media optimization" is exactly what bench scientists search for. Culture media have a dozen or more components — carbon sources, nitrogen sources, phosphate, magnesium, calcium, trace metals, vitamins, buffering agents — and testing them one at a time is hopeless. A Plackett-Burman screen tests them all together.
The standard two-stage recipe is well established in fermentation literature. First, a Plackett-Burman design screens every candidate component, each set to a sensible low and high concentration, to identify the few that significantly change titer or biomass. Second, those significant components advance to a response-surface design (central composite or Box-Behnken) that maps curvature and locates the optimum concentrations. Inert components are simply fixed at their cheaper level or dropped.
This screen-then-optimize sequence routinely lifts product titers by 1.5–3× over an unoptimized base medium while testing a fraction of the combinations a brute-force search would require. It applies equally to microbial fermentation and to mammalian cell culture media, where feed and supplement screening follows the same logic.
Worked 7-factor media screen
Here is a complete 12-run Plackett-Burman screen of seven medium components for a microbial fermentation. The response is product titer (g/L). Each factor is run at a low (−) and high (+) concentration. Columns 8–11 are left unassigned and serve as dummy columns to estimate noise.
| Run | A | B | C | D | E | F | G | Titer (g/L) |
|---|---|---|---|---|---|---|---|---|
| 1 | + | + | − | + | + | + | − | 63 |
| 2 | − | + | + | − | + | + | + | 50 |
| 3 | + | − | + | + | − | + | + | 56 |
| 4 | − | + | − | + | + | − | + | 43 |
| 5 | − | − | + | − | + | + | − | 40 |
| 6 | − | − | − | + | − | + | + | 33 |
| 7 | + | − | − | − | + | − | + | 48 |
| 8 | + | + | − | − | − | + | − | 62 |
| 9 | + | + | + | − | − | − | + | 66 |
| 10 | − | + | + | + | − | − | − | 53 |
| 11 | + | − | + | + | + | − | − | 53 |
| 12 | − | − | − | − | − | − | − | 33 |
Factors: A = glucose, B = yeast extract, C = trace metals, D = MgSO₄, E = CaCl₂, F = thiamine, G = antifoam. The effect of each factor is the mean titer at its high level minus the mean at its low level — the same arithmetic used in any factorial design, applied column by column.
Computing the main effects
Each factor sits at + in 6 runs and at − in 6 runs. The effect is (mean of the six + runs) − (mean of the six − runs).
Glucose (A): + runs are 1,3,7,8,9,11 (63,56,48,62,66,53 → mean 58.0); − runs are 2,4,5,6,10,12 (50,43,40,33,53,33 → mean 42.0).
Effect A = 58.0 − 42.0 = +16.0 g/L.
Yeast extract (B): + runs 1,2,4,8,9,10 (63,50,43,62,66,53 → mean 56.2); − runs 3,5,6,7,11,12 (56,40,33,48,53,33 → mean 43.8).
Effect B = 56.2 − 43.8 = +12.3 g/L.
Trace metals (C): + runs 2,3,5,9,10,11 (50,56,40,66,53,53 → mean 53.0); − runs 1,4,6,7,8,12 (63,43,33,48,62,33 → mean 47.0).
Effect C = 53.0 − 47.0 = +6.0 g/L.
The rest (D–G): running the same arithmetic gives MgSO₄ +0.3, CaCl₂ −1.0, thiamine +1.3, and antifoam −1.3 g/L — all near the noise floor that the dummy columns confirm at roughly ±1.3 g/L.
Conclusion: glucose, yeast extract, and trace metals stand well above the noise and are the critical few. MgSO₄, CaCl₂, thiamine, and antifoam are inert in this region and can be fixed at their cheaper levels. The three winners advance to a response-surface optimization.
Limitations (confounded interactions)
The defining limitation of a Plackett-Burman design is that it cannot estimate interactions. As a resolution III design, every main effect is partially aliased with the two-factor interactions among the other factors. In the non-geometric designs (12, 20, 24 runs) this aliasing is spread thinly across many interactions rather than concentrated on one — a subtle advantage, but it still means a large estimated main effect could in principle be inflated or masked by a real interaction.
This carries two practical risks. First, a factor with no main effect but a strong interaction can be wrongly dismissed as inert. Second, an apparent main effect may partly reflect a hidden interaction. Both are acceptable during screening — the goal is a shortlist, not a final model — but they are the reason you never stop at a Plackett-Burman result. Always confirm the critical few with a design that resolves interactions.
| Design | Levels | Estimates | Interactions? | Best for |
|---|---|---|---|---|
| Plackett-Burman | 2 | Main effects | No (aliased) | Screening 5–11+ factors |
| Fractional factorial | 2 | Main + some 2FI | Some (res IV+) | Screening with key interactions |
| Full factorial | 2 | Main + all interactions | Yes | Optimizing 2–4 factors |
| Central composite / Box-Behnken | 3+ | Main + 2FI + curvature | Yes | Final optimization |
Build it free
You do not need JMP, Minitab, or Design-Expert to run a Plackett-Burman screen. A free screening DOE generator builds the balanced 8-, 12-, 16-, or 20-run design, assigns your factors to columns, leaves the rest as dummy columns, and randomizes the run order — all in the browser, with no install and no licence.
Enter your factor names and their low/high levels, choose the run count that gives you a few spare columns, and the tool returns a randomized run sheet ready for the bench. After the runs, enter the responses to rank the main effects and read off the critical few. It works as a general screening doe generator for any process, not just media. When you are ready to optimize the survivors, the same tool builds the response-surface follow-up.
Generate your Plackett-Burman run sheet now
A free, no-install DOE generator: balanced screening matrix, dummy columns, randomized run order, and main-effect ranking.
Frequently Asked Questions
What is a Plackett-Burman design?
A Plackett-Burman design is a two-level screening design that estimates the main effects of up to N−1 factors in just N runs, where N is a multiple of 4. The 12-run version screens up to 11 factors. It is built to find the critical few factors that drive a response, deliberately sacrificing the ability to estimate interactions so that many factors can be tested cheaply.
How many factors can a Plackett-Burman design screen?
A Plackett-Burman design with N runs screens up to N−1 factors. The 12-run design is the workhorse and screens up to 11 factors; the 20-run screens up to 19, and the 24-run up to 23. Any unused columns become "dummy" columns that estimate the noise floor, which helps you judge which real effects are significant.
What is the difference between Plackett-Burman and fractional factorial designs?
Both are resolution III screening designs, but a fractional factorial run count is a power of 2 (8, 16, 32) with a clean defining relation, while Plackett-Burman run counts are multiples of 4 (12, 20, 24) and have complex partial aliasing — each main effect is partially confounded with many two-factor interactions rather than fully aliased with one. Plackett-Burman is more run-efficient when you want to screen, say, 11 factors in 12 runs instead of jumping to 16.
Can Plackett-Burman designs detect interactions?
No. Plackett-Burman designs are resolution III, so two-factor interactions are aliased with main effects and cannot be estimated separately. They assume interactions are negligible during screening. Once the critical few factors are identified, you follow up with a full factorial or response-surface design to resolve interactions and curvature.
Why are Plackett-Burman run counts multiples of 4?
Plackett-Burman designs are built from Hadamard matrices, which exist only at orders that are multiples of 4. That is why the available designs are 8, 12, 16, 20, 24 runs and so on. The construction keeps every factor column perfectly balanced and orthogonal, so each main effect is estimated independently of the others.
How is Plackett-Burman used for media optimization?
In media optimization, a Plackett-Burman design screens many candidate components — carbon and nitrogen sources, salts, trace metals, vitamins — in a single small experiment to find which few actually affect titer or growth. The significant components then advance to a response-surface design for fine optimization, while the inert ones are fixed or dropped. This screen-then-optimize sequence is the standard statistical route to a better medium.
Related Tools
- DOE Experiment Generator — Build Plackett-Burman, fractional factorial, and response-surface designs free in the browser with randomized run order.
- Media & Feed Cost Estimator — Cost the medium components you are screening so the optimization targets price as well as titer.
- Fermentation Economics Calculator — Translate a titer improvement from media screening into cost of goods.
References
- Plackett, R.L. & Burman, J.P. (1946). The design of optimum multifactorial experiments. Biometrika, 33(4), 305–325. DOI: 10.1093/biomet/33.4.305
- Chauhan, K., Trivedi, U. & Patel, K.C. (2007). Statistical screening of medium components by Plackett–Burman design for lactic acid production by Lactobacillus sp. KCP01 using date juice. Bioresource Technology, 98(1), 98–103. DOI: 10.1016/j.biortech.2005.11.017
- Mandenius, C.F. & Brundin, A. (2008). Bioprocess optimization using design-of-experiments methodology. Biotechnology Progress, 24(6), 1191–1203. DOI: 10.1002/btpr.67