Home / DOE / Create Designs / Plackett-Burman Designs / Plackett-Burman How-To
Plackett-Burman How-To¶
This walkthrough builds a 12 run Plackett-Burman design for seven factors, and shows the property that makes it a screening design and nothing else.
Nothing here needs data. Every number below is determined by the design.
Steps¶
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Start the builder
QXL DOE New > Create Design. Choose Plackett-Burman and press Next.
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Choose the size
The page carries Select number of factors: and Select number of runs:. Type 7 factors, and choose 12 runs. Press Next.
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Name the factors
Seven factors, each with a low and a high. Press Next, name one output, and press Next.
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Finish
Leave replicates at 1 and the blocking list at No blocking, leave the centre points at 0, and press Finish.
What you get¶
Twelve runs for seven factors, where a full factorial would need 128 and even a quarter fraction would need 32.
The array holds eleven columns, one less than the run count, and your seven factors take the first seven. Press Copy for Excel and paste the block into an empty part of the worksheet to compare it against your sheet; in coded units all twelve runs are:
| Run | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| 1 | +1 | +1 | -1 | +1 | +1 | +1 | -1 |
| 2 | -1 | +1 | +1 | -1 | +1 | +1 | +1 |
| 3 | +1 | -1 | +1 | +1 | -1 | +1 | +1 |
| 4 | -1 | +1 | -1 | +1 | +1 | -1 | +1 |
| 5 | -1 | -1 | +1 | -1 | +1 | +1 | -1 |
| 6 | -1 | -1 | -1 | +1 | -1 | +1 | +1 |
| 7 | +1 | -1 | -1 | -1 | +1 | -1 | +1 |
| 8 | +1 | +1 | -1 | -1 | -1 | +1 | -1 |
| 9 | +1 | +1 | +1 | -1 | -1 | -1 | +1 |
| 10 | -1 | +1 | +1 | +1 | -1 | -1 | -1 |
| 11 | +1 | -1 | +1 | +1 | +1 | -1 | -1 |
| 12 | -1 | -1 | -1 | -1 | -1 | -1 | -1 |
Each row is the row above shifted one place to the right, with the value that falls off the end wrapping round to the front. Check run 2 against run 1 and you can see it. The twelfth run is the exception: it is all -1, and no shift produces it.
Every column is balanced, six runs at each setting, so each main effect is estimated from a fair comparison.
The property that decides how you use it¶
A Plackett-Burman design estimates main effects only. With twelve runs there are eleven degrees of freedom to spend and seven go to your factors, so there is nothing left to estimate an interaction with.
The interactions do not vanish, they spread. In a fractional factorial each two-factor interaction is aliased with one specific other effect, and the alias table names it. Here each two-factor interaction is partially aliased with every main effect it does not contain, in fractions rather than whole units.
That is why this design is for screening: it tells you which of seven factors are worth pursuing, and you follow it with a design that can separate the interactions among the few that survive.
Take a large effect as a signal to investigate, not as a measured coefficient. If two factors interact strongly, the interaction is smeared across the other main effects and can make an unimportant factor look important.
Things to try next¶
- Type 8 factors and watch the run count. The 12 run array holds eleven columns, so it takes up to eleven factors; ask for more and the next size up is offered.
- Ask for 20 runs with the same seven factors. The extra runs go into the array's spare columns, and the partial aliasing between the main effects and the interactions gets weaker.
- Follow it with a two-level factorial on the two or three factors that stood out. That design can separate their interactions, which this one cannot.
See Also¶
- Plackett-Burman Designs, what the design is and the sizes that exist
- Options, every control on every page of the builder
- Math Details, how the array is generated
- Two-Level Factorial Designs, the follow-up design