Plackett-Burman design for 20 runs
In a similar way, the following resolution III Plackett-Burman design can be used for 16-19 factors in 20 runs instead of the 32 runs that would be required for a fractional factorial experiment. (For fewer than 19 factors, just use any subset of the columns in the table.)
Factor | |||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Run | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S |
1 | + | + | - | - | + | + | + | + | - | + | - | + | - | - | - | - | + | + | - |
2 | - | + | + | - | - | + | + | + | + | - | + | - | + | - | - | - | - | + | + |
3 | + | - | + | + | - | - | + | + | + | + | - | + | - | + | - | - | - | - | + |
4 | + | + | - | + | + | - | - | + | + | + | + | - | + | - | + | - | - | - | - |
5 | - | + | + | - | + | + | - | - | + | + | + | + | - | + | - | + | - | - | - |
6 | - | - | + | + | - | + | + | - | - | + | + | + | + | - | + | - | + | - | - |
7 | - | - | - | + | + | - | + | + | - | - | + | + | + | + | - | + | - | + | - |
8 | - | - | - | - | + | + | - | + | + | - | - | + | + | + | + | - | + | - | + |
9 | + | - | - | - | - | + | + | - | + | + | - | - | + | + | + | + | - | + | - |
10 | - | + | - | - | - | - | + | + | - | + | + | - | - | + | + | + | + | - | + |
11 | + | - | + | - | - | - | - | + | + | - | + | + | - | - | + | + | + | + | - |
12 | - | + | - | + | - | - | - | - | + | + | - | + | + | - | - | + | + | + | + |
13 | + | - | + | - | + | - | - | - | - | + | + | - | + | + | - | - | + | + | + |
14 | + | + | - | + | - | + | - | - | - | - | + | + | - | + | + | - | - | + | + |
15 | + | + | + | - | + | - | + | - | - | - | - | + | + | - | + | + | - | - | + |
16 | + | + | + | + | - | + | - | + | - | - | - | - | + | + | - | + | + | - | - |
17 | - | + | + | + | + | - | + | - | + | - | - | - | - | + | + | - | + | + | - |
18 | - | - | + | + | + | + | - | + | - | + | - | - | - | - | + | + | - | + | + |
19 | + | - | - | + | + | + | + | - | + | - | + | - | - | - | - | + | + | - | + |
20 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
The pattern in this table is again that each row is identical to the one above, but shifted one place to the right, except for the final last row which is all -1 (necessary to ensure the same number of +1 and -1 for all factors).
Again, all factor main effects are orthogonal.
Other Plackett-Burman designs
Similarly constructed Plackett-Burman designs exist for any number of runs that is a multiple of four, so designs with 24 runs (for up to 23 factors) and 28 runs (for up to 27 factors) could be useful.
It is stressed that Plackett-Burman designs are resolution III, so main effects are confounded with 2-factor interactions. Therefore:
Plackett-Burman designs should only be used when interactions can be assumed to be relatively small compared to main effects and only used for screening purposes (to rank factors by their main effects).