https://doi.org/10.1351/goldbook.10080
Incomplete experimental design to estimate main effects for which each combination of factor levels for any pair of factors appears the same number of times.
Notes:
- Plackett–Burman designs are typically given for two levels, with a number of experiments that is a multiple of 4 but not a power of 2. (The latter case is a fractional-factorial design).
- For \(4 \times N\) experiments, \(4 \times N − 1\) main effects and the mean are estimated.
- If less than \(4 \times N − 1\) factors are being studied, dummy factors are inserted which allow estimation of the repeatability standard deviation of the measurement results.
Example: The coded experimental design for \(4 \times N = 12\), where \(+1\) and \(-1\) represent the two levels of factors \(X_{1}\) … \(X_{11}\) is given below. The order of performing the runs should be randomised.
| Run | Pattern | X1 | X2 | X3 | X4 | X5 | X6 | X7 | X8 | X9 | X10 | X11 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | +++++++++++ | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 |
| 2 | -+-+++---+- | -1 | +1 | -1 | +1 | +1 | +1 | -1 | -1 | -1 | +1 | -1 |
| 3 | --+-+++---+ | -1 | -1 | +1 | -1 | +1 | +1 | +1 | -1 | -1 | -1 | +1 |
| 4 | +--+-+++--- | +1 | -1 | -1 | +1 | -1 | +1 | +1 | +1 | -1 | -1 | -1 |
| 5 | -+--+-+++-- | -1 | +1 | -1 | -1 | +1 | -1 | +1 | +1 | +1 | -1 | -1 |
| 6 | --+--+-+++- | -1 | -1 | +1 | -1 | -1 | +1 | -1 | +1 | +1 | +1 | -1 |
| 7 | ---+--+-+++ | -1 | -1 | -1 | +1 | -1 | -1 | +1 | -1 | +1 | +1 | +1 |
| 8 | +---+--+-++ | +1 | -1 | -1 | -1 | +1 | -1 | -1 | +1 | -1 | +1 | +1 |
| 9 | ++---+--+-+ | +1 | +1 | -1 | -1 | -1 | +1 | -1 | -1 | +1 | -1 | +1 |
| 10 | +++---+--+- | +1 | +1 | +1 | -1 | -1 | -1 | +1 | -1 | -1 | +1 | -1 |
| 11 | -+++---+--+ | -1 | +1 | +1 | +1 | -1 | -1 | -1 | +1 | -1 | -1 | +1 |
| 12 | +-+++---+-- | +1 | -1 | +1 | +1 | +1 | -1 | -1 | -1 | +1 | -1 | -1 |