Plackett−Burman design

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:
  1. 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).
  2. For \(4 \times N\) experiments, \(4 \times N − 1\) main effects and the mean are estimated.
  3. 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.
RunPatternX1X2X3X4X5X6X7X8X9X10X11
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
Source:
PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 416 (https://doi.org/10.1515/pac-2015-0605)