In 1946, Plackett and Burman demonstrated how a full factorial design can be highly fractionalized to yield saturated designs, where the number of runs is a multiple of four, rather than a power of two. A Plackett-Burman (PB) DOE can screen the maximum number of main effects with the least number of experimental runs in case of two-level factors. PB designs are very economical designs, and are efficient in screening when only main effects are of interest. This is because the main effects in a PB design are, in general, heavily confounded with two-factor interactions. The PB design in 12 runs, for example, may be used for an experiment containing up to 11 factors.
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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 |
Plackett-Burman Design in 12 Runs for up to 11 Factors
• | Only 2-level variables can be used. |
• | The Number of runs is a factor of four. |
• | The maximum number of variables you can use is 35. |
• | Best suited for problems where the interactions are expected to be minimal and the main effects dominate. |
• | Any data in the inclusion matrix is combined with the run data for post-processing. Any run matrix point which is already part of the inclusion data will not be rerun. |
In the Specifications step, you can change the following settings of Plackett_burman from the Settings tab.
Parameter |
Default |
Range |
Description |
Design |
AutoSelect |
AutoSelect, pbdgn12, pbdgn20, pbdgn24, pbdgn28, pbdgn36, None |
AutoSelect will pick the lowest number of runs sufficient to study effects. pbdgn stands for Plackett Burman design. |
Resolution |
III |
III |
Resolution of the DOE. |
Number of runs(npt) |
Dependant upon design selected. |
12-36 |
Number of designs to be evaluated. |
Use Inclusion Matrix |
false |
true or false |
Concatenation without duplication between the inclusion and the generated run matrix. |