pg_0105
5.
Process Improvement
5.3.
Choosing an experimental design
5.3.3.
How do you select an experimental design.
5.3.3.5.
Plackett-Burman designs
Plackett-
Burman
designs
In 1946, R.L. Plackett and J.P. Burman published their now famous paper "The Design
of Optimal Multifactorial Experiments" in Biometrika (vol. 33). This paper described
the construction of very economical designs with the run number a multiple of four
(rather than a power of 2). Plackett-Burman designs are very efficient screening designs
when only main effects are of interest.
These
designs
have run
numbers
that are a
multiple of
4
Plackett-Burman (PB) designs are used for screening experiments because, in a PB
design, main effects 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.
12-Run
Plackett-
Burnam
design
TABLE 3.18 Plackett-Burman Design in 12 Runs for up to 11 Factors
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
5.3.3.5. Plackett-Burman designs
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