3.1.13 Plackett-Burman Design

The Plackett-Burman design is a two-level design for examining n parameters in k = n+1 runs. Plackett and Burman [41] supply signs^3.2 for the first row of the design matrix shown in Table 3.5.

Table 3.5: The first row for Plackett-Burman designs.

n	k	String
11	12	+ + - + + + - - - + -
15	16	+ + + + - + - + + - - + - - -
19	20	+ + - - + + + + - + - + - - - - + + -
23	24	+ + + + + - + - + + - - + + - - + - + - - - -

All other rows of the design are built by shifting the previous one. An extra row is added to the design consisting of the minimum values of all parameters. In Table 3.6 a Plackett-Burman design for 11 parameters is shown.

Table 3.6: The Plackett-Burman design for 11 parameters.

	A	B	C	D	E	F	G	H	I	J	K
1	+	+	-	+	+	+	-	-	-	+	-
2	-	+	+	-	+	+	+	-	-	-	+
3	+	-	+	+	-	+	+	+	-	-	-
4	-	+	-	+	+	-	+	+	+	-	-
5	-	-	+	-	+	+	-	+	+	+	-
6	-	-	-	+	-	+	+	-	+	+	+
7	+	-	-	-	+	-	+	+	-	+	+
8	+	+	-	-	-	+	-	+	+	-	+
9	+	+	+	-	-	-	+	-	+	+	-
10	-	+	+	+	-	-	-	+	-	+	+
11	+	-	+	+	+	-	-	-	+	-	+
12	-	-	-	-	-	-	-	-	-	-	-

Footnotes

... signs^3.2

The "-" sign correspond to the minimum value and the "+" sign correspond to the maximum value of the input parameter range