Plackett-Burman Design: Difference between revisions

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{{Reference Example|{{Banner DOE Reference Examples}}}}
{{Reference Example|{{Banner DOE Reference Examples}}}}
This example validates the calculation of a Placket-Burman design in DOE++.
This example validates the calculation of a Plackett-Burman design in Weibull++.


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{{Reference_Example_Heading1}}
The data is from Example 8-8 on page 346 in the book ''Design and Analysis of Experiments''  by Douglas C. Montgomery, John Wiley & Sons, 2001.
The data are from Example 8-8 on page 346 in the book ''Design and Analysis of Experiments''  by Douglas C. Montgomery, John Wiley & Sons, 2001.


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[[Image:plackett_burman_anova.png|center]]
[[Image:plackett_burman_anova.png|center]]


The final equation in terms of actual factors is:
The final equation in terms of the actual factors is:


[[Image:plackett_burman_equation.png|center]]
[[Image:plackett_burman_equation.png|center]]

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Plackett-Burman Design

This example validates the calculation of a Plackett-Burman design in Weibull++.

Reference Case

The data are from Example 8-8 on page 346 in the book Design and Analysis of Experiments by Douglas C. Montgomery, John Wiley & Sons, 2001.

Data

Run A B C D E F G H J K L Response
1 -1 1 1 1 -1 -1 -1 1 -1 1 1 220
2 -1 1 1 -1 1 1 1 -1 -1 -1 1 207
3 -1 -1 1 -1 1 1 -1 1 1 1 -1 175
4 1 1 -1 -1 -1 1 -1 1 1 -1 1 185
5 -1 1 -1 1 1 -1 1 1 1 -1 -1 217
6 1 -1 1 1 1 -1 -1 -1 1 -1 1 229
7 1 -1 -1 -1 1 -1 1 1 -1 1 1 183
8 1 1 -1 1 1 1 -1 -1 -1 1 -1 231
9 1 -1 1 1 -1 1 1 1 -1 -1 -1 230
10 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 168
11 -1 -1 -1 1 -1 1 1 -1 1 1 1 176
12 1 1 1 -1 -1 -1 1 -1 1 1 -1 181


Result

From the book the ANOVA table is:

Variable Regression Coefficient Sum of Square
Overall Average 200.167
A 6.333 481.333
B 6.667 533.333
C 6.833 560.333
D 17.000 3468.000
E 6.833 560.333
F 0.500 3.000
G -1.167 16.333
H 1.500 27.000
J -6.333 481.333
K -5.833 408.333
J -0.167 0.333


Results in DOE++

The software results match the book results. The ANOVA table is:

Plackett burman anova.png

The final equation in terms of the actual factors is:

Plackett burman equation.png
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