Plackett-Burman Design: Difference between revisions

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


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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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From the book the ANOVA table is:
{| {{Table}}
!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
|-
|}


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Your text here.


{{Reference_Example_Heading4|DOE++}}
{{Reference_Example_Heading4|DOE++}}
Your text here.
The software results match the book results. The ANOVA table is:
 
[[Image:plackett_burman_anova.png|center]]
 
The final equation in terms of the actual factors is:
 
[[Image:plackett_burman_equation.png|center]]

Latest revision as of 21:09, 18 September 2023

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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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