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| [[Image:plackett_burman_anova.png|center]] | | [[Image:plackett_burman_anova.png|center]] |
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| The final equation in terms of actual factors is: | | The final equation in terms of the actual factors is: |
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| [[Image:plackett_burman_equation.png|center]] | | [[Image:plackett_burman_equation.png|center]] |
Revision as of 22:06, 29 July 2015
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This example validates the calculation of a Placket-Burman design in DOE++.
Reference Case
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.
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:
The final equation in terms of the actual factors is:
