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Plackett-Burman Design |
Validate the calculation of a Placket-Burman design.
Reference Case
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 actual factors is:
The results from the softwware match the results in the book.