 |
New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images and more targeted search.
As of January 2024, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest references at DOE examples and DOE reference examples.
|
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:
.