Just curious why you would want to do this? I mean, Cross product arrays are a fantastic idea for robust design, but a 4-level factor? Is the 4-level factor continuous or categorical? While I know there are a number of 2-level orthogonal arrays, Taguchi, philosophically, suggests 3-level designs for the design factors (he doesn't really believe relationships are linear). Also for the outer array, since you will have to have 4 combinations (3 DFs) you might as well add a third noise variable for the 3rd DF since you don't care about noise-by-noise interactions.
To the best of my recollection (this was a long time ago), the way Taguchi did it was to take three columns from the orthogonal array (3 DFs, same for a 4-level factor). That will give you 8 possible combinations. Set those to 4 levels like this:
| A |
B |
C |
|
D |
| -1 |
-1 |
-1 |
|
1 |
| 1 |
-1 |
-1 |
|
2 |
| -1 |
1 |
-1 |
|
3 |
| 1 |
1 |
-1 |
|
4 |
| -1 |
-1 |
1 |
|
1 |
| 1 |
-1 |
1 |
|
2 |
| -1 |
1 |
1 |
|
3 |
| 1 |
1 |
1 |
|
4 |
Don't use the 3 columns used to create the 4 level factor (obviously). But I could be completely wrong...LOL
"All models are wrong, some are useful" G.E.P. Box
