Fractional Factorial Design when some factors have more than 2 levels Let's say I was conducting an experiment with 4 factors.
Three of them have qualitative settings, so I can simply designate one as +1 and one as -1. But one of the factors is numeric, and I would like to investigate three levels.  If the other three were numeric as well I could treat this as a 2^4 with center points, but that's not the case.
The full general factorial is thus 24 design points per replicate.  Is there a fractional approach in this case?  Any references for how to proceed?
 A: There is fractional approaches also in the mixed levels case, but less straightforward than for the $2^{n-k}$-designs.  One idea is to use orthogonal arrays (OA), see wikipedia.
In your case $2^3\cdot 3$ a full factorial have 24 runs, so we can try for a half-fraction, with 12 runs. We use symbols 0,1 for the 2-level factors, 0,1,2 for the 3-level factor. We start writing down columns as we would for a $2^3$-design. What is important is that all possible symbol combinations, at least taken two columns a time, will appear with the same frequency (that will give an OA of strength 2).
0 0 0 0
0 0 1 1
0 0 0 2
0 1 1 0
0 1 0 1
0 1 1 2 
1 0 1 0
1 0 0 1
1 0 1 2 
1 1 0 0 
1 1 1 1 
1 1 0 2

Note that filling in the third column, reaching halfway down we had to "mirror" the pattern. Note that taking one two-level and the 3-level column, there are $6=2\cdot 3$ possible combinations, so the maximum possible strength is two, which is achieved. For two 2-level columns, there are 4 possible combinations, so 3 copies of each is possible (and obtained). So the 3 first columns by itself is an OA of strength 3.
