We are running a DOE to determine the best shape of a speed vs. time curve. Our moulding machine allows us to split the injection speed into 10 segments to allow controlled flow of plastic into the part. We know that at the end of the injection the speed should be lower.
Seg 1 - 7 Levels are 2.2 - 3.4
Seg 8 levels are 1.8 - 3.0
Seg 9 levels are 1.0 - 2.4
Seg 10 levels are 0.5 - 1.1
Restrictions:
Segment 1 - 7 are greater than or equal to 8 and 9
Segment 8 is greater than or equal to 9
Segment 10 is less than 1-9
DOE (Response Surface 4 factors, 2 levels, 2 blocks)
The items marked x in the restricted columns I would not be able to run due to restrictions.
This looks like a CCD design, which is a good place to start. Unfortunately, the limitations that you have cut way back on the allowed combinations.
Of the 25 different sets of levels in the design, only 10 seem to be left after the restrictions. I’d be really wary about that few combination, especially since you would have 14 parameters if you are doing a full quadratic fit. You would end up with significant aliasing.
You could try adjusting some of the restricted runs to some close-by allowed set. That would be an improvement over just skipping the runs.
One “fancy” option would be a d-optimal design. You would need to find a list of some of the allowed combinations (I think there are 130 total in your case). Then use some software (like minitab) to choose an optimal subset to acheive the goals you desire. It takes a little more computer power to create the design and a little more to analyze, but it should give the most robust results.
Option 2: Use the concept of Sliding Levels. This is a Taguchi approach but, used with care, does work. See http://www.gaasmantech.org/Digests/2002/PDF/11e.pdf
and http://files.aws.org/wj/supplement/05-2002-ALLEN-s.pdf
for examples. This requires some prior understanding of the process to establish sliding levels. An example of this is curing rubber. Rubber cures faster at higher temperatures, so the cure time must slide with the temperature. At 350 degrees, the time may be 90 and 120 seconds, while at 450 degrees, the times may be 30 and 45 seconds.
Option 3: Use EVOP or Evolutionary Operation. See http://www.visteon.com/utils/whitepapers/20_ccwdq.pdf
for a White Paper on this approach. This is fairly simple and requires no prior knowledge of the process. If your main interest is optimization without developing a model of the process, this is your best option.