What to do if the range of an input factor changes after running the experiment?

Question

I am gaining my first experiences in Designing Experiments and here where I am stack:

An experiment has been run with some continuous input factors: x1, x2, ..., x5. The goal of the experiment was to optimize some continuous output factor y. As the output of the experiment, the optimal combination of the levels for all five input factors were determined to get the desired output of y. After a short time, the range of the values of the input variable x1 has been changed from 10-20 to 10-30 (different supplier of material). The levels(x1) were chosen as {10, 15, 20}. Lets assume that the upper boundary, which is 30 now has a big practical meaning and should be included to the design, i.e now levels(x1) has to be chosen as {10, 15, 30}.

1. What should be done in this case?
2. Does the experiment which has been done initially make still sense?
3. Is there a need to repeat the whole experiment with the new upper boundary or is there any smarter way/strategy which can help to avoid repeating the whole experiment? Can we use the initial experiment outputs for that? How?
4. Is there any literature/concept which can help me to handle such situations?

Thank you a lot.

Answer 1

1. What should be done in this case?

   • This depends on your current running conditions. Is x1 currently running close the old limit of 20?

2. Does the experiment which has been done initially make still sense?

   • Yes the experiment was valid for the initial sample space and is still valid for the newer larger sample space. The question is are you still running at the optimum conditions?

3. Is there a need to repeat the whole experiment with the new upper boundary or is there any smarter way/strategy which can help to avoid repeating the whole experiment? Can we use the initial experiment outputs for that? How?

   • No, the entire experiment does not need to be repeated. The conclusions from the first experiment are still valid. The first experiments should have highlighted the important input interactions and possibly eliminated a few factors as not significant.
   • Yes, Depending on your model you may be able to extrapolate and predict the performance in the new sample space.
   • Another option is to design a smaller DOE where x1 takes the current value & 30 and one only looks at the other significant factors from the first DOE experiment.

4. Is there any literature/concept which can help me to handle such situations?

   • Review the "method of steepest ascent", a good DOE text should cover it.
   • Another slightly out of favor technique is the "Taguchi method". Which a strategy of small incremental DOE experiments to move to the optimum conditions