How to build a prediction model of multi-step process: some runs don't have all the steps

Question

Hello,

I am hoping to get some advice in modelling based on the historical data. For the process the model is based on, it has 3 steps dep1->dep2->etch3, for each step there are 3 continuous factors. So in total, I have 3*3 factors, 9 factors. However, for some historical runs, there is no step 3etch but 1 and 2. Could I take the "3 steps run" and "2 steps run" as one table and build model out of it? Should I put "0" for step 3 factors for when there is no step 3?

Sometimes, it could also be dep1->etch2->dep3, which is different from dep1->dep2->etch3. Is JMP able to deal with this kinds of multi-step DOE...?

statman · Answer

Since you are data mining, you can try different approaches.  The one you suggest is worth a try.  Create a column and call it "steps", then fill out accordingly.  Once this is done you can look for the effect of "steps", you can run regression procedures by "steps", do lots of data plots within and between steps, etc.

Fruit325 · Answer

Hi @statman

Thanks for your advice! That's true that for historical data there are so many noises from the measurement, time effects, etc. for modelling and according to your advice I am going to do some data mining to try to pick up the important factors that would be helpful to build next orthogonal DOE.

The question is.... because the historical runs, some have only two process steps, some have three process steps, how could I combine these two senarios into one to be analyzed? Can I put "0" for those factors in the 3rd step for the runs where there are only two steps? Thanks!

statman · Answer

Sorry, just not enough information to provide specific advice.  Here are my thoughts, though you may not like tyhem.

Since you are using only historical data, the best you can do is data mine. (look for patterns in the data and possible association of factors to develop hypotheses).  Historical data lacks context.  There's too much information not included in your data set to create any useful prediction models.  Now, you might get clues to develop hypotheses that can be tested with experimental design, but that would be the extent.  For example, though you don't provide what the response variables are, do you know the measurements errors associated with the x's and the y's?  Are there other factors not recorded that varied over the time period of your historical data.  Are the x's collinear?  Do x's have a lagged effect?

Just use data plots and regression (e.g., stepwise, PLS maybe even PCA) to get clues to help you design an experiment to provide some confidence in a useful model.