Best way to estimate contributors to process mean drift?

[#1]

Suppose I have a response metric Y which is seeing a sudden uptick in mean, while variance is similar. Assume it is influenced by upstream process factors, P1, P2, P3, P4.  What is the best way to estimate which of the process factors P1-P4 contributed most to the mean uptick? I have run POV analysis before to estimate contributors to variance, but is there a way to quantify similar effect on the mean drift? 

[#2]

Hi @jmdz ,

Is the process a continuous time series? If not, predictor screening is a good starting point, as well as forming a Fit Model with the linear terms (P1, P2, P3, P4) and potentially including some interactions or curvature (i.e. P1*P2, P1*P1).

Thanks,

Ben

[#3]

Thanks Ben. No, the process factors are categorical (e.g. recipes, batches, etc.). Will try predictor screening. While fitting model, should I include time as a factor, to check if the categorical process factor shifted/drifted at a certain point? 

[#4]

HI @jmdz ,

Yes its worth including time, although if it's something that's changing with time you might want to use Fit Model, and include time as a single variable (Time) and crossed variable (Time*X1) to see if time is causing the effect of the categorical factors to change. Other option would also be just to segment your batches to a 'Before' and 'After' values that you could place into the model.

Hope that helps!
Ben

[#5]

Best way? First I would start with hypotheses. Are there rational, logical hypotheses for the factors P1-P4 to have an effect on the mean? Then design an experiment with those 4 factors. Everything else is correlation.

[#6]

Thanks statman, agree to your point, but we do not always have the time to run DOEs and confirm hypotheses. Correlations is what we rely on for initial guidance and troubleshooting.