Need help with 3x3x3 Full Factorial DoE Data Analysis

[#1]

Hello!

I am new to the community and I would like to get some advice on the data result after completing DoE (3x3x3 full factorial) experiment.

I have three factors (sodium chloride, sodium citrate, and glycine) and tested at 3 levels (0,100,200mM sodium chloride; 0,50,100mM sodium citrate; and 0,50,100mM glycine). Tested all 27 runs. The response is the %monomer intensity. Ideally, I want to achieve close to 100% in monomer intensity based on these three factors.

At the end of the experiment however, the data does not have a clear trend (the lowest p value was 0.27 for sodium chloride and the second lowest p value was 0.28 for sodium chloride*sodium citrate. Everything else (glycine and other two way interactions) have at least P value of 0.5 (glycine at 0.9).

How can I interpret this data if the outcome was not close to the 100% monomer? I suspect that the highest level for each factor was not high enough to generate more useful data. Perhaps none of these factors has huge impact on the % monomer improvement.

Please let me know how to interpret this data based on the result (file JMP attached). How can I make conclusions based on the result?

Thank you!

[#2]

First I'd like to add my welcome to the community.

Mark and Pete have provided great feedback and I'm not sure I can add much, but here are my thoughts:

1. You mention instability a couple of times in your posts.  What you are trying to do, I think, is optimization.  This should only be done on stable processes as the optimization will be different under different "levels of stability".  Perhaps you should experiment (or sample) to understand why there is instability first?  Also the level setting suggests you are still in the "understanding causal structure" space, not in the optimization space (you should already know the first order model).  This is akin to mapping the base of the mountain.  First get to the top of the mountain, then map it.

2. It seems like you are in the world of mixtures where there is a constraint on the % of each component in the "batch"?  As you increase the amount of 1 component in the mixture, you will have to decrease the amount of another...they have to add up to 100%

3. You must be aware of what "creates" the MSE estimates when interpreting p-values.  In your experiment there are no degrees of freedom to estimate random errors.  You have no replication, so the MSE is a function of higher order effects in your design (e.g., quadratic-by-linear interactions).  If these are active, then your MSE will be large and your F-values will be small and your p-values will be large.  If you run several of the "identical" trials from your first experiment again, what do you get?

4. The variability in your data explained by your model is quite low (and your residuals look "funky").  This is a clue there is noise (variables unaccounted for in your model) that may be accounting for the variation.  This could be measurement error, ambient conditions, set-up, raw material variation, etc.