I'm studying a complicated welding process where I have 12 continuous factors and 1 categorical factor that interact to produce a dense weld ( the good part). To determine whether a part is good or not the density of samples is determined using the Archimedes technique. I used Minitab's definitive screening to find out which factors are most significant to the quality of the part and to understand how these factors are interacting together.

Experimental setup (please see attachment):

13 factors, 6 replicates over 3 blocks (2 reps each) with a total of 180runs.

Going through the statistical diagnostics, I find that if I analyse the model without a Box-Cox transformation, I have normal residuals (P-value 0.415) but a significant lack of fit. Applying transformations does not improve this lack of fit and to be honest i'm not sure what the implications are in this situation.

Note: I used "stepwise" to reduce the model and my R-sq was 96%, R-sq(adj) 95.9% and R-sq(pred) 95.4%.

- Does this lack of fit mean I can trust the pareto chart showing what are my significant factors but cannot use the model to predict an optimum combination due to this lack of fit?
- Is there anything obvious I'm missing to fix this lack of fit?
- Do these good R-sq values mean anything when I have a significant lack of fit?
- Generally speaking, can I rely on the DSD optimiser results to make predictions if I have enough replicates in the model?

I'm not a statistician and all this is self taught really so forgive me if my questions are basic, but i'm very keen to learn and I hope you will take the time to shed some light on this to help me out.