I’m planning to augment PB design to full factorial. But not able to understand statistically am I correct or not? Let me explain with example. Initially I had 11 factors & conduct PB using 12 runs. Let’s assume out of 11 only 3 factors are showing significant effect (using ANOVA). Now instead of conducting experiments separately using only screened 3 factors, wanted to use the same data points (response values). So now I’ve 3 factors with 12 runs which is more than required full factorial runs. Now I can estimate the higher order interactions as well. Statistically what is wrong in that approach?
This should work ok. You'll have some combinations of the 3 factors duplicated, but all combinations should be present without having to augment the design at all. However, you need to use software to analyze the design that can handle unbalanced allocation of observations to factor combinations.