DOE analysis with centerpoint runs

[#1]

Hi...

I am analysing a DOE with centerpoint runs, since we want to know if there are significant quadratic effect.

known info:

1. 4 factors are involved with 4 replications in the center point
2. the factorial portion of the design is a full-factorial that includes 2^4=16 runs
3. so, the total number of runs of your design is 20
4. each run produced 20 values (readings) a total of 20 x 20 = 400 readings

In the analysis, only 1 quadratic effect has P-value, as far as i know, as far as i have enough number of runs to estimate all the main and 2nd degree effects (2-way interactions and quadratic), JMP should be able to compute for all the needed p-values. But why am i getting this result? See attached

Please correct my understanding if im wrong, and thanks to help figure out the problem with my data

 

[#2]

Your design does not support the estimation of the full quadratic model. It is a two-level design, which supports only the estimation of the first order model. The center points provide a third level but they can only be used for either a lack of fit test (LOF) or the estimation of one arbitrarily selected quadratic effect. The data are incapable of uniquely determining the factor attributable to the non-linear effect.

I would deleted the quadratic terms for all the non-linear effects and fit the model. Is LOF significant? If so, then I would augment the design after adding the quadratic terms to the model. If not, then there is no significant non-linearity to account for, so your first order model is sufficient.

[#3]

To pile onto my colleague @Mark_Bailey's comments...next time if you have 4 factors and want to estimate all main effects, two factor interactions, and quadratic effects, you may want to consider using JMP's Custom Design platform rather than the Classic Catalog design it appears you defaulted too? Using optimal DOE techniques, if you have a resource constraint of 20 runs...you can still create a design that will work. If you default to the classic Box Behnken or Central Composite design your are up to 26 or 27 runs. Sure these two designs will have improved power, lower prediction variance, etc. but that's the trade off from doing NOTHING if you've got a upper run constraint of 20 runs. Also, you can use JMP's new Compare Designs platform to compare the three design properties I mention. See the attached Journal where I compare a CCD with a 20 run I - optimal design.