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Significant uncontrolled factor estimation

Dear community members,

I have a question regarding uncontrolled factor added in a DoE.

I understand that the effect of these factors will be captured in the error of the model.

Imagine the error is significant, I would therefore consider modeling one of these uncontrolled factors to see its effect and see if the model error decreases.

How would you manage this factor estimation ?

Should I add some more runs in the DoE before executing it so as to proactively be able to estimate such an uncontrolled factor ?

In this situation, the problem is about collinearity as this uncontrolled factor would variate with other factors and will never be orthogonal ?

Therefore, would you augment the design adding runs a posteriori with this uncontrolled factor orthogonal to the other factors ?

Thanks,

Hugo

Re: Significant uncontrolled factor estimation

Many thanks for the input Mark.

Re: Significant uncontrolled factor estimation

No, you add the uncontrolled factor to the design along with the other factors. The values for the uncontrolled factor are left missing. You specify the model as usual, including the anticipated effects of the uncontrolled factor. You record the observed value for the uncontrolled factor along with the response during each run. The effects will be estimated along with the rest of the parameters.

You cannot specify the levels of the uncontrolled factor so you cannot achieve orthogonality by design. Randomization, as always, will help mitigate collinearity. Parameter estimates do not have to be orthogonal to be estimated. The higher the correlations among the estimates, though, will inflate the variance of the estimates.