With DOE you analyze how the factors (Xs) affect the output (Y) on average.
If your Y is variance, you have two ways. Note tht in both ways you will need more than 1 part for each experimental condition, and of course the more the better. Also note that the “”sample size” in this case is not the number of parts, but the number of “variances” calculated for each experimental condition.
a) Take n parts for each experimental condition and calculate the variance. The sample size is 1. You don’t have degrees of freedom left for the error, then you will have to do a pool up or a grphical method.
b) Take n “subgroups” of m parts each for each experimental condition (i.e. n times m parts por each experimental condition). Calculate the variance of each subgroup. The sample size is n. Use ANOVA.
We did this only one with both methods. The method b) resulted sensitive to the combination of n and m (i.e. is it better to take 3 subgroups of 5 parts or 5 of 3?), so some “border” factors resulted “significant” in one combination and “non significant” in the other, with the same confidence level. The method a), as known, does not consider any confidence level. Specially the graphical approach, it is up to you to define how far from the stright line should the factor be to be considered as significant. Anyway, the most significat factors resulted the same with all methods, and because the discrepancy about “how significant is significant” between the methods, I would use the graphical approach and define it myself.
Anyway, be aware that we did it only once, and that this approach was improvised in that moment without previous advice about how to handle this situation. May be a Taguchi noise-to-signal approach would do the job… so any other feedback is welcomed.
Hope this helps
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