# DOE sample size where response is variance

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• #29414

Jamie Shortt
Participant

I’m looking for a method to calculate the number of replicates for a experiment if the respose is variance (not interested in mean). Does anyone know how to do this.
Thanks,
Jamie

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#75321

TCJ
Member

The more samples the tighter the variance, so what do you want your results to look like. ;-)

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#75332

Gabriel
Participant

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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#75335

RR Kunes
Member

Why would you structure a DOE to have an output be a variance?  Your safeest approach is to rethink your DOE and the manner in which you capture the output data.

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#75337

Gabriel
Participant

RR,
I can’t speak for Jaime, but this is why we did it.
We wanted to improve a process cycle time (Y). In the team we identified many process parameters (Xs) that could be controlled and could affet the cycle time. But we realized that touching those parameters (speeds, pressures, times, distances, etc.) could also affect some quality characteristics such as roughness and ovality, and also could affect the variation of the most important characterisitc (the diameter of the product) thus reducing the process capability (Cp).
The goal was expressed as “Improving the cycle time without worsening the quality nor the capability” So we had several Ys. One was the cycle time and the others were roughness, ovality and diameter’s variance.
I imagine that another good reason to make a DOE taking the variance as the output is because you want to improve the process capability and you want to know how the several process parameters and their interaction affect the variation of the output.

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#75340

Robert Butler
Participant

I’ve built and analyzed a number of DOE’s where the response variable was variance.  The simplest approach is to replicate the entire design and compute the variance of the two samples for each experimental condition.  Granted, variability based on two samples is not what one would normally want when estimating variance as a Y response but this approach does work.  My approach has been to use saturated designs in order to screen as many variables as possible and to replicate the design 3 times.  Three times guards against the loss of a single run and thus against the loss of an experimental data point for the analysis of variables impacting the variance.  Of course, with such an approach you also can analyze for variables impacting mean shift as well.  If 3 reps is too many you can get by with 2 but if one of the horses die you will need to run regression diagnostics on the leftover design in order to determine what X variables you can still use for an analysis of the variance.

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#75386

Ø6 Sigma BB Coordinator
Participant

I use KISS approach.
I just use simple table/ROT developed by Air Academy Associate.
These examples are from the top of my head.
L4 – sample size = 9 / run
L8 – sample size = 5 / run
L12, L16 – sample size = 4 / run
Then I will get S-hat model, using ROT deveoped by AAA.
For more detail, see “Understand Industrial Designed Experiment” by AAA. see http://www.airacad.com
This is a simple method. It is easy to use. However, some experts suspect in its statistical validity.
Hope this helps
Six Sigma Black Belt Coordinator

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