# Assessing Process Capability on Variation (Hardware Adjustment Mean Shift)

G

#### garbagex

Hi All,
I am trying to assess capability on a process that can have adjustment done (hardware mean shift) so the critical parameter is how wide is the spread of data. Each machine produces 1 subgroup of 50 data points with summary mean and stdev statistics. Each machine must pass bilateral +/- limits on the variation=3 sigma and the mean is for reference only.

Before embarking on improvement activities, I need to have a proper and correct understanding of the current capability of this process and I need your advice on what would be a proper way to do this (process is in control and data is normal). What is important to me is to make sure the spread does not exceed the limits as I can always bring any mean shift back through adjustment.

1. I think calculating Cpk by using each subgroup mean value as 1 data point is wrong. By doing so, we lose the within subgroup variation component.
2. Calculating Cpk from variation= 3 sigma with limits 0 and USL is wrong as well as this is calculating variation of the variation, if you get what I mean.
3. The nearest logical measurement that I can think of to only report the Cp instead so we know the spread relative to the tolerance. By using the between/within formulas I can come up with summary Cp values that makes use of each subgroups' mean and stdev, without losing valuable data.

Pardon the long writeup above, I hope my description of the problem provides enough details for discussion.
Please comment if what I am doing is correct, or if you think there is a better or more accurate way to assessing a spec that controls variation. Thanks in advance!

B

#### Barbara B

Re: Assessing capability on variation

Could you please provide some data? It gets much easier to give a precise answer if we could take a look at it

Thanks,

Barbara

G

#### garbagex

Re: Assessing capability on variation

Hi Barbara,
Here are some sample data as requested. The parameter of interest is S, S_Avg and S_Stdev are the raw data from each individual unit, while the computed S_Var (=3*S_Stdev) is used to determine pass/fail. These are data from an early batch with some outliers, so please ignore the control and normality as I just want to check the methodology.

I'm doing this by method 3 mentioned in my earlier post. I have added formula to crunch between/within capability by re-interpreting the variation limits (LSL 0 USL 4) to S limits (LSL -2 USL 2).

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B

#### Barbara B

Re: Assessing capability on variation

Thanks for the data.

If you're only interested in the spread, every capability index with a "k" is useless as it takes spread and deviation into account.

But what I don't understand is your method of estimating the variation using the between-within-approach. The variation between subgroups is caused by differences between the means - and you're not interested in this because differences in means could be adjusted (if I've understand your goal correctly).

Is there a special cause why you don't use a more common subgroup variation formula like the pooled standard deviation?

Regards,

Barbara

G

#### garbagex

Re: Assessing capability on variation

Hmm that is a good logical question indeed. I started off with the 'normal' or within way of calculating capability by using only sigma.within for Cp/Cpk. Then after discussion with some colleagues we think it's better to do between/within which gives us a more complete picture of the total production variation.

Now that you mentioned it, it does make more sense to calculate within capability only as each individual unit are adjusted differently on their own. Hence the between component does not matter subsequently.

Yet another question if you may, should I be assessing Cpk AFTER adjustment to see how good is the actual adjustment to nominal?

Does this assessment flow make sense: raw production (within Cp) -> adjustment (between/within Cpk)