# Cpk / Ppk units of measure

Six Sigma – iSixSigma Forums Old Forums General Cpk / Ppk units of measure

Viewing 14 posts - 1 through 14 (of 14 total)
• Author
Posts
• #50499

Baker
Participant

Are there different methods for calculating Cpk depending on the units of measurement? For example, I’m working with power units and get different Cpk values when I do the calculation in dBm vs mW. Everything I’ve found says that the units don’t matter. If that is the case, why do I get different Cpk values?

0
#173627

Laura
Participant

You may want to check whether the target value is in the same units that you are using for the process average.If target is in dBm and average is in mW, then Cpk may not be correct.Thanks.

0
#173628

Baker
Participant

All of the data and upper/lower specs and target value is in dBm.  However, when I convert everything (specs, data, target) to mW, I get a different Cpk value.

0
#173631

Ron
Member

One significant and common mistake is the order of yoiur data. To truly do a capability study you must maintain the order in which they data was taken i.e sample 1, 2,etc. if you rearrange the order you will get different values.

0
#173650

Participant

Ron, what is that?  The order is not important for calculating CpK.  Err…if it is, please explain it to me. I am always open to learn something.
To the original question. There should be no difference in the CpK. This statististic is not related to the measurement unit. You may have a rounding error, or since I am not familiar with your transformation, the two units of measure are not simple multiples of each other. But, I would check my data first for errors.
Good luck.

0
#173664

DaveS
Participant

Order of the data for Cpk is essential for individuals because the moving range is profoundly influenced by order and std deviation is estimated by control chart methods. If subgroups are used, this is not the case as range within subgroups is not order dependant. Ppk is not affected at all since the RMS std. dev. estimate is used.
To the original posters question, I modeled a simple set of data, using 50 values from N(5,3) and then transformed this simulated mW set to dBm using 10{log(base10)(mW)}.
The mW set was normal of course but the dBm set was skewed right to best be fit by 3 param Weibull. I suspect that is why you are getting differing metrics. The Cpk metric is somewhat sensitive to the normality assumption and a non-linear transform of the data like the dB conversion is NOT just a simple change of units of measure. It fundamentally changes the shape of the data.

0
#173680

ROSS
Member

I agree with Daves point. There is a non-linear relationaship between dBm and mW and the distribution of the data in each type of unit should be explored to ensure normality by transformation if necessary. At the end of the day “which unit of measure is most important to the customer – dBm of mV”? That is the one that should be used.

0
#173690

scoben
Member

Ron (or should I say math professor),
What school of mathematics did you go to?  Run order has nothing to do with capability.  Run order is important for things like control charts, but you better go back and look at how capability analysis is performed.  Data collected goes into buckets based on how well your measurement system can detect one value from another and then compares those buckets to your spec range.  There are different types of distributions and different types of capability analysis that can be performed and none have anything to do with run order.  My suggestion is you test this out by taking a data set, maintaining run order, and perform capability analyis.  Then mix up the data and repeat the analysis.  You will get the same results.

0
#173692

scoben
Member

Another math wizard.  I think you are confusing control charting with capability analysis.
Michael was 100% completely correct in his response.  If the conversion from one unit to the other is linear then the Cpk results should be equivalent.

0
#173696

ncwalker
Participant

Ron went to the right school of mathematics.In the auto industry, at least, incorrect calculation of Cp/Cpk is rampant. Most are calculating Cp asCp = (USL – LSL)/6sigmaand Cpk asCpk = min(USL – mean, mean – LSL)/3sigmaThat sigma is the population, or RMS standard deviation. These calculations are for Pp and Ppk – the LONG TERM capability indices.The true calculation of Cp and Cp is short term and it uses ranges and estimates of ranges to estimate sigma. Order DOES matter very much.Try this – generate a population of random normal data in Minitab. Run the capability sixpack function.Then SORT the list and re-run the capability sixpack. You will see the Pp/Ppk number don’t change whereas the Cp/Cpk numbers change drastically.Do you homework before you bust on someones answer. There are lots of people who use this forum as a learning tool. Off the cuff doesn’t cut it.

0
#173699

Participant

Thanks for the support Scoben, but even I agree with Ron, etal., a little.  If you mix the observation between samples or use the individual and moving range chart, then you might get some different results. Since the range will change if different extreme points are in the sample, the estimated standard deviation from the range can also change.
Now, if the samples throughout the process were drawn from the same population, thus the range estimate would be a good long-term measure, the results would be the same.
Thanks also to Mr. Bothe for verifying my assumption about the data transformation.

0
#173701

walden
Participant

Scoben,
Run order can and does have an effect on Cpk. This is a reason why one of the first rules for capability studies is maintaining the order of production. I’ve been working with this for over 20 years and have seen examples of the order changing Cpk values many, many times.
Depending on the subgroup size, variation in the data, etc, the effect on Cpk can be negligible or quite significant. Anyone who says it doesn’t make any difference on Cpk, doesn’t understand. I agree that it shouldn’t have any effect on Ppk, but Cpk is a different story.
What software are you using to calculate Cpk? I assume you are estimating Cpk using the Rbar/d2 formula.
Chris

0
#173703

George Chynoweth
Participant

If I remember properly from my audiophile days, a 3db increase requires twice the power (watts). So, if 50 watts gives you 100 dbm, 100 watts will give you 103 dbm. This power relationship, as mentioned previously, is what is tripping up your calculations.hth,
G

0
#173733