Cpk / Ppk units of measure
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 This topic has 13 replies, 10 voices, and was last updated 14 years, 1 month ago by Michael Mead.

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July 8, 2008 at 3:18 pm #50499
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?
0July 8, 2008 at 5:13 pm #173627You 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.
0July 8, 2008 at 5:23 pm #173628All 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.
0July 8, 2008 at 6:10 pm #173631One 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.
It’s all about the mathematics0July 9, 2008 at 1:10 am #173650
Michael MeadParticipant@MichaelMead Include @MichaelMead in your post and this person will
be notified via email.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.0July 9, 2008 at 2:52 pm #173664Order 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 nonlinear 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.
0July 10, 2008 at 7:44 am #173680I agree with Daves point. There is a nonlinear 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.
0July 10, 2008 at 11:58 am #173690Ron (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.0July 10, 2008 at 12:02 pm #173692Another 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.
0July 10, 2008 at 1:08 pm #173696
ncwalkerParticipant@ncwalker Include @ncwalker in your post and this person will
be notified via email.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 rerun 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.
0July 10, 2008 at 1:28 pm #173699
Michael MeadParticipant@MichaelMead Include @MichaelMead in your post and this person will
be notified via email.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 longterm measure, the results would be the same.
Thanks also to Mr. Bothe for verifying my assumption about the data transformation.0July 10, 2008 at 2:20 pm #173701Scoben,
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.
Chris0July 10, 2008 at 2:44 pm #173703
George ChynowethParticipant@georgechynoweth Include @georgechynoweth in your post and this person will
be notified via email.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,
G0July 11, 2008 at 1:40 am #173733
Michael MeadParticipant@MichaelMead Include @MichaelMead in your post and this person will
be notified via email.I think eveyone understands that moving an observation from one sample subgroup to another can mess up the calculation. But rearranging the observations within the sample, or moving the sample to another position in a list of samples will have no effect. COnsider this:
1 2 3 4 5 Range = 4, Average = 3
2 4 1 5 3 Range = 4, Average = 3
Since the calculations for CpK are based on the average range, where an individual range is essentially the 2 extreme values in a subgroup, order within the subgroup is inconsequential.
Also, the average range is just the average range, it does not care which subgroup comes first, or last, or anywhere within the group of samples.
However, if an observation is taken from one subgroup and placed in another, this can change the range of one or both subgroups which can alter the average range of all subgroups.0 
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