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# Ppk & Cpk - Within Subgroup Variation is always smaller than Total Variation

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Post Number #1
31st August 2011, 04:32 AM
 Stevenli Total Posts: 45
Ppk & Cpk - Within Subgroup Variation is always smaller than Total Variation

There are a lot of thread to discuss the Cpk and Ppk, short-long vs. long term, or in other words within subgroup varaiation vs. total variation. My question is within subgroup variation is always smaller than total varation, so the Ppk is smaller than Cpk in Minitab. Is this true? I have run a case in Mintab that Cpk is smaller than Ppk. I am confused that how it comes.

Does anyone have some good ideas of that?

Thanks a lot.

Best Regards
Steven

Post Number #2
31st August 2011, 08:48 AM
 Darius Total Posts: 553
Re: Ppk & Cpk - Within Subgroup Variation is always smaller than Total Variation?

Well in "Advanced topics on SPC" Don Wheeler said that this can be the case (ppk<Cpk) if there is wrong sample grouping, I can fire out a case, if there is a small difference between them (aka almost equal values), remember that this variation estimates are only that "estimates", so the possible variation on that estimate can produce this effect (ppk<Cpk), but in reallity are just the same value.

Total Variation = Within Variation + between variation + trend Variation
 Thank You to Darius for your informative Post and/or Attachment!
Post Number #3
31st August 2011, 12:37 PM
 Bev D Total Posts: 3,592
Re: Ppk & Cpk - Within Subgroup Variation is always smaller than Total Variation?

yes within subgroup variation is always less than total variation, so Ppk will be less than Cpk for the same dataset.

Ppk can be mathematically greater than Cpk IF you have chunky data AND particularly if you are using the Range method of estimating the datandard deviation.

If you post your data set, we can provide a specific answer
 Thank You to Bev D for your informative Post and/or Attachment!
Post Number #4
19th January 2014, 11:01 PM
 Venx Chen Total Posts: 5
Re: Ppk & Cpk - Within Subgroup Variation is always smaller than Total Variation?

15.00 18.00 16.00 18.00 15.00 15.00 18.00 16.00 18.00 15.00 19.00 18.00 16.00 18.00 15.00 15.00 18.00 16.00 15.00 15.00 15.00 18.00 16.00 18.00 15.00
20.00 13.00 13.00 16.00 16.00 20.00 13.00 13.00 16.00 16.00 15.00 13.00 13.00 16.00 16.00 20.00 13.00 13.00 16.00 16.00 20.00 13.00 13.00 16.00 16.00
16.00 16.00 18.00 16.00 13.00 16.00 16.00 18.00 16.00 13.00 12.00 16.00 18.00 16.00 13.00 16.00 16.00 18.00 16.00 13.00 16.00 16.00 18.00 16.00 13.00
17.00 18.00 15.00 20.00 12.00 17.00 18.00 15.00 20.00 18.00 17.00 18.00 15.00 20.00 13.00 17.00 18.00 15.00 20.00 18.00 17.00 18.00 15.00 20.00 12.00
12.00 18.00 12.00 16.00 16.00 12.00 18.00 12.00 16.00 16.00 16.00 18.00 12.00 16.00 16.00 12.00 18.00 12.00 16.00 12.00 12.00 18.00 12.00 16.00 16.00

hello My data as above. why is the PPK greater than CPK? thanks
Post Number #5
20th January 2014, 07:18 AM
 Bev D Total Posts: 3,592
Re: Ppk & Cpk - Within Subgroup Variation is always smaller than Total Variation?

Off hand I would say it is because you have chunky data (lack of resolution, only a few values represented)

However, to provide a more comprehensive answer, we need to know how the data is subgrouped, what the characteristic being measured is, what the process is and what the spec limits are....
 Thanks to Bev D for your informative Post and/or Attachment!
Post Number #6
23rd January 2014, 12:18 AM
 Venx Chen Total Posts: 5
Re: Ppk & Cpk - Within Subgroup Variation is always smaller than Total Variation?

thanks for your reply, Bev. here is another group data which PPK is greater than CPK as well. i can give you much more info.this dimension is the height of a injection part, spec.:2.50+/-0.25, measured by projector machine. the samples are taken continuously. could you help to analysis? thanks
BTW, you said it has been discussed a lot in this forum, but couldn't find the thread or post..
n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2.53 2.47 2.45 2.56 2.54 2.50 2.51 2.55 2.47 2.54 2.45 2.50 2.51 2.51 2.42 2.60 2.55 2.52 2.48 2.55
2 2.52 2.60 2.48 2.54 2.50 2.52 2.48 2.55 2.53 2.46 2.48 2.45 2.42 2.44 2.46 2.48 2.53 2.50 2.51 2.46
3 2.48 2.40 2.45 2.53 2.44 2.49 2.59 2.49 2.58 2.55 2.50 2.42 2.54 2.42 2.60 2.55 2.40 2.57 2.55 2.48
4 2.52 2.58 2.51 2.51 2.56 2.49 2.51 2.47 2.53 2.48 2.52 2.50 2.48 2.46 2.48 2.51 2.50 2.61 2.44 2.51
5 2.58 2.48 2.51 2.46 2.49 2.47 2.47 2.50 2.50 2.55 2.50 2.55 2.56 2.52 2.52 2.50 2.51 2.46 2.53 2.53
n 21 22 23 24 25
1 2.56 2.50 2.41 2.46 2.47
2 2.47 2.45 2.53 2.43 2.48
3 2.56 2.46 2.59 2.48 2.51
4 2.42 2.54 2.55 2.56 2.48
5 2.57 2.50 2.52 2.50 2.51
Post Number #7
23rd January 2014, 07:03 AM
 Bev D Total Posts: 3,592
Re: Ppk & Cpk - Within Subgroup Variation is always smaller than Total Variation?

Is Your subgroup size 5 with 25 subgroups?

Pasting the data into the post loses all formatting and is difficult to work with. It is better to attach an excel file with data properly formatted...
Post Number #8
23rd January 2014, 10:23 AM
 Steve Prevette Total Posts: 2,513
Re: Ppk & Cpk - Within Subgroup Variation is always smaller than Total Variation?

As usual, I must state "IT DEPENDS"

If all of the components going into the total variation are independent from each other, then the component variation will be less than the total.

However, I may have two components that are dependent upon each other, which have more variation than their total. As a simple example, consider the following six results from two production lines:

A: 0, 1, 0, 1, 0, 1
B: 1, 0, 1, 0, 1, 0

The total variation of these two processes is ZERO!
 Thanks to Steve Prevette for your informative Post and/or Attachment!

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