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Related Topic Tags
process capability, statistical analysis and studies, variation (misc), variation (process), data subgroups, cpk (related to process capability), ppk (related to process performance)
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  #1  
Old 31st August 2011, 04:32 AM
Stevenli's Avatar
Stevenli

 
 
Posts: 31
Please Help! 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

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  #2  
Old 31st August 2011, 08:48 AM
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Darius

 
 
Posts: 533
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!
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  #3  
Old 31st August 2011, 12:37 PM
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Bev D

 
 
Posts: 2,960
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!
  #4  
Old 19th January 2014, 10:01 PM
Venx Chen

 
 
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
  #5  
Old 20th January 2014, 06:18 AM
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Bev D

 
 
Posts: 2,960
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!
  #6  
Old 22nd January 2014, 11:18 PM
Venx Chen

 
 
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
  #7  
Old 23rd January 2014, 06:03 AM
Bev D's Avatar
Bev D

 
 
Posts: 2,960
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...
  #8  
Old 23rd January 2014, 09:23 AM
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Steve Prevette

 
 
Posts: 2,334
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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