# Ppk or Cpk - Preliminary Process Capability vs. Process Performance

B

The 2nd edition of PPAP says we are suppose to calculate "Preliminary Process Capability" in the form of Ppk, and yet the SPC Ref. Manual says Ppk is "Process Performance" while Cpk is "Process Capability" ….so what gives?

Also by the definition of Ppk and Cpk formula, Ppk value cannot be greater than Cpk since the "sigma" in Ppk includes both common and special causes of variation. And yet the acceptance for Ppk is supposedly 1.67 but for Cpk it's 1.33.

Anyone's got an insight to this?????

Staff member
First, although some time ago, I found this in a search from 1997:

David McGan
Contributor posted 03 August 1997 11:08 AM
----------------------
I'm almost embarrassed to ask the question, but I've not been able to find a good, clear explanation of the real difference between the Ppk and Cpk indices. Ppk, I know, is usually specified for short-term study results, and uses the calculated standard deviation in its determination. Cpk, on the other hand, is used for long-term study results, and uses the estimated standard deviation in its calculation. But can anyone give me the statistical rationale for this?
-----------snippo-----------

I'm a generalist. Take a look at http://Elsmar.com/ubb/Forum10/HTML/000021.html and see if that helps. Also see http://Elsmar.com/ubb/Forum10/HTML/000024.html

If those don't help, come back to this thread, or post a reply in either (or both) of the threads.

[This message has been edited by admin (edited 01 October 1999).]

D

#### Don Winton

Hmmm. Lets see. First, thanks for ‘lighting the bulb.’ I have been busy this past few weeks and had forgotten this was posted. My apologies for the delayed response.

First, as seen in the links Marc gave I have made my feelings about this whole Ppk thing known. I feel it is just a gimmick that the AIAG group uses to muddy the water. Just MHO.

Typically, Ppk uses sample standard deviation (s) while Cpk uses an unbiased estimate if sigma (sigma hat). The reason (I suppose) is that there may be occasions where this is more applicable. This is not true. Even with small sample sizes, an unbiased estimate of sigma can still be obtained.

As far as the 2nd edition of the PPAP manual goes, I ain’t gotta clue. As I have stated before, I do not do the QS thing.

Regards,
Don

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Just the ramblings of an Old Wizard Warrior.

D

#### DPeter

Ppk vs Cpk

Cpk is the 6 sigma range of a process's inherent variation where Sigma is estimated by R bar (Range Average) / D2 for the Sample Size.

Ppk is the 6 sigma range of a process's total variation where Sigma is estimated by the samples standard deviation.

Cpk is an on-ging activity. Ppk is used as a "snapshot" of the process variation at any given point in time. Ppk is useful to determine if a process will be capable (Cpk) if process conditions maintain stability. It is also useful for determining if a continious improvement activity has had an effect on the process.

Daryl

B

#### Bill Pflanz

First, although some time ago, I found this in a search from 1997:

David McGan
Contributor posted 03 August 1997 11:08 AM
----------------------
I'm almost embarrassed to ask the question, but I've not been able to find a good, clear explanation of the real difference between the Ppk and Cpk indices. Ppk, I know, is usually specified for short-term study results, and uses the calculated standard deviation in its determination. Cpk, on the other hand, is used for long-term study results, and uses the estimated standard deviation in its calculation. But can anyone give me the statistical rationale for this?
-----------snippo-----------

I'm a generalist. Take a look at http://Elsmar.com/ubb/Forum10/HTML/000021.html and see if that helps. Also see http://Elsmar.com/ubb/Forum10/HTML/000024.html

If those don't help, come back to this thread, or post a reply in either (or both) of the threads.

[This message has been edited by admin (edited 01 October 1999).]
This is an interesting resurrection of some old threads.

First, it shows how much message boards have advanced since 1999.

Second, it shows that the topic of how to calculate and interpret Cpk has not advanced at all since 1999.

Third, it is humorous that Don Winton suggested reading Sun-Tsu's The Art of War to understand Cpk. I read the book imore than 10 years ago and I am positive it did not mention Cpk so Don must have been taking some literary license in referring to it. I asked for the history of Cpk in another thread but I believe we can narrow it down to happening between the death of Sun-Tsu (470 BC) and 1990 if that helps anyone remember.

Bill Pflanz

#### niotusen

##### Registered Visitor
Cpk is the 6 sigma range of a process's inherent variation where Sigma is estimated by R bar (Range Average) / D2 for the Sample Size.

Ppk is the 6 sigma range of a process's total variation where Sigma is estimated by the samples standard deviation.

Cpk is an on-ging activity. Ppk is used as a "snapshot" of the process variation at any given point in time. Ppk is useful to determine if a process will be capable (Cpk) if process conditions maintain stability. It is also useful for determining if a continious improvement activity has had an effect on the process.
//

Back to my problem!
When our customers want information of our process they always want a Cpk value, this value should it bee Ppk or Cpk?

The Ppk tells me how the process has been or lokked like? Or should I present the cpk value at "right" this time when we are processing our process, because this only take some of the near subgroups/samples depending how many soubgroups (50 or sometimes 25 subgroups deepending of the process) my calculations take to the Cpk calculation from the process?

Should the customer ask for Ppk value instead? Cpk value is more for us as a producer who can control the process?
Any suggestions?
Thanks!

#### Darius

##### Quite Involved in Discussions
niotusen said:
Should the customer ask for Ppk value instead? Cpk value is more for us as a producer who can control the process?
Any suggestions?
Thanks!
The main issue of Cpk (against ppk) is altho both use the same data (or could use it), ppk's variation estimate (total variation) is affected with the outliers a lot more than it's conterpart ( Cpk uses within variation estimate).

There are other effects that affect Cpk that most of the SPC software don't take in account (like autocorelation, a shame...). If, and only "if", the process it self is not represented by the Cpk value, you may have such kind of problem. And too much variation on indicator could be because of the sample size, many take Cpk or ppk indicators as an absolute value without the sample size concern.

Maybe not the common way to put the things, but if ppk is a good indicator.. why the control limits are using the within variation estimate?. The within variation estimate for variation show us the process variation not the data variation, it's like with "normalizing" data, you can obtain estimates that with the raw data (all) you will need much more data points.

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#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Yes, it still amazes me that people don't yet understand the Cpk/Ppk thing. It is very clear in the literature how to calculate and use each one...although as time goes by tpp many practitioners have looked for the "cliff notes" version wich too often was written by soemone who really didn't understand Cpk and Ppk...and the AIAG shortcut approach makes it worse (they aren't wrong - just not clear on why they do what they do and so there is a lot of confusion). This is further compounded by too many people usign "Cpk" when they Mean Ppk...(everytime I've probed this - >50 separate organizations - I find that hte formula teh requestor wants is the formual for Ppk, they just call it Cpk...ARRGH!

But even with the above said, Cpk and Ppk are really just psuedo statistics: trying to reduce variation to a single number. Maybe it's voodoo statistics??

back in 1992 the journal of quality technology ran a full issue of capability index articles...then editorially stated that they woudl never accept another article on capability indexes because they weren't statistically appropriate. (Although I believe tehy have given on that statement since then). Perhaps we should follow their initial lead and pass citizen based referendums to outlaw the use of these indexes???

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Bev D said:
Perhaps we should follow their initial lead and pass citizen based referendums to outlaw the use of these indexes???
Where can I sign?

By the way, I am teaching an MBA course on Operational Management this quarter. The textbook I am to teach from tells me that when doing SPC, you put the target value as the center line and calculate the control limits about that.

No wonder our MBA's in this country are so . . . well, hosed up.

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#### Tim Folkerts

Super Moderator
While I empathize with the desire to get rid of capability indices because they oversimplify compex processes to a single number, it begs the question as to what is a reasonable simplification.

Should we ban the calculation of averages, because it oversimplifies the central tendency to a single number?
Should we ban the calculation of st dev's, because it oversimplifies variation to a single number?

The opposite extreme would be to simply pass on the raw data and make the customer/boss/auditor draw their own conclusions.

Of course, both extremes are sometimes useful, and both extremes sometimes obscure interesting information. The challenge is to find a reasonable degree of simplification for the need at hand. Sometimes a single number, like Cpk or mu, is helpful. Sometimes it is almost valueless.

(The challenge of choosing the right index and performing the correct calculations is problematic, but it is a separate issue. )

Tim F

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