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?

I'm embarrassed to answer after 3 years or so, so I guess we're belatedly even...

I was reviewing some posts during a search and found this oldie. Well, most questions get answers (sooner or later)...

I can't give you a statistical rational - maybe Don will see this and comment.

The differences are:

Pp

The Pp index is used to summarize a system's performance in meeting two-sided specification limits (upper and lower). Like Ppk, it uses actual sigma (sigma of the individuals), and shows how the system is actually running when compared to the specifications. However, it ignores the process average and focuses on the spread. If the system is not centered within the specifications, Pp alone may be misleading.

The higher the Pp value...
...the smaller the spread of the system’s output. Pp is a measure of spread only. A process with a narrow spread (a high Pp) may not meet customer needs if it is not centered within the specifications.

If the system is centered on its target value...
...Pp should be used in conjunction with Ppk to account for both spread and centering. Pp and Ppk will be equal when the process is centered on its target value. If they are not equal, the smaller the difference between these indices, the more centered the process is.


Ppk

Ppk is an index of process performance which tells how well a system is meeting specifications. Ppk calculations use actual sigma (sigma of the individuals), and shows how the system is actually running when compared to the specifications. This index also takes into account how well the process is centered within the specification limits.

If Ppk is 1.0...
...the system is producing 99.73% of its output within specifications. The larger the Ppk, the less the variation between process output and specifications.

If Ppk is between 0 and 1.0...
...not all process output meets specifications.

If the system is centered on its target value...
...Ppk should be used in conjunction with the Pp index. If the system is centered on its target value, Ppk and Pp will be equal. If they are not equal, the smaller the difference between these indices, the more centered the process is.


Pr

The Pr performance ratio is used to summarize the actual spread of the system compared to the spread of the specification limits (upper and lower). The lower the Pr value, the smaller the output spread. Pr does not consider process centering.

When the Pr value is multiplied by 100, the result shows the percent of the specifications that are being used by the variation in the process. Pr is calculated using the actual sigma (sigma of the individuals) and is the reciprocal of Pp. In other words, Pr = 1/Pp.


Cp

The Cp index is used to summarize a system's ability to meet two-sided specification limits (upper and lower). Like Cpk, it uses estimated sigma and, therefore, shows the system's potential to meet the specifications. However, it ignores the process average and focuses on the spread. If the system is not centered within the specifications, Cp alone may be misleading.

The higher the Cp value...
..the smaller the spread of the system’s output. Cp is a measure of spread only. A process with a narrow spread (a high Cp) may not meet customer needs if it is not centered within the specifications.

If the system is centered on its target value...
Cp should be used in conjunction with Cpk to account for both spread and centering. Cp and Cpk will be equal when the process is centered on its target value. If they are not equal, the smaller the difference between these indices, the more centered the process is.


Cpk

Cpk is a capability index that tells how well as system can meet specification limits. Cpk calculations use estimated sigma and, therefore, shows the system's "potential" to meet specifications. Since it takes the location of the process average into account, the process does not need to be centered on the target value for this index to be useful.

If Cpk is 1.0...
...the system is producing 99.73% of its output within specifications. The larger the Cpk, the less variation you will find between the process output and specifications.

If Cpk is between 0 and 1.0...
...not all process output meets specifications.

If the system is centered on its target value...
...Cpk should be used in conjunction with the Cp index. Cpk and Cp will be equal when the process is centered on its target value. If they are not equal, the smaller the difference between these indices, the more centered the process is.


Cpm

The Cpm index indicates how well the system can produce within specifications. Its calculation is similar to Cp, except that sigma is calculated using the target value instead of the mean. The larger the Cpm, the more likely the process will produce output that meets specifications and the target value.

Cr

The Cr capability ratio is used to summarize the estimated spread of the system compared to the spread of the specification limits (upper and lower). The lower the Cr value, the smaller the output spread. Cr does not consider process centering.

When the Cr value is multiplied by 100, the result shows the percent of the specifications that are being used by the variation in the process. Cr is calculated using an estimated sigma and is the reciprocal of Cp. In other words, Cr = 1/Cp.

[This message has been edited by Marc Smith (edited 15 February 2000).]

I'm not Don, but I'll open the door for Don to agree or disagree with what I've understood the difference to be :)

I think the key is the fact that the estimated std. dev used for Cpk, being R-bar/d2 from the control chart, and the PPk be an actual std. dev. calculated on 100 individuals. R-bar/ d2 only takes into account "within subgroup variation", not "between subgroup variation" which the Ppk calculation would. If "all" process variation is present within the subgroups, then Cpk and Ppk will be very close. Selection of your sampling plan for the control chart are very relavant to the R-bar/d2 calculation.

Picture a process which has extremely tight within subgroup variation, but due to other circumstances, has variation - possibly acceptable variation...when the room warms up, tool wear, batches of raw material, etc. 5 consecutive pieces may have a Range near zero, but during a 20 day period x-bar's move. R-bar /d2 is not a good estimate of overall process variation. I never calculate a Cpk or Ppk without looking at the control chart. Moreso than looking at the control chart, you need to know how the numbers are generated to determine appropriate "rational subgroups."

Laura,

You are correct. I have been on a ten-week hiatus while I sorted some things out. I am now back at work and trying to get caught up.

Personally, I find all this Cpk/Ppk stuff too confusing. For almost 15 years, the 'C' values were working just fine, then all this 'P' stuff popped up. I ignore the 'P' stuff and just keep with what I know. This is my take on the difference.

In 1990, while a member of the Technical Staff at Hughes Aircraft Company, a gentleman named Suozzi wrote an excellent paper on process capability. It is the basis for the CPK.PDF paper of mine posted here at the PDF zone.

For Cpk calculations to be used, an unbiased estimate of sigma should be used. Calculations for Cpk use either the sigma symbol of the word "sigma." More accurately, the symbol sigma-hat should be used, since this is the graphical symbol for an unbiased estimate of sigma. Typically, sample sizes greater than 60 give an unbiased estimate of sigma so close to the actual sigma that correction factors are not needed. When the sample size is less than 60, a correction factor (designated C4) is used to obtain a more accurate estimate of sigma (this is explained in Souzzi's paper as well as mine and is based on a derivation from Grant and Leavenworth). Since the inception of Cpk, all the work I have seen has used either sigma or sigma-hat as the representation of the standard deviation.

Going back to basic stats for a moment, the calculation for standard deviation has either one of two possibilities in the denominator: n-1 or n. In school, when you knew the data for the population, you used n. When you did not know the data for the population, you used n-1. The two different types of standard deviation were designated by either sigma (population) or a lower case s (sample). Thus, just using simple logic, you would assume that Cpk is calculated for the population.

I asked the question here once what the AIAG used (I stay as far away from their stuff as I can. Gives me headaches), as the symbol in their method of calculating Ppk and the answer was the lower case s. Thus, it would seem to indicate that Ppk is the process capability for a sample and Cpk is the process capability for the population.

For process capability taken from a control chart, the same rules apply. If you have readings on more than 60 samples, a correction is not needed, less than 60, it is. Personally, I do not like this method and prefer to calculate process capability based on observed data, not recorded data. But, that is just my preference.

And I still think all this is too confusing.

Regards,

Don

[This message has been edited by Don Winton (edited 29 March 2000).]

Now that certainly clears everything up! Thanks.

yea!!

is too confusing, only that i´m sure on ppap requirements gm wants to use a ppk > 1.67 or Cpk> 1.33.

so when i need to re-ppap my parts for some reason i presented to them ppk and guess what ???

they are happy !!!!

bye

By the way, Don, your paper CPK.pdf has been downloaded 525 times so far this month alone.

By the way, Don, your paper CPK.pdf has been downloaded 525 times so far this month alone.

I am glad some are finding it useful. Or at least, I hope they are.

Regards,
Don

[This message has been edited by Don Winton (edited 29 March 2000).]

Main Entry: ca·pa·bil·i·ty
Pronunciation: "kA-p&-'bi-l&-tE
Function: noun
Inflected Form(s): plural -ties
Date: 1587
1 : the quality or state of being capable; also : ABILITY
2 : a feature or faculty capable of development : POTENTIALITY
3 : the facility or potential for an indicated use or deployment {the capability of a metal to be fused} {nuclear capability}

As I have re-read this and other posts concerning process capability, it occurred to me that an assumption is being made that just ain't so:

Process capability is not a metric. But, it appears that is the assumption. The process capability index is a calculation made based upon data collected that determines if the process has the ability or potential[/b] to produce conforming product. There is no guarantee the process will do so.

Regards,

dWizard

Received my copy of Juran's Quality Handbook, 5th Edition a couple of days ago and found this of interest:

Ppk = Cpk-hat

The handbook defines Cpk as process capability and Ppk as process performance (Page 22.18).

Also, page 22.18 uses sigma in the denominator, but page 22.20 uses 's'.

Regards,

dWizard

I have only recently (just like your postings ironically) been trying to figure out the difference between Cpk and Ppk. I first went to the QS-9000 SPC manual for guidance. I may be mistaken, but the manual seems to indicate that Cpk is a measure of process capability after disregarding any data recorded during a "special cause". "Special cause" being something that is not normal machine operation. Cpk seems to be calculated only with data collected under steady-state (?) and the process is under control. Therefore, the sigma used to calculate Cpk would be smaller than an unbiased sigma. The unbiased sigma would take into account all data, regardless of control. As I understand it, Ppk is calculated using this unbiased sigma. Resulting in Ppk values being smaller than Cpk values. It is assumed that Cpk values would be calculated with a smaller sigma, since the sigma is biased. This has all been a learning experience, but I am still unsure if my thinking is correct or not. Cpk = process capability under process control, disregarding "special causes"? Ppk = actual capability taking into account all data? It would seem that customers would demand higher Cpk values than Ppk values. I think I am confusing myself now! Think I have more reading to do. Any help out there?

http://elsmar.com/pdf_files/Cp.gif
Used by permission of Red Road.

http://elsmar.com/pdf_files/Cpk.gif
Used by permission of Red Road.

There are other Cpk definitions. For instance, for the french automakers the Cpk must be calculated using the actual standard deviation calculated on individuals. With this definition the only difference between Cpk and Ppk is the way to take the samples for the calculation: for the Ppk, samples are taken in a row, minimising the sources of variation. Check http://www.cnomo.com to see how Cpk is calculated using the norm of the french automakers.

I'm very glad to see that I'm not the only one confused by the Ppk / Cpk choice.

Trying to put this into an example situation:-

Let's say we were in the process of purchasing a new M/C'ing line for a component. The M/C tools would first undergo a PDI at the M/C Tool manufactures site involving a limited part capability run.

After breaking down, shipping and re-building at the production plant, the individual M/C's and the line as a whole would then be subject to further capability studies.

From the previous corespondences, would I be correct in deriving the following?

60 part individual M/C tool capability run at M/C tools manufactures site:- Cpk
60 part individual M/C tool capability run at production plant:- Cpk
Larger line capability study at production plant:- Ppk

Am I going down the correct street or can someone re-direct me.

Thanks,
Iain

Some thoughts:

From: "Wayne Lundberg"
Newsgroups: misc.industry.quality
Subject: Re: what is Cpk ?????????
Date: Thu, 18 Jan 2001 01:13:22 GMT

"Jed Palmer" wrote in message
news:944h0g$arq$1@news6.svr.pol.co.uk...
> The term Cpk is used in statistical techiniques. Could someone tell me what
> it actually means, and any other helpful information would be gratefully
> received.
>
> Jed

What it boils down to - is your process capable of making the parts within the required tolerances. If your part must be half inch plus or minus 5 thousandths, then a Cpk of 100 would mean that you should make parts within those tolerances day in and day out as long as the process is under control. So a lot of buyers are demanding 120 or more Cpk which means your system is 120% (roughly) capable of making the parts within tolerance. Then add to this the three and six sigma stuff and it really gets confusing.

Bottom line - make sure your process can make the required tolerances within the one sigma of 68% and will never go to the second or third sigma. Fine tune, adjust, maintain, fine tune, adjust and maintain process control. That's how you get zero defects.

**********************************

From: "Michael Schlueter" philips.com
Newsgroups: misc.industry.quality
Subject: Re: what is Cpk ?????????
Date: Thu, 18 Jan 2001 13:52:24 +0100
Organization: Customer of UUNET Deutschland GmbH

A practical tool to make this process a success is utilizing Taguchi's method.

A warning: do not try to optimize on Cpk. Do not even think to do so. Optimize your intended result instead.

Example: Assume you have to manufacture weights of different masses. You could *monitor* this process by monitoring its Cpk's. To improve the process itself, you should compare "intended mass (x-axis)" with "manufactured mass (y-axis)". If your process works fine, you will have a straight line, with slope 1.00 and very little deviation from the linear curve (intended result). If you have problems you will see it as deviation from this linear case (symptoms, unwanted conditions).

Taguchi provides a signal-to-noise ratio (SNR=10*lg(beta^2/sigma^2)) for these kinds of problems. The objective is to increase SNR. This means in turn: reduce sigma down to zero. If you read all equations properly you will see that Cpk-improvement is very closely related to SNR-improvement. The difference between SNR and Cpk is simple: SNR is known to be more predictable.

That is, if you change one parameter, which will increase SNR and another, which will also increase SNR, you can expect that both changes together will increase SNR even more. Look for "Parameter Design" in your library. Parameter Design helps you also to avoid a common (fatal) 'game': adjust tolerances with respect to measured process spread to 'improve Cpk'. It is just vice versa: fix tolerances, even narrow down tolerances and drive sigma towards zero, while increasing Cpk.

Michael Schlueter

Does anyone have any knowledge on this?

> From the previous corespondences, would I be correct in deriving the
> following?
>
> 60 part individual M/C tool capability run at M/C tools manufactures site:-
> Cpk 60 part individual M/C tool capability run at production plant:- Cpk
> Larger line capability study at production plant:- Ppk
>
> Am I going down the correct street or can someone re-direct me?

It's really pretty simple:

Cp - process CAPABILITY if process was centered and fully stable - the very best the process could be - assumes process is stable and centered on target - no subsample to subsample variation

Cpk - process CAPABILITY if instability were removed - assumes process is not necessarily centered - assumes process is fully stable - no subsample to subsample variation

Pp - process PERFORMANCE if centered on target - assumes process is centered on target but uses the actual process variation, including any instability (subsample to subsample variation)

Ppk - the actual process PERFORMANCE - including both lack of center variation and instability (subsample to subsample variation)

By comparing these four indices to each other you can understand the extent how off-target and unstable the process is, although it would be easier to just give the mean & standard deviation of the process and then visually compare it to the specs.

Ken is got it...........
to explain it Mathmatically

Cp = USL-LSL / 6 Sigma (Where sigma is a estimate [Rbar / d2] from a control chart. It looks at ranges within subgroups and estimates sigma. It does not account to subgroup to subgroup varations.

Pk = USL-LSL / 6 Sigma (where sigma is calculated from the entire sample (RMS))

So if you had 100 parts in 20 subgroups of 5. PPk looks at all 100 to determine, where Cp is going to estimate sigma based on the ranges of the 20 subroups, and then averages all 20 of the Ranges to give you Rbar. then based on your subgroup size (in this case 5) your use a constant d2 to determine estimated sigma, or sigma hat.

PPK or Cpk used the same equations except for how it calculates the sigma in the denominator.

Min. of [(USL-Mean) / (3 Sigma)] or [(Mean - LSL) / (3 Sigma)] .

where USL=Upper Spec Limit &
LSL = Lower Spec Limit

Hope that clears it up.

OK, time for me to chime in. I realize I,m so far down the page, this probably won't be read, but here goes.
In this whole discussion over the differences in the two calculators (Cpk,Ppk,)the wrinkle is which one to use and when. First, let me premise my statement by using an excerpt from Dr. Demings book "Out of Crisis",
"The aim in production should be not just to get statistical control, but to shrink variation. Cost go down as variation is reduced. It is not enough to meet specifications. Moreover, there is no way to know that one will continue to meet specifications unless the process is in statistical control. Until special causes have been identified and eliminated, one dare not predict what the process will produce the next hour... Your process may be doing well now, but yet turn out parts beyond the specification limits later."
My point in bringing this up comes from my experience as a former CMM operator who worked for a machine manufacturer. We built machines that made various parts for our customers. Those customers required that our machines met certain Capability requirements and would continue to meet those requirements over an extended period of time.
I wrote programs to inspect the dimensions of their parts and stored all the data from those parts in the statistical register of the software.
HERE IS THE POINT. While the set-up technician was in the process of tool-setting to meet the parameters, there would be a series of "pre-runoff" trials in which we would collect the data and render capability numbers based upon Ppk, because the individual population variation was of the utmost importance to discover and remove "special cause" variation. Once all special cause variation had been removed, and the process had been centered on the mean or target value, and the values were consistently running at 50-75% of the spec. limits, which will render Ppk values at 1.0 or better, then we began to tweak the process to bring Cpk values to meet the customer requirements.
Once we were running an "In-Control & Centered Process", then we proceeded with the machine run-off and provided the data to the customer that proved the machine would consistently run at 1.33 for major characteristics and 1.67 Cpk for critical characteristics over a period of time designated by the customer.
The KEY here is that each individual was important until all special cause variation was identified and removed. Once the process was running "in-control" and centered, THEN using Cpk which includes the subgroup variation to help center the process on the target was what we used.
Hope this helps. Dave.

------------------
Dave S.

Thanks for the explanation. That makes more sense than just about anything else I've heard -- I guess because it's from a user's standpoint. (And I did read it -- how about that!)

Also see:
http://Elsmar.com/ubb/Forum10/HTML/000028.html

To Ppk or Cpk, that is the question.

Let me see if I can get to the skinny of things in 50 words or less.

Cpk – The capability index for a stable process. The estimate of sigma is based on within subgroup variation. Cpk can only be calculated when the process is stable.

Ppk – The performance index. The estimate of sigma is based on total variation. Ppk is to be calculated if less than 100 samples or when the process is chronically unstable but meeting the specifications and in a predictable pattern.

… well unfortunately that was 67 words. But as you see there is a difference in the definition between the two. Now you will know if some body reports a process index using the Cpk calculation, you know that the process is stable and mature. And if you receive a Ppk calculation, you know that the process is either in it’s infant stages or chronically unstable but meeting the specifications and has a predictable pattern.

Did this clear or muddy up the water of your understanding of the difference between Cpk / Ppk.

You say that one can assume that someone reporting Ppk is indicating one thing and someone reporting Cpk is indicating something else. I doubt it, in most cases, because there is so much confusion or variation of interpretation (as witnessed by the replys above). But what you say makes sense.

I agree by reading the above posts that there appears to be some level of confusion. However, the definition I have provided comes straight from the beautiful blue books we have all grown to love, the QS manuals. In my opinion, there is very little “wiggle room” on its interpretation.

Section I.2.2.9.2 of the PPAP Third Edition clears up this whole Cpk – Ppk thing.

Hello!

Is there any formulas to count Percent Nonconforming from the CPK? The PDF says to find Z-Score curve area in the standard normal table but I just have an Excel chart where I would like to have Percent Nonconforming values calculated automatically in the basis of CPK.

Jari Maatta:

Just my opinion, but I would be wary using a Cpk value to determine % nonconforming. Cpk values can be based upon too many variables such as sample size, frequency, etc... The "Z" table assumes a perfect situaton.

There is a general guide in the AIAG FMEA manual (page 39) and what is the PDF?

ASD...

Which metrics to use?

The point of my earlier post was that ALL of them can and should be used - IF you understand the differences.

If you have someone who doesn't understand their meaning, use the Pp & Ppk (where the estimate of the sigma is the simple sample standard deviation of all the data glommed together - this is EXACTLY what the pre-AIAG Cp & Cpk was.) These reflect the actual performance of the process.

How to calculate %-nonconforming?

My advice is to calculate the mean and sample standard deviation and then use the z-statistic to calculate the probablitiy of observing a variate outside the spec limits.

Using Excel notation:

%-nonconformance = =100*(NORMDIST(LSL,Mean,StdDv,TRUE)+(1-NORMDIST(USL,Mean,StdDv,TRUE)))

For upper/lower bound just remove the relavent portion.

Good morning from Finland again. :)

Ken K, your formula seems to work very fine! I checked the results with Minitab too and it seems to give ~ same results for percent non-conforming! And as PDF, I meant Don Winton's "Process Capability Studies" document. But thanks again, I'll ask you again if I have some problems with my calculations.. ;)

Oh, I didn't know you are using MINITAB. By all means, they'll give you the correct % nonconformance - assuming you've entered the spec limits in correctly. I've had some people check the Hard Limit boxes by mistake. MINITAB treats these as a lower/upper bound (they even label it that way on the chart), and assumes that the process CANNOT go beyond that point, therefore it treats this as a one-sided spec and doesn't calculate %-nonconforming beyond those bounds.

By the way, how's the weather in Finland?? It has been kind of warm (30C+) and rainy in Chicago the last few days. More so than usual. Good for the crops though.

Hello!

Yes, we have Minitab but we have so many results that all have different spec limits so it's almost impossible to go and give the limits manually.. that's why I made a program using VB that collects the data and calculates required values automatically. Or do you know a way to make Minitab-script or something that reads spec limits automatically..?

Weather in Finland .. umm .. heh .. let's say it isn't quite summer yet -- in the morning it was +1.5°C and snowing. =) It isn't very nice to go work about 7 kilometers by bike in the morning in that weather, trust me.

I've actually been discussing that with Minitab. It seems a lot of users have such a situation - where they have lots of parameters, each in a seperate column, and the spec limits listed somewhere else (another column or two).

It would be nice if there was an option to do "bulk" capability analysis as follows:

Data columns: enter one or more columns with data

Subgroup size: enter a constant or a column that identifies the subgroups

Lower Spec: enter a constant or one column that contains the lower specs. A * value indicates a one-sided upper spec.

Upper Spec: enter a constant or one column that contains the upper specs. A * value indicates a one-sided lower spec.

I don't know how to deal with the lower/upper bound issue with multiple data columns yet. Any ideas?

If only one column of data were entered, the output would be as it is now.

If multiple columns were entered, the analysis would show metrics in tabular format only, maybe with an option to show graphs for columns with a Cpk/Ppk less than some given value.

Ken K.

Cpk suffers from three maladies 1. lack of economic consideration in the metric 2. A numerator which has questionable limits (and process for determining them) and 3. The denominator which does not consider off center and mean shift separately.

Consider the following: If the cost of scrapping poor products is the same as the loss incurred by sending the part (or assembly or product to the next ) then Cpk is probably ok. If, however, the loss exceeds the cost, which is mostly the case, then higher Cpk numbers should be required to balance the $ differential.
my 2 cents.

I received this interesting e-mail today. I wonder if any of you folks have any comments about the statement that the definitions of Cpk and Ppk have 'flipped'. I am not posting his e-mail address because I'm not sure if he wants this to be public, it being in an e-mail to me rather than a post in the forums where he could explain.
On 10/30/02 at 1:36 PM EST, T wrote:

> Marc:
> I've read several of the postings about the confusion of Cpk and Ppk.
>
> First - Who am I?
> XXX is the world's largest manufacturer of XXX.
>
> Many of our employees are receiving training is the six sigma methodology.
> Within Six Sigma applications you will discover that the terms Cpk and Ppk
> have been changed. It use to be that Cpk meant Long Term Process Capability,
> and Ppk was Short Term Process Capability. Six Sigma has reversed these
> terms. Why and how this has happened is a long explanation. I just wanted to
> mention it since I did not notice reference to this in any of the postings
> on the Forum. This may add to some of the confusion people have.
>
> Second, I wanted to pass along a simple SPC program I developed in Excel.
> You may make it available to your readers.
> It will calculate Cp, Cpk (R-Bar/d2 method); Pp, Ppk (n-1 method) and PPM.
> It can be used with either Bilateral or Unilateral
> tolerances.
>
> Let me know if this is of any help to your readers;
>
> Best Regards;
> T

Now - that said I wrote back:Tim,

I appreciate your e-mail. However, I am not the expert. The experts are those in the forums so I will defer to them to debate.

No - I must admit, I interpret Cpk and Ppk as defined earlier in this thread. I know six sigma enthusiasts claim quite a lot. Six sigma its self has been debated rather severely in the forums (see Six Sigma - Statistical Tools - Valid or Hype? Value? Can a CQE do the same? (http://Elsmar.com/Forums/showthread.php?t=3823) ) as to whether it's Motion Lotion that works or totally over hyped sales indoctrination.

I must admit that I believe a lot of the Six Sigma is sales. I was privileged to be trusted by the Motorola Semi-Conductor Sector (or what was) with internal documents (the old 'You tell and we shoot you') and my impression was, and is, that this is nothing more than understanding statistics and using data to manage. From one document:In early 1987 the concept and goal of Six Sigma capability was introduced.
There was nothing really 'secret' in the documents, but rather techniques and theories.

My background was biology with chemistry and anthropology as minors in college. I dealt with processes on the level of atomic / molecular reactions. So when I got into 'product' manufacturing I was amazed at how few companies used statistics to manage their processes. In biology I saw the Cause and Effect thing up close. Root Cause in manufacturing, which few really understand, was part and parcel of a biological system and understanding failure modes at the molecular level. This was particularly helpful to me when I had to work in micro-electronics where the cause of a component failure was often an upstream component 'event' - hard to diagnose. Bottom line is we're talking complex systems.

Cpk and Ppk are essentially unitless numbers used to indicate whether a process is 'in control' or not using distribution, location and probability as a base.

I would very much appreciate your discussion on this in the forums. You state:Why and how this has happened is a long explanation.
We would all really like to hear the long version. The more specifics the better.

With respect to your Excel spreadsheet offer, I can bet over 500 downloads if you post it as an attachment (Which means you agree that it is acceptable per, as a minimum, the constraints as defined at: http://www.opensource.org/licenses/gpl-license.php ). Or, if it too large to attach to your post, send it to me as an e-mail attachment and I'll put it in the 'Free Files' (Free Fils directory (http://Elsmar.com/pdf_files/) ) for you.

There is no doubt in my mind that your contributions - both your reasoned, detailed explanation of how and why Cpk and Ppk definitions have switched due to Six Sigma - and your gracious offer to share your spreadsheet - will be appreciated by folks around the world!

My Regards and My Thanks!

Marc T. Smith

What say ye, Elsmar Cove Forum Folks?

Yes, the terminologies of 'Long Term' and 'Short Term' have flipped somewhere along the way.

Cpk could be called as 'long term' due to its predictive nature, since d2 used to predict std deviation is an imperical constant.

Cpk could also be called 'short term' since we evaluate the std. deviation on the basis of limited range values selected over a specific horizon. We also do not take cognizance of long term drifts, and supress the effects of outliers by averaging the range values.

Your definition depends on which view you take.

In fact the Long/Short terms cause so much confusion that I have stopped using these terminologies . I simply refer to them as Cp/Cpk and Pp/Ppk. The formulae for these still remain the same, and lead to no ambiguity.

This is all good statistical fun at its best! (err, hmmm, well. . . . )

The way I have always used ppk/ cpk is this:
Cpk determines your potential process capability
Ppk determines your actual performance.

Therefore, in my opinion, when trying to determine the performance of say a manufacturing process, I would and do use Ppk. But when trying to determine the potential capability of a manufacturing process I would/ do use Cpk.

But, and it’s a very BIG BUT! The hierarchical authority within businesses that I have worked in seems only to grasp the very basic of ‘idea’ of Cpk! And the idea they consider Cpk is incorrect anyway! Most people see Cpk as Ppk but no nothing of Ppk?

I’m all in a muddle now with p-p-p-k-c-c-k-p-c-k-p coming out of all orifices!

Lee01

Hi all

I just stumbled on this thread, and have read (and learned)with great interest. There is one thing missing, I think, though I have been wrong before. Don't these metrics "assume" normality? If so, than it seems to me that the use of z or t to estimate the % nonconforming would be somewhat dangerous unless very large, very near normal sample sizes are used. Right??

I would be very interested if the mystery emailer would share more of their story.

The only regret I have about these forums is that it took me so long to find them...Thanks Marc

Well said Craig! Step no further unless Normality is confirmed.

Hi:
This is my first time posting anything. I just found the site. It looks like a fantastic forum for all kinds of Quality related issues.

Yes, the terms have been reversed. The explanation I have is: Although the big 3 developed the Statistical Guidelines as published by AIAG, Chrysler actually never agreed with the terminology. Dr. Mikel Barry (of Motorola fame) used the Chrysler definitions; Cpk = short term, Ppk = long term. Dr. Barry was/is involved in the Six Sigma Academy and ASQ. They adopted the same use of the terms. MiniTab software used this same interpretation. Now we are all stuck trying to make sense out of it.

To add further to the problem, in Ford’s specific guidelines for ISO/TS 16949, they refer to Cpk as “the Historical Process Capability” ( Pg 72). See their guidelines posted at: www.ioab.org

As we all know, the calculations using R-bar/d2 and n-1 are used to develop the Cpk and Ppk indices, respectively. To use these, the process must be stable and in control. To use Cpk the samples within the sub-group must be taken sequentially and each sub-group taken consecutively over time. Since Ppk is based on the population, the samples do not need to sequential. Cpk averages the effects of variation, Ppk does not. These are simple but important concepts. The factor that must be understood is time. Was the data gathered in a short period? I fully agree with earlier postings that suggest Ppk be used when reporting short term data, and Cpk is used when reporting long term data. Our company suggests that when reporting process capability, it should be stated that the index is the result of a short term or long term study.

This all becomes very important when reporting capability after several set-ups. Example: a process is set-up 3 times: 1 – at the mean, 2 – slightly below mean (but capable), 3 – slightly above mean (but capable). If Ppk is used, it would be an average of the entire spread of each set-up. Not Good. Cpk would be an average of each sub-group and would provide a better picture of the process. ( Of course short run SPC methods would be better)

Also, in response to requests for help calculating PPM, I have attached (hopefully I succeed) an Excel program I developed for capability studies. It can be used for bilateral or unilateral specifications; and with sub-groups of 2, 3, 4, or 5. I removed our corporate name and logo; you can add your own.

I have revised the attachment - see below tim

Welcome and thanks for the input and for the spreadsheet contribution.

Cp and Pp have come up a lot recently where I am working. I have a twist to this, however.

Different companies have different volumes. As an example, let's say at a company a good run is 1200 parts over 36 hours. Other runs may be as high as 10,000, but some are as low as 100 over 24 hours. One part is simple and run at rate is 1800 and hour.

My question is: How does volume affect using these different indices?

I don’t believe volume has an effect on the indices; at least not directly. However, volume does affect the sample size. The MIL standard clearly shows that relationship; as well as confidence tables. The number in the sub-groups (5 vs 3) and frequency of the samples (5 pcs/ 1/2 hrs vs 3 pcs/2 hrs) would thus have an effect on the indices. The more samples, the better picture you have of the process.

Nice capability form. What about where you take 30 random samples from a lot and do a study? Attached is a form I have used.

You can use the form I provided for your example. The form may be used for sub-groups of 2 to 5 pcs. However, since your example is based on random individuals taken from the population, the form will still work. In this case you must use the Ppk index and ignore Cpk and the chart. For your example the chart must be for individuals, not X bar & R.

Ppk is based off of the sigma calculation for the population (n-1). The samples may be taken randomly from anywhere in the lot. This also means that the samples are not sequential or consecutive. Sample 19 may have been produced before sample 6.

Cpk is based off of the average of the sub-groups and the samples must be sequential and consecutive. Cpk sigma is based off of the average using R-bar/d2.

Therefore, either form will provide the correct result; however, the form you provided is incorrectly labled. Since the calculation is based off of n-1 for the population, the index should be Ppk not Cpk. Additionally, your form can only be used for this type of analysis.

It all comes down to understanding the data. (I hope I understood it correctly)

For your comparison, attached is my form using 2 sets of data from your example.

:bigwave:
I am re-attaching the Capability Study form I submitted earlier. In reviewing the problem above, I noted an error in the Range Chart scale.

I have also added the calculation for Machine Capability Study.

The attached Capability Study Form may be used for:
- Bilateral or Unilateral tolerances
- Data from Sub-groups or Individuals
- Machine Capability using a specified Target Value

The above may be done in various combinations. The form includes several built-in demonstrations.

I hope this is helpful. :)

Hi Don
I am a new subscriber and don't know where to find your cpk.pdf
Appreciate if you could guide me.

ye

I can understand confusion about Pp, Cp, Ppk and Cpk due to different books and software use same symbols with different meaning to indicate for short term or long term capability. It is desirable to use plain english word like "short term" capability or "long term capability" to make sure that other person is on same page about interpretation.

There is again confusion regarding what to call as short term or long term. The term refers to sources of variation which influences process output. It could be raw material variation or tool wear or any other common cause variation. Short term capability generally refers to a batch produced & is expected to be more homogeneous compared to variation from batch to batch which will have higher sources of variation. Six sigma always refers to short term capability.
Due to additional uncontrollable sources of variation, long term capability is always lower than short term.
Here is some useful tips.

Cp or Pp-
1) Higher the better.
2) Considers only spread of the distribution and compares with specifications.
3) DOES NOT consider where mean value of data lies with respect target (which in many cases is mean of upper and lower specification)
3) Lower the spread, higher is the value.
4) Can not be a negative value

Cpk or Ppk
1) Also higher the better
2) Can never be higher than corresponding Cp or Pp. In limiting case it can equal corresponding Cp or Pp when mean of data coincides with target.
3) Considers where mean lies with respect to target
4) Can be negative if mean value of data lies outside the specification.

-----------Sigma value ------------Short term capability-------Long term capability
------------3.0----------------------1.0------------------------0.5
------------4.0----------------------1.33-----------------------0.83
------------5.0----------------------1.67-----------------------1.17
------------6.0----------------------2.0-------------------------1.50
To summarize above table.
a) Long term sigma= Short term sigma-1.5
b) Capability= Sigma/3

Which one of the following is a "low hanging fruit" ?
Consider two scenarios?
a) Cp or Pp= 1.07, Cpk or Ppk= 1.03
b) Cp or Pp= 2.2 Cpk or Ppk= 0.8

Making improvement is process a) is a tough job because reducing spread or variability is always difficult.
Making improvement process b) is relatively easy since spread is already low as seen from high Cp value. All that you need to do is to shift mean to the target which maintenance or skilled trade person can do quite satisfactorily.

Arvind

Hi Don
I am a new subscriber and don't know where to find your cpk.pdf
Appreciate if you could guide me.

ye

Welcome to the Cove, yetint.

Here's the link for the file you are looking for:
http://elsmar.com/pdf_files/CPK.pdf

Hi All,
I am new to this forum.I have gone thru the info given for Cp and Cpk and its very much handy. I would like to get my doubt clarified regarding estimated sigma i.e R-Bar/d2. Actually I am writing formula to calculate Cp and Cpk. Can anyone pls let me know from where should I get the D2 value in order to calculate R-bar/d2.

You have given one chart where D2 values are pre defined. Pls tell me how and on what basis those values have been defined. I need more info about D2.

Thanks one & All....
aWaiting ur reply
Ur help will be greatly appreciated

Sangisetti.Vk
tata consultancy services

we actually addressed this very question in a previous thread ("Formulas for Factors d2 and d3 for range charts") but in summary:

d2 comes from a table. Any decent stats book will have such a table. There are formulas for the calculation but they are sadistic.

if you have a large sample size and can't find a table that has a d2 value for that sample size - use the standard deviation. It's a better estimator of the variation anyway...

Here is a ppt. on CpK and PpK. As for how mini-tab handles stats. don't use it.

just my :2cents:

Thanks Bev,
In our case we are calculating Cp for individual memebers, I mean to say there is no group. I think in our case sub group size is always 1..is it right?

Sangisetti

Thanks Bev,
In our case we are calculating Cp for individual memebers, I mean to say there is no group. I think in our case sub group size is always 1..is it right?

Sangisetti

If you are measuring individual parts you shoudl be using an "individuals, Moving Range" chart (or similar depending on the distribution).
If using the I, MR chart your subgroup is 2: range of the first value to teh second, second to the third, etc. d2 for n=2 is 1.128

If you are trying to use only the individual values and calculating the control limits directly there is no need for d2 as there is no subgroup range. (Note: I am not recommending this...)

I have a little study on SPC. CPk is caculated when the process is stable which means there is no special variance in the process( only commen variance exists). PPk does not take care of the condition whether the process is stable or not. PPk is an overall caculation, but CPk is a within the subgroup analysis.
Any question, please call me.
86-13761644301
mail:aaronan2006***********

for Ppk and Cpk, I think these very confusing , but if we think about how we caculate these two indices, it is easy to distinguish these two:

1. if we group data , then we may caculate st. devi. as Rbar/d2, that means we consider how the varience appeard within group, so Cpk just tell us how is our process stability during limited time, this means short period;
2. If we caculate st. Dev. per individule data against true value, we get a lont term varience of our process,so Ppk tell us how is our process stability during all period,this means long term.
3. So, I interpret Ppk as: it indicate potential capability of all process( with one statistical status).Cpk indicate capability of production period.

hope for your comments!

Hello sir,

I came in to the forum today mainly to understand the definition and the usage of the capability indices (Cpk and PpK).

Now in my shop floor we have several machining processes including some important finishing process like Grinding, in which I have lot of doubts in calculating Cpk/Ppk. Basically we are piston rings making cmpany where we do finally a Grinding operation to control the axial thickness.Now we are checking the samples for every 25 pcs and based on the output we give the wheel wear compensation and this steps is continued till the end of the shift.

Now in this scenario how to calculate Cpk/Ppk considering the fact that the output is varying due to factors like the wheel wear , coolant temperature fluctuations and so on.

Can you help me pelase.

Shesh

Investigate if EWMA (exponentially weighted moving average) will work in your case. Some info on it (http://www.google.com/search?q=ewma&rls=com.microsoft:en-us&ie=UTF-8&oe=UTF-8&startIndex=&startPage=1)

A company that I worked for in the past used this technique for a similar process.

Now in this scenario how to calculate Cpk/Ppk considering the fact that the output is varying due to factors like the wheel wear , coolant temperature fluctuations and so on.

Can you help me pelase.

Shesh

the causes of variation and your reaction to them don't matter. The calculation of Cpk/Ppk are simply a quantificationof the actual variation in the output that you actually experience. How and why you have that variation does not obviate the validity of the calculation.

If youare expereinceing systemic drift due to tool wear, etc. you will have more of a uniform distribution than a bell shaped curve. THIS will effect which formula you should use and what your result means. If you search this forum for tool wear, Cpk and uniform distribution you will find ample information on hwo to handle this situation...

If the specification is in of one side data like length 35.5 +0/-0.3
Are there any change in Cpk calculation.

Regards,

Hamed

Hello Friends

What about CpK for one side specification like length 125.5 +0/ -0.3 is same way in calculation for two sides data 125.5+/- 0.3

Many Thanks,

Hamed

Hello Friends

What about CpK for one side specification like length 125.5 +0/ -0.3 is same way in calculation for two sides data 125.5+/- 0.3

Many Thanks,

Hamed

Hamed - one of the reasons your post from October wasn't answered is that it has been answered numerous times before. try a search of the site and see if you dont' find the answer you are looking for.

I have a SQE that is referanceing the AIAG manual that shows capability of 1.67 is required. It does not show if it is a Cpk or Ppk. He is holding me to a Ppk of 1.67 which is very tight.

Can anyone shed some light on which would apply?

I have a SQE that is referencing the AIAG manual that shows capability of 1.67 is required. It does not show if it is a Cpk or Ppk. He is holding me to a Ppk of 1.67 which is very tight.

Can anyone shed some light on which would apply?

Hello! Welcome to The Cove Forums! :bigwave: :bigwave:

What AIAG manual is your SQE referring to? PPAP? SPC?
Is this for an initial PPAP submission?

If this is what your customer wants and you contractually agreed to it, then you have to meet that requirement.

You may also want to do a search here on Cpk and Ppk.

Good luck! :agree1:

Stijloor.

there used to be a requirement for 1.67 if your process wasn't in statistical control? It's been so long since I was in automotive I can't remember the specifics. maybe this will spark someone's memory...

Stijloor

Thanx for the input. He is taking his comments from the AIAG PPAP manual. I have looked at it closer and am going to discuss it with him further. The way I see that it reads in Note 1 on page 9 "Meeting the initial process study capability acceptance criteria is one of a number of customer requirements that lead to an approved PPAP.

Since they refer to capability acceptance rather than performence I intend to use this to support my argument that the manual refers to Cpk

A PPAP is normally provided for new or changed product.

If the product is new, you only have short term data available, so can only provide Cpk results.

If the product is changed, you should have long term data available for the unchanged characteristics, but may only have short term data available for changed characteristics. Unchanged characteristics would have Ppk available and changed characteristics would only have Cpk available.

OK I'm making a classic mistake and trying to remember the requirement. but I'll proceed anyway.

I think the requirement is that when you dont' have long term process data (multiple subgroups) the requirement is to calculate the 'short term' capability by using data from only one setup or raw material batch and calculating the standard deviation for that single large subgroup. So the standard deviation is Stotal instead of Swithin . Stotal is the calculation for Ppk and Swithin is the calculation for Cpk. So in this case, you are using the Ppk formula to calculate the short term (Cpk) value! Of course if you have multiple setups, raw material lots and different operators then you can use the Cpk formula to calculate the short term capability.

Still don't remember the 1.67 requirement tho. For some reason I'm thinking they are two separate issues...it woudl be helpful if someone could quote chapter and verse from the manual!

I also seem to remember that both issues have been discussed in this forum before in some detail, but my memory of the automotive world was erased long ago!

:applause:Nice

By

RENGARAJ..M



:thanx: