Ppk vs Cpk - A Good, clear explanation and How Mini-Tab Handles Certain Statistics

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?

Used by permission of Red Road.

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 https://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:[email protected]...
> 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.

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Dave S.