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Author Topic:   Ppk
Dawn
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posted 25 March 1999 08:20 PM     Click Here to See the Profile for Dawn   Click Here to Email Dawn     Edit/Delete Message   Reply w/Quote

I have a customer who takes a 30 piece sample and determines a Ppk.
He tells me we do it wrong. This is how we do it:
We take subgroups of five, and get X bars. Then we take the X bars and average them together to get a double X bar.
Then we take the double X bar and substitute it in the Cpk formula where the X bar is. Are we doing this right? HELP!!!

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Batman
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posted 26 March 1999 08:29 PM     Click Here to See the Profile for Batman   Click Here to Email Batman     Edit/Delete Message   Reply w/Quote
Hi Dawn.
Very simply, Ppk is the capability calculation using the estimated sigma calculated from the Rbar/d2 (read Rbar devided by d2,) as opposed to the Cpk calculation using the population sigma. The d2 factor is in any look-up table, and is based on the subgroup size.

Remember, when utilizing a SPC type chart, where you determine variation over time, and thus calculate Xbar and Rbar, the Ppk calculation holds up if the plots are "in control," so 5 subgroups may be a stretch for determining an "in control" condition.

If you are taking a 30 piece sample from a lot of parts, you may consider a Cpk calculation, if the sample is random. You may even consider NOT taking that sample if the parts come from a process that has demonstrated good control and good capability.

There is much more to this, I know a couple of wizards nearby that would love to enhance this. Also I believe there is a very good Cpk / Ppk explanation in the PDF zone elsewhere in this site.

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Don Winton
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posted 27 March 1999 12:42 AM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message   Reply w/Quote
Dawn,

Batman said it all, and there is not much I can add. Your method will satisfy the 'statistically valid' parameter, if asked, based on the information you supplied.

Regards,
Don

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Dawn
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posted 27 March 1999 04:59 PM     Click Here to See the Profile for Dawn   Click Here to Email Dawn     Edit/Delete Message   Reply w/Quote
Thanks, I will look for the definition in the pdf files.
Next, I am told if I don't use the range in a capability study, I am doing Ppk not Cpk.
Also, if I calculate sample standard deviation, I am doing Ppk . Standard deviation is Cpk. Any takers?

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Mark W
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posted 29 March 1999 08:56 PM     Click Here to See the Profile for Mark W     Edit/Delete Message   Reply w/Quote
I don't claim to be a capability index guru, but the SPC Manual in the QS9000 documents gives a pretty clear definition of Cpk and Ppk. If using a control chart method for variable data (i.e. Xbar/R), Cpk (Capability Index) is derived from the chart with an estimate of the standard deviation taken from the control chart, s=Rbar/d2. It is used to determine long term process capability assuming a stable process and demonstrated with the control chart. The Ppk (Performance Index) is a measure of how the process is performing to the specifications based upon a sample from the population and the estimated sigma is derived using the sample standard deviation formula SqRoot(Sum(Xn-XBar)^2/(n-1)) (?or something like that?).

I believe your customer may be referring to these definitions when they state their way of calculating the Ppk index. Someone please let me know if I am way off base here.

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Batman
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posted 30 March 1999 12:47 AM     Click Here to See the Profile for Batman   Click Here to Email Batman     Edit/Delete Message   Reply w/Quote
Sorry, I didn't mean to confuse, but Mark is right. 'Process Capability,' called Cpk, IS from X-r chart, and is a capability index for 'common cause' only variation, that is, from a 'stable' process. This is the Rbar/d2 calculation. Yes, Dawn, Cpk uses the range chart.

Ppk is calculated from the sample standard deviation, or also called the population standard deviation.

Ref page 80-81 QS9K SPC manual.

Mark - use the calculator, it's easier. Heh heh.

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Kevin Mader
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From:Seymour, CT USA
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posted 30 March 1999 09:46 AM     Click Here to See the Profile for Kevin Mader   Click Here to Email Kevin Mader     Edit/Delete Message   Reply w/Quote
Question:

Is the sample standard deviation (s, n-1) the same as the population standard deviation (sigma, n)? While the resultant is generally very close for averages above 25-30 samples, below you run more significant differences. When calculating Cpk, the denominator in the formula uses the 'population' estimate for the standard deviation, while in Ppk, the 'sample' estimate for the standard deviation is used.

Second Question:

I may be off base on this, but I thought that Ppk was used because the population standard deviation (sigma) is unknown? In this case, the biased calculation is used to normalize your results.

Anyone?

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Don Winton
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posted 30 March 1999 12:19 PM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message   Reply w/Quote
All this Ppk and Cpk stuff gives me a headache. Where the heck the concept of Ppk came from is beyond me. But Kevin, you raised an interesting point. I definitely do not envy you QS folks. Anyway:

quote:
Is the sample standard deviation (s, n-1) the same as the population standard deviation (sigma, n)?

No. When sigma is unknown, it is normally estimated. An unbiased estimator of sigma is given in Grant and Leavenworth, page 107 (too cumbersome to go into here). Statistically speaking, in a manufacturing environment, sigma is never known, and must always be estimated. Sorry, the statistical purist in me. For practical applications, s is usually a reliable estimate of sigma after 60 data are available. When less than 60 data are available, page 5 of Cpk.pdf (in the PDF Zone here at the Cove) gives Īcorrectionā factors that also give an unbiased estimate of sigma. A derivation of these factors is also given at the end of Cpk.pdf for those interested.

For simplicityās (please) sake, derive the unbiased estimate of sigma and use Cpk and avoid all this Ppk nonsense. It appears to be more trouble than it is worth. The unbiased estimate of sigma satisfies the Īstatistically validā requirement, so it should not be questioned.

Does this help, or did I just muddy the water.

Regards,
Don

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Kevin Mader
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posted 30 March 1999 01:18 PM     Click Here to See the Profile for Kevin Mader   Click Here to Email Kevin Mader     Edit/Delete Message   Reply w/Quote
Don,

Ppk. Never heard of it until I got into the automotive world. Ppk from my understanding is used to prequalify processes in early Control Planning/PAPP. I do not know enough about its derivation, so I can't dub it as complete "nonsense" although I feel in my gut that it is. My gut tells me that it is just another fine creation from the automakers to make life simpler and create useful shortcuts. What's the sense if it is scrutinized? Oh well.

Back to the group...

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Don Winton
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posted 30 March 1999 06:19 PM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message   Reply w/Quote
quote:
Ppk from my understanding is used to prequalify processes in early Control Planning/PAPP.

I thought so as well. Personally, I do not see anything 'wrong' with a designation of Ppk using s rather than sigma. Other than what I stated earlier, that it is sometimes rare that sigma is actually known. But, that is too deep for here.

quote:
My gut tells me that it is just another fine creation from the automakers...

Yea, I would tend to agree with that.

Regards,
Don

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Kelly Speiser
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posted 30 April 1999 01:52 PM     Click Here to See the Profile for Kelly Speiser   Click Here to Email Kelly Speiser     Edit/Delete Message   Reply w/Quote
In my humble opinion the formulas are exactly the same for Ppk and Cpk values(mostly because a population standard deviation is always unknown in mfg. therefore always estimated - same as Don Winton said). The difference could not be in the math but the period of time the measurements are collected. Cpk represents a process from a longer period of time, say covering all 3 shifts, all vendors, potential operators, gages, etc. It is to represent parts the customer will get over the long haul. Perhaps the study covers one or two whole weeks. Ppk is (as was stated before) pre-liminary or over a shorter period of time, say one day. Therefore the index for Ppk is higher 1.67 instead of 1.33 to accomodate for the less variation.

Thanks for considering a differnt point of view.

Kelly Speiser

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Don Winton
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posted 30 April 1999 08:17 PM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message   Reply w/Quote
quote:
Thanks for considering a different point of view.

Always welcome here. Continue to provide them, please, please. Anyway, on with the show:

quote:
...mostly because a population standard deviation is always unknown in mfg. therefore always estimated...

Thank you. Thank you. Thank you. I am glad that someone understands this concept. I just wish the AIAG (?) folks would leave statistics to those more qualified (not me, please) and the quality engineering stuff to those who do know (not me, please).

OK. Ramble time (Sorry folks, but it is Friday night).

There are those that review some sort of Īpublishedā criteria and accept it as fact. There are those that do not accept Īpublishedā criteria as fact (me). Then, there are those between.

Folks,

When you accept the publications of some ćsupposedlyä standards group as the final word, look further, please. Speaking strictly as someone trained (somewhat) in statistics, I have never, before the QS thing, thought that Ppk was required, nor necessary (never heard of it, actually). Ppk is something for those who do not understand the difference between Īpopulationā and Īsample.ā The unbiased estimate of sigma should be more than enough.

Cpk is just an extension of the Z-Score concept, which is based in statistical theory. For those not trained in statistical theory, do not be fooled by ćwanna beās.ä If the AIAG (?) is determined to FORCE the concept of Ppk on suppliers, learn from statistical concepts. This will help in the explanation to your assessor.

BTW, elsewhere in this forum there is a reference to Cpk3? I would really like input to Īwhat exactly the heck is this.ā

Regards,

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Batman
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posted 01 May 1999 09:52 PM     Click Here to See the Profile for Batman   Click Here to Email Batman     Edit/Delete Message   Reply w/Quote
If we can stand a little more explanation on Ppk / Cpk, here's a little more. (Wizard Don, you MUST get more involved in QS9000, it is so INTERESTING . And anyway, it IS a customer requirement, so we gotta do it when required...)

The SPC manual for QS9000 states the Ppk is the "Performance" index from Rbar/d2 sigma calculation. AND this Rbar/d2 is the process "Inherent" variation, from common cause variation only. This information usually comes from a "Control" chart. (You can use other variation calculation - sbar/c4 - for instance.)

The usual sequence in a new or revised project is to create an initial control chart over time, calculate control limits, then determining the Ppk from that data. It is, I think, standard practice to NOT use data that is "Out of Control" - special cause - on this chart for the control limits calculations. Therefore only common cause variation is used. This is then where the Ppk calculation comes in. Later in the life of the project, as special causes are removed, the Ppk calculation continues to be used, as the data is available from the control chart.

Some refer to the Ppk as a "Process Potential" due to the fact that only common causes are used in the calculations and the process has the "Potential" of performing at some [higher] level if all special causes are eliminated. Also it takes on this connotation of "Potential" because Ppk is usually determined during the first running or early part of a new or revised process.

If one is to take a random sample of the output of a process, one would use the s (n-1) sigma calculation, since this sample would include the [inferred] "Total" process variation, including common and special causes that may exist. Using the s in the calculations, in QS parlance, this is the Process "Capability" index - Cpk. This would be represented graphically as some from of distribution, and of course be "normally distributed." Cpk calculations are sometimes used when there is no SPC chart type data available.

There are different reasons and times for determining process performance and / or process capability.

I usually recommend the Ppk when possible as it is more in line with the "loss function" concept (this is also stated in the QS SPC manual) as it uses the data from an effort to control variation around a center. Cpk is only a little less desirable, sometimes a little like walking on the edge of a cliff.


A question for the experts, oops, I mean the folks highly trained and knowledgable in statistics -
Can one say that the sigma is unknown, as Kelly suggests? It isn't exactly known, and in particular you can't know it in a new process until it runs, but if after some timeframe, from a process that has some form of a control chart, and after removing most of the special causes of variation, and as long as the chart demonstrates some form of control, can't you get (always have) a good estimate of sigma from the control chart?

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Don Winton
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posted 02 May 1999 08:51 PM     Click Here to See the Profile for Don Winton   Click Here to Email Don Winton     Edit/Delete Message   Reply w/Quote
quote:
Wizard Don, you MUST get more involved in QS9000, it is so INTERESTING

No thanks. My plate is full with the ISO and FDA thing and besides, the QS stuff is sorta junk.

quote:
Can one say that the sigma is unknown, as Kelly suggests?

Yes. Speaking as a purist, it is safe to say that sigma is never KNOWN, but is always estimated. Sorry, but to think that a ĪPpkā is a way to estimate the process capability is using the AIAGās way of thinking. See Cpk paper published in the Cove. OK, vent time.

As I stated above, when you use a published document as a Īlawā you are looking for failure. Do not confuse someoneās Īstandardā as the only available source of data. Batman, I do not claim to be a QS expert, but I do know something about statistics, and the Ppk thing is totally something the AIAG folks use to try advance their own agenda.

Sorry, but that is how I feel.

Oh, and BTW, it is late on Sunday and I am tired.

Regards,
Don

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Kevin Mader
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posted 03 May 1999 09:39 AM     Click Here to See the Profile for Kevin Mader   Click Here to Email Kevin Mader     Edit/Delete Message   Reply w/Quote
Batman,

Interesting post. Looks like you have done a bit of research.

Ppk, I have to agree with Don that this is the automotive folks creation. I had statistics courses in highschool and college, but never heard of Ppk until I joined an organization supporting the automotive industry. Sounds interesting but I am not sold on it yet.

What I find interesting is the connection made Taguchi's "Loss Function" (I believe in the Function over Tolerancing). A process measurement showing the 'potential' in a process at producing to a level, could be meaningful. However, this is true, regardless of Cpk or Ppk calculations, for any process. My take is that the automotive industry would like their suppliers to use this formula to "seal their fate". Commit your organization to a "potential" capability, and they will expect that from you. If later you determine that the variation that exists in a process is inherent to that process and not a special cause as originally thought, it may be too late. You already made the claim. Sounds a bit like handcuffing your own hands and stepping into a barrel of water. Maybe a bit extreme there, but I think Don is right that this was cooked up to drive the OEMs' agenda.

I enjoyed your post though, many interesting tid bits of information and it got me thinking this Monday a.m..

Regards,

Kevin

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Marc Smith
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posted 19 February 2001 06:27 AM     Click Here to See the Profile for Marc Smith   Click Here to Email Marc Smith     Edit/Delete Message   Reply w/Quote
For a good thread on Cp, Cpk, Ppk, etc., see:
https://elsmar.com/ubb/Forum10/HTML/000001.html

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