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Statistical Techniques and 6 Sigma Ppk vs Cpk

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Author  Topic: Ppk vs Cpk 
David McGan Forum Contributor Posts: 19 
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 shortterm study results, and uses the calculated standard deviation in its determination. Cpk, on the other hand, is used for longterm study results, and uses the estimated standard deviation in its calculation. But can anyone give me the statistical rationale for this? IP: Logged 
Marc Smith Cheech Wizard Posts: 4119 
posted 15 February 2000 06:42 AM
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)... There is a great web site I found (well, great may or may not be the word  it's a nice, informative site). It is www.qualityadvisor.com Specifically for the Cp vs Cpk vs Ppk, I found www.qualityadvisor.com/capabilityindexppk.htm 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 twosided 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... If the system is centered on its target value...
Ppk is an index of process performance which tells how well a systemÊis 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... If Ppk is between 0 and 1.0... If the system is centered on its target value...
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.
The Cp index is used to summarize a system's ability to meet twosided 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... If the system is centered on its target value...
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... If Cpk is between 0 and 1.0... If the system is centered on its target value...
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).] IP: Logged 
Laura M Forum Contributor Posts: 299 
posted 15 February 2000 10:05 AM
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 Rbar/d2 from the control chart, and the PPk be an actual std. dev. calculated on 100 individuals. Rbar/ 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 Rbar/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 xbar's move. Rbar /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." IP: Logged 
Don Winton Forum Contributor Posts: 498 
posted 23 March 2000 03:27 PM
Laura, You are correct. I have been on a tenweek 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 sigmahat 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 sigmahat 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: n1 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 n1. 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 [This message has been edited by Don Winton (edited 29 March 2000).] IP: Logged 
David McGan Forum Contributor Posts: 19 
posted 23 March 2000 04:57 PM
Now that certainly clears everything up! Thanks. IP: Logged 
chuy sanchez Forum Contributor Posts: 14 
posted 23 March 2000 05:00 PM
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 reppap my parts for some reason i presented to them ppk and guess what ?? they are happy !!!! bye IP: Logged 
Marc Smith Cheech Wizard Posts: 4119 
posted 23 March 2000 06:48 PM
By the way, Don, your paper CPK.pdf has been downloaded 525 times so far this month alone. IP: Logged 
Don Winton Forum Contributor Posts: 498 
posted 29 March 2000 08:20 AM
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. [This message has been edited by Don Winton (edited 29 March 2000).] IP: Logged 
Don Winton Forum Contributor Posts: 498 
posted 31 March 2000 12:23 PM
Main Entry: caápaábiláiáty Pronunciation: "kAp&'bil&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 As I have reread 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 to produce conforming product. There is no guarantee the process will do so. Regards, IP: Logged 
Don Winton Forum Contributor Posts: 498 
posted 07 April 2000 10:03 AM
Received my copy of Juran's Quality Handbook, 5th Edition a couple of days ago and found this of interest: Ppk = Cpkhat 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, IP: Logged 
dave v unregistered 
posted 26 April 2000 03:44 PM
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 QS9000 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 steadystate (?) 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? IP: Logged 
Marc Smith Cheech Wizard Posts: 4119 
posted 12 May 2000 05:43 AM
Used by permission of Red Road. [This message has been edited by admin (edited 17 January 2001).] IP: Logged 
Marc Smith Cheech Wizard Posts: 4119 
posted 12 May 2000 05:44 AM
Used by permission of Red Road. [This message has been edited by admin (edited 17 January 2001).] IP: Logged 
Enrique unregistered 
posted 02 June 2000 01:49 PM
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. IP: Logged 
Iain MacDougall unregistered 
posted 16 August 2000 10:46 AM
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 rebuilding 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 Am I going down the correct street or can someone redirect me. Thanks, IP: Logged 
Marc Smith Cheech Wizard Posts: 4119 
posted 18 January 2001 02:33 PM
Some thoughts: From: "Wayne Lundberg" [email protected] "Jed Palmer" 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" [email protected] 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 (xaxis)" with "manufactured mass (yaxis)". 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 signaltonoise 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 Cpkimprovement is very closely related to SNRimprovement. 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 IP: Logged 
Marc Smith Cheech Wizard Posts: 4119 
posted 18 January 2001 02:35 PM
Does anyone have any knowledge on this? > From the previous corespondences, would I be correct in deriving the IP: Logged 
Ken K. unregistered 
posted 20 January 2001 08:55 PM
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 offtarget 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. IP: Logged 
Rob 6Sigma BB in training unregistered 
posted 21 January 2001 05:55 PM
Ken is got it........... to explain it Mathmatically Cp = USLLSL / 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 = USLLSL / 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 [(USLMean) / (3 Sigma)] or [(Mean  LSL) / (3 Sigma)] . where USL=Upper Spec Limit & Hope that clears it up.
IP: Logged 
David Drue Stauffer Forum Contributor Posts: 25 
posted 24 January 2001 01:26 PM
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 setup technician was in the process of toolsetting to meet the parameters, there would be a series of "prerunoff" 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 5075% 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 "InControl & Centered Process", then we proceeded with the machine runoff 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 "incontrol" 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.  IP: Logged 
David McGan Forum Contributor Posts: 19 
posted 24 January 2001 01:39 PM
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!) IP: Logged 
Marc Smith Cheech Wizard Posts: 4119 
posted 19 February 2001 06:28 AM
Also see: https://elsmar.com/ubb/Forum10/HTML/000028.html IP: Logged 
AJLenarz Forum Contributor Posts: 25 
posted 22 February 2001 12:23 PM
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 ö 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 ö 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 itâs 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. IP: Logged 
David McGan Forum Contributor Posts: 19 
posted 23 February 2001 08:54 AM
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. IP: Logged 
AJLenarz Forum Contributor Posts: 25 
posted 23 February 2001 09:43 AM
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 ãwiggle roomä on its interpretation. Section I.2.2.9.2 of the PPAP Third Edition clears up this whole Cpk ö Ppk thing. IP: Logged 
Jari Maatta unregistered 
posted 16 May 2001 01:48 AM
Hello! Is there any formulas to count Percent Nonconforming from the CPK? The PDF says to find ZScore 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. IP: Logged 
Al Dyer Forum Wizard Posts: 622 
posted 16 May 2001 05:15 AM
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... IP: Logged 
Ken K. unregistered 
posted 16 May 2001 03:39 PM
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 preAIAG 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 zstatistic to calculate the probablitiy of observing a variate outside the spec limits. Using Excel notation: %nonconformance = =100*(NORMDIST(LSL,Mean,StdDv,TRUE)+(1NORMDIST(USL,Mean,StdDv,TRUE))) For upper/lower bound just remove the relavent portion. IP: Logged 
Jari Maatta unregistered 
posted 17 May 2001 03:05 AM
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 nonconforming! 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.. IP: Logged 
Ken K. unregistered 
posted 17 May 2001 11:01 AM
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 onesided 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. IP: Logged 
Jari Maatta unregistered 
posted 21 May 2001 05:55 AM
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 Minitabscript 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. IP: Logged 
Ken K. unregistered 
posted 22 May 2001 10:20 AM
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 onesided upper spec. Upper Spec: enter a constant or one column that contains the upper specs. A * value indicates a onesided 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. IP: Logged 
[email protected] unregistered 
posted 22 May 2001 06:14 PM
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. IP: Logged 
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