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This topic contains 25 replies, has 19 voices, and was last updated by Mike Carnell 10 years, 9 months ago.
I know the difference between Cpk and Ppk, I also know that Cpk is the lower of Cpu or Cpl.
What is the formula for calculating Ppk?
use the same formula as Cpk, but use different standard deviation.
The purpose of the Ppk calculation is to determine whether a process, given its long-term variation, meets established customer requirements or specifications. Ppk considers the centering of the process. Ppk is a ratio of the measured distance between the overall mean of the process and the closest specification limit to half of the total process spread.Some assumptions to consider when calculating Ppk are first that it is used on continuous data. Furthermore, Ppk assumes that the process is statistically stable and that its data is approximately normally distributed. If the distribution of the data is very skewed, the data should be transformed. Using Ppk indices without the information provided by the Cp and Cpk indices may lead to the wrong interpretations of the capability of the process.Given this, I am including how to calculate all three:1. CpCp= USL-LSL/6(short-term Std. Dev.)2. CpkCpk = min{Cpl, Cpu}Cpl = xbar – LSL/3(short-term std. dev.)
Cpu = USL – xbar/3(short-term std. dev.)3. PpkPpk = min{Ppl, Ppu}Ppl = xbar – LSL/3(long-term std. dev.)
Ppu = USL – xbar/3(long-term std. dev.)In terms of interpretation, if Ppk = Pp (calculated as follows:Pp = USL-LSL/6(long-term std. dev.)If Ppk and Pp are equal then the mean of the data is on-target.
If Ppk = 0 then the mean of the data falls on one of the specification limits which means that 50% of the data is out of specification.
If Ppk < -1 then the mean is completely outside of specification limits meaning that 100% of the data is out side of the specification.I hope that this helps.JIm Johnson
You should also consider differences in how you run the experiment and sampling plan when you talk about the differences between Cp/Cpk and Pp/Ppk.
Cpk studies should only examine short-term process variability. Therefore, only run your process for a short time, with controlled lots, operators, and other external sources of variation controlled.
For Ppk studies, run your process long enough that you include multiple lots, multiple operators, shifts. Examine multiple mold cavities if applicable, etc. Tear down the die and put it together again – anything to simulate what the process will see while turned over to long-term production. This will give much more accurate long-term knowledge of capability than will the 1.5 shift.
Could someone on this thread provide a clear operational definition of long-term and short-term variation?Ken
Ken, I bet you already know the answer to your question, but here is my (quick) answer anyway.
Short term: RBar/d2 (“sigma-prime”).
Long term: the sample standard deviation (that’s the one with n-1 in the denominator).
I hope no one has any complaints with this explanation. It’s not very detailed, but if you think about it, most processes demonstrate very little variability within subgroups (short-term) when compared to subgroup-to-subgroup variability, over time (long-term).
Jim
Bernie,
To get Ppk instead of Cpk, simply substitute the sample standard deviation (the one that uses n-1 in the denominator) for RBar/d2 (“Sigma-prime”). It’s the same for Pp, Ppl, and Ppu.
Jim
The formula is the same.
The difference is regarding lot size and duration.
Ppk is from a short term study, let say 25 sample, where you know the potential of your process.
Cpk is from a long term production data.
Jen: You are correct, thanks for the clarification.
Jim
You know guys, I seem to have been running for over 25 years with the wrong understanding about this stuff… Before the AIAG invented Process Performance Indices there existed short versus long term variation. These lay terms were typically used to describe within(short-term) versus between(long-term) subgroup variation. These terms have evolved to compel one to use the total variation of the entire sample group in the denominator of the original Process Capability equations in order to compute was is called Process Performance indices. Here’s the problem. There’s no way to insure the total variation is statistically stable unless you use standard control charting techniques, and both the average and range(or SD) charts are statistically stable. I’ve observed common practice in the Automotive and other industries taking a large batch of mixed machined parts or other products aggregated together, estimating the total variation of a critical dimension or two, and computing Process Performance indices from this estimate. In many cases, the PP indices were computed with data whose underlying origin were unknown. This is common practice among many of the suppliers of automotive deliverables. There is also a widely held myth that using Capability Indices assumes the between subgroup variation is automatically established at +/-1.5sd. In previous discussions I’ve tried to indicate the operating window for the average is determined by the subgroup sample size in the control limit equations. The last term of these two equations are +/-3s/sqrt(n). Again, if n=4 then the operating window for a stable process controlled using SPC would in fact be +/-1.5sd. However, if better control is desired on the process, then increasing the sample per subgroup decreases the operating window for the average. I’ve used this approach in past work to control the process output to about +/- 1.0sd with n=8 samples per subgroup. The downside is the increased sampling cost. Therefore, one needs to weigh the benefit of a reduced operating window for the average against the increased sampling cost. The best trade-off for many processes is n=4 or 5 for the subgroup samples. Ego an operating window in the range of about 1.3 to 1.5 standard deviations.When using Process Capability indices the desired goals should be Cp=>2.0 and Cpk>1.5 for a Six Sigma process, period. These two indices combine to fully describe the performance of the process for a given period of time, and given the operating conditions at the time of the study. When conducting an initial capability study, holding all factors constant, you are in essence determining the “best” possible performance for the process assuming the measurement variation is not too great. You do this because you want to set controls that are referenced to the best operating conditions for the process. If the process remains stable for a long period of time, a very rare occassion, then you have the option to recompute reliable Capability Indices again using the within(short-term) subgroup variation. If these indices remain at previous levels, then your “doubly” assured the process is performing at or above the desired Sigma level. I say “doubly” assured because if a short term capability study yielded control limits that establish the goals for long-term process performance, and the process remains within these control limits, then you can visually observe via the control chart the process is continuing to perform at the same level established earlier. There is really no need to recompute Capability and/or Performance indices after making this observation. So, what is the reason to compute PP indices for a long-term study? I submit that was not the intent of these indices. In fact, the original intent was to give the automotive suppliers a leg up on very demanding quality requirements set by the industry.2.0 and Cpk>1.5 for a Six Sigma process, period. These two indices combine to fully describe the performance of the process for a given period of time, and given the operating conditions at the time of the study. When conducting an initial capability study, holding all factors constant, you are in essence determining the “best” possible performance for the process assuming the measurement variation is not too great. You do this because you want to set controls that are referenced to the best operating conditions for the process. If the process remains stable for a long period of time, a very rare occassion, then you have the option to recompute reliable Capability Indices again using the within(short-term) subgroup variation. If these indices remain at previous levels, then your “doubly” assured the process is performing at or above the desired Sigma level. I say “doubly” assured because if a short term capability study yielded control limits that establish the goals for long-term process performance, and the process remains within these control limits, then you can visually observe via the control chart the process is continuing to perform at the same level established earlier. There is really no need to recompute Capability and/or Performance indices after making this observation. So, what is the reason to compute PP indices for a long-term study? I submit that was not the intent of these indices. In fact, the original intent was to give the automotive suppliers a leg up on very demanding quality requirements set by the industry.2.0 and Cpk>1.5 for a Six Sigma process, period. These two indices combine to fully describe the performance of the process for a given period of time, and given the operating conditions at the time of the study. When conducting an initial capability study, holding all factors constant, you are in essence determining the “best” possible performance for the process assuming the measurement variation is not too great. You do this because you want to set controls that are referenced to the best operating conditions for the process. If the process remains stable for a long period of time, a very rare occassion, then you have the option to recompute reliable Capability Indices again using the within(short-term) subgroup variation. If these indices remain at previous levels, then your “doubly” assured the process is performing at or above the desired Sigma level. I say “doubly” assured because if a short term capability study yielded control limits that establish the goals for long-term process performance, and the process remains within these control limits, then you can visually observe via the control chart the process is continuing to perform at the same level established earlier. There is really no need to recompute Capability and/or Performance indices after making this observation. So, what is the reason to compute PP indices for a long-term study? I submit that was not the intent of these indices. In fact, the original intent was to give the automotive suppliers a leg up on very demanding quality requirements set by the industry.1.5 for a Six Sigma process, period. These two indices combine to fully describe the performance of the process for a given period of time, and given the operating conditions at the time of the study. When conducting an initial capability study, holding all factors constant, you are in essence determining the “best” possible performance for the process assuming the measurement variation is not too great. You do this because you want to set controls that are referenced to the best operating conditions for the process. If the process remains stable for a long period of time, a very rare occassion, then you have the option to recompute reliable Capability Indices again using the within(short-term) subgroup variation. If these indices remain at previous levels, then your “doubly” assured the process is performing at or above the desired Sigma level. I say “doubly” assured because if a short term capability study yielded control limits that establish the goals for long-term process performance, and the process remains within these control limits, then you can visually observe via the control char
t the process is continuing to perform at the same level established earlier. There is really no need to recompute Capability and/or Performance indices after making this observation. So, what is the reason to compute PP indices for a long-term study? I submit that was not the intent of these indices. In fact, the original intent was to give the automotive suppliers a leg up on very demanding quality requirements set by the industry.1.5 for a Six Sigma process, period. These two indices combine to fully describe the performance of the process for a given period of time, and given the operating conditions at the time of the study. When conducting an initial capability study, holding all factors constant, you are in essence determining the “best” possible performance for the process assuming the measurement variation is not too great. You do this because you want to set controls that are referenced to the best operating conditions for the process. If the process remains stable for a long period of time, a very rare occassion, then you have the option to recompute reliable Capability Indices again using the within(short-term) subgroup variation. If these indices remain at previous levels, then your “doubly” assured the process is performing at or above the desired Sigma level. I say “doubly” assured because if a short term capability study yielded control limits that establish the goals for long-term process performance, and the process remains within these control limits, then you can visually observe via the control chart the process is continuing to perform at the same level established earlier. There is really no need to recompute Capability and/or Performance indices after making this observation. So, what is the reason to compute PP indices for a long-term study? I submit that was not the intent of these indices. In fact, the original intent was to give the automotive suppliers a leg up on very demanding quality requirements set by the industry.Most of the concepts above are well established, and have been so for over 70 years now. These concepts have been explained numerous times by such folks as Juran, Deming, Feigenbaum, Wheeler, Shewhart, and others. There was no need then, as there is no need now to invent new indices that provide little or no ability to predict the future ability of a process to produce acceptable product. Just because a group of people in the Automotive Action Interest Group decided to give their suppliers an edge against tough quality requirements does not make the statistic useful. I ask that you look a bit closer at the fundamentals of basic SPC, and after thinking a bit about what I’ve said above place some well chosen comments and/or questions onto this thread. Remember, for me this is not an emotional issue. I fully understand what I’ve said above. If you feel the need to get emotional about this stuff, ask yourself a simple question: Do my comments directly challenge you, or do my comments directly challenge the concepts you hold dearly?Ken
“The formula is the same.
The difference is regarding lot size and duration.
Ppk is from a short term study, let say 25 sample, where you know the potential of your process.
Cpk is from a long term production data.”
I agree. To sharpen the point a bit, long term capability is the Cpk calculated from data from a process that has been controlled long enough so that:
a) all sources of non-random variation have been eliminated and
b) all sources of random variation have been encountered.
In other words, the chart says that the process is stable. My operational definition of random variation is the total of the relatively small, undifferentiated effects of the process ‘Y’s” that are more or less constantly present in the process over a relatively brief period of time. Note that this definition does not employ tight, precise definitions. It is not intended to.
Obviously the above criteria are ideal and there needs to be some practical accomodation made. As far as I know, only experience can teach one when this practical point has been reached.
Marc Richardson,
Sr. Quality Assurance Engineer
Marc,
I just wanted to say: Excellent ! You have nicely clarified what a long term capability study is.
Thanks
MSAFAI
Gentlemen, I am a bit confused. The initial replies (Jim, Jen) state that Cpk relates to short term, while Ppk relates to long term….. the later replies (Marc, Dermeval) state that Cpk relates to long term, and Ppk to short term…. Have I missed something here?
Dewayne
Ken,
I agree with most everything you said. In addition your comment: “the original intent was to give the automotive suppliers a leg up on very demanding quality requirements
” there is another reason why Ppk, Pp, Pr were developed.
As we all know, Cpk is calculating using sigma in the denominator. “Sigma” is a generic term and can be calculated using the within or the between subgroup variation. Confusion began as to which sigma should be used to calculate Cpk. Remember, before AIAG’s Fundamental Statistical Process Control Reference manual was published, Ppk was not widely used. As of this publication, it is now clear that Cpk is calculated using the within subgroup variation and Ppk is calculated using the between subgroup variation.
Matt
I confused as well Dewayne.
In my calculations, Cpk is determined by pooled sample standard deviation (the one with n-1 in the denominator) which is usually smaller if subgrouped properly. Ppk is calculated by using the overall (population) standard deviation (the one with N in the denominator).
Dewayne,
I don’t know where these other guys are coming from, but Cpk reflects short-term variability. By definition, Cpk uses RBar/d2 in the denominator, not standard deviation. RBar reflects within subgroup variability. By definition, RBar measures short-term variability. Standard deviation however (the one with n-1 in the denominator) reflects variability over much, much longer periods of time (many subgroups) and is used for Ppk (long term variability). Cpk is approximately equal to Ppk is when the control charts are in-control. That’s about like saying that short-term and long-term variation are equal. You can also say that capability and performance are equal when the charts are in control. When out of control long tern variation is generally larger than short term variation. Hence Ppk will be a smaller number than Cpk.
If anyone is still confused about this, I’ll have to post the ASQ reference. It’s at home, I don’t have it here.
Well, it looks like Bernie opened yet another lively discussion supporting Capability vs. Performance indices. I truely chuckle when I look at some of the responses in this message thread, because I’m sure some of you are still very confused about all of this stuff. :-?Matt, to respond to your posting dated the 11th, see link: http://www.isixsigma.com/forum/showmessage.asp?messageID=5071no one, and I mean no one uses the between subgroup dispersion statistic to compute anything, let alone capability and/or performance indices. The AIAG reference does NOT suggest doing this either. Please let me quote from the AIAG SPC Manual, page 14, the last paragraph:”When a process has been found to be STABLE and CAPABLE of meeting the requirements in the short term[study], a different kind of study is subsequently performed. Long-term capability studies consist of measurements which are collected over a longer period of time. The data should be collected for long enough, and in such a way, as to include all expected sources of variation. Many of these sources of variation may not have been observed in the short-term study. When sufficient data have been collected, the data are plotted on a control chart, and IF NO SPECIAL CAUSES ARE FOUND, long-term CAPABILITY and PERFORMANCE indices can be calculated. One use for this study is to describe the ability of the process to safisfy customer requirements over periods of time with many possible sources of variation included–i.e. to quantify process performance.” Notice above that the SPC Manual suggests that you compute both the Capability and Performance indices with the same data… Hmm. I wonder why!On pages 156 and 157 of the same manual definitions for Pp, Ppk, and the standard deviation used to compute these statistics are given. The definition for the standard deviation used for these statistics are as follows:”The estimate of the standard deviation of a process using the sample standard deviation of a set of individuals about the average of the set.”Note: The sample standard deviation includes both between and within subgroup variation.I hope the above information clarifies what is used to compute the Performance Indices. I will suggest there are two camps that hotly debate the use of Performance Indices. I can tell you as Jim Parnella suggests that the difference between Pp and Cp, Ppk and Cpk are typically within 10% of each other when the data are statistically stable. So, why do we need an additional set of indices, when at best they only approximate the real performance of the process? I not sure what the framers of the AIAG SPC standard were thinking, but in many instances computing Performance Indices is just busy work. The use of Cpm for non-centered targets within the specification is however a valid index.I believe a well written iSixSigma article is in order here, as this topic has come up at least 4 times over the last year’s discussions. Anybody up for the job, or would like to co-author?Ken
Excellent Jim
I just wanted to add the following.
long term std.dev = 1.3*short term std.dev
Assumption……..
Ken-
I agree with everything you are saying, but using capability measurements in the context of a Six Sigma project may take a different approach. We use short-term capability (actually we prefer Cp using S) to identify process potential. We use Ppk measurements to identify where the process actually stands (stable or in most cases unstable). We use the entire population (not subgroups) to calculate Ppk (using the population standard devaition, sigma). Whether these numbers are perfect or not doesn’t matter. (I realize we never have a true reprentation of the population). We search and identify (snoop) for our best subroup through quality tools (run charts etc.) and it points us in a direction using a Z Contol vs. Technology chart to whether the process is “out-of-control” or has low technology. We don’t worry about labeling our processes as 4, 5 or 6 sigma but evaluate improvements or reduction in defects through Analyze, Improve and Control phases. Project successes are based upon reduction in defects and monetary savings , not by Cpks and Ppks.
Mike,
Thanks for your input above. The use of within subgroup standard deviation over the range to compute Cp is fine. Using Ppk with an unstable process provide little useable information, but it appears you’re not using the process indices to drive your improvement efforts. Instead, as I understand you are using other run indicators to signal opportunities for process improvement.
I believe you have hit upon the real purpose of SQC. That being to not spend your time computing indices, or trying to make sense of the differences between them. Instead, your using the run charts to signal areas where improvements can be made, and you’re working to make them. Bravo! This is the real work of any viable continuous improvement effort… Again, thanks for your input to this discussion.
Ken
I have read the initial question and then some of the answers. I thought I had misread the initial question so I went back and read it again. Then I thought I had mis read the answers and went back and read them again. If we are all SS people we seem to have lost track of the problem.
The question stated that Bernie understood the difference between Cpk and Ppk and just wanted a formula.
It should be as simple as the first answer which said: same formula, different std. dev. or the difference between within group vs between groups.
One benifit of consulting is we get to see lots of different stuff. One of the more interesting thing lately is that in some places Cpk is short term and Ppk is long term; however in some areas it is opposite which can be seen in the responses as well.
I like the Minitab approach which associates them by the way the std dev is calculated. This way the doers can get on with doing and the philosophers still have something to pontificate.
On Monday, 8th October 2001 there was a message posted about short term and long term capability that stated – “The difference is regarding lot size and duration. Ppk is from a short term study, let say 25 sample, where you know the potential of your process. Cpk is from a long term production data.”
What specifically, about lot size and duration dicates Ppk for short term and Cpk for long term? Why do the specific sigma calculations more accurately represent each sample?
Does anyone have an Excell Spreadsheet set-up to caculate Cpk, Ppk?
Or do you know how to make Excell do it for you?
The previous explanation for Ppk and Cpk is reversed.
A caveate here is that Cpk is a long term capability index with measurements taken over a large number of manufactoring cycles. This index works exactly right only for a Gaussian distribution and is an approximation for all the rest. Additionally, its reliability could be suspect due to sources of uncertainity in the sampling procedures and sampling error [Gunter, 1989]. For these reasons, and for purposes of simplification, the discussion that follows later on quality cycles will deal only with the Cp index.
What is long -term and short term std.dev.
Lim Chee Hiong,
You are not getting any response because the answer is on this website if you just do a search for yourself. You should be able to get it on Googla as well.
Nobody is going to help if they don’t believe have put any effort into looking for yourself.
Good luck
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