Cp/Cpk vs Pp/Ppk (Short term using population sigma) - Formulas to use?

A

Atul Khandekar

#11
Process capability is an idealistic state assuming that all variation is due to common cause only and the process is centered. It is measured by taking variation measurements over TIME from a process that is statistically stable (only common cause variation present).
Agree with you completely Rick. However, we do have two different Process Capability indices, Cp and Cpk. Cp just compares spec width with process spread but does not provide any indication of centering. So Cp alone is not enough. With Cpk we have some indication of center shift.
-Atul.
 
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R

Rick Goodson

#12
Atul,

Good point. Thanks for the clarifiaction. By the way, I looked at the website you referenced. Excellent article by Dr. Mehernosh Kapadia. Thanks for the tip.

Regards,

Rick
 
B

Brian Dowsett

#13
Here's a thing.....
Back in my Ford days, Ppk meant Preliminary Process Capability, and was an initial assessment prior to getting the SPC up and running for Cpk.

However, current thinking seems to say that Ppk means "Performance index" and is used to assess actual process performance OVER TIME.
This is confirmed in the QS9000 SPC manual (page 80 in my old copy)and also in Minitab software (which calls Ppk long term) and also in my black belt training.
Formulas are as they always were.
Big difference is that I used to expect Ppk to be bigger than Cpk, now it's the opposite.

Funny old world......
 
#14
Brian,
Same here.
I pulled out my old copy of "Continuing Process Control and Process capability improvement" by Ford and found nothing, in the form of an ea quation , relating to Cp, Pp, or Ppk.
 
A

Atul Khandekar

#15
:confused:

I am still under the impression that Cpk (estimated with rbar/d2) is long term and Ppk (...n-1) the short term capability. Minitab's interpretation is the other way. I must say this is confusing.

Is it:
1.Ppk as in preliminary capability: you may take n data points consecutively. Use the (n-1) formula
2.Ppk (minitab version): n data points come from SPC study, over time, Use the (n-1) formula
3. Cpk:n data points come from SPC study, over time. Use subgrouping and estimate with rbar/d2.

:confused:
Help!!
 
K

KenK - 2009

#16
Forget the "long term" vs "short term" thing. I don't know where it originated (M. Harry?), but using the definitions of Cpk and Ppk from the AIAG SPC Reference Manual, they just don't apply.

Even MINITAB no longer uses long-term & short-term. As of Release 13 they changed their terminology so it now associates Cpk with the descriptor "Potential (Within)" and Ppk with the descriptor "Overall".

The user can calculate Cpk and Ppk at any time, assuming subgroups are involved. Even if subgroups aren't involved, MINITAB calculates the Cpk using a standard deviation estimate based upon a moving range of size two (see the Estimate option).

Think of Ppk as being the actual performance of the process since its estimate of variation includes ALL observed variation - it has absolutely nothing to do with being "preliminary".

Think of the Cpk as the the potential performance, or the potential capability. This is, it is what we'd get for the Ppk IF we removed all instability between subgroups (that is, the control chart line is completely flat).

Think of the Cp as the best potential performance. Not only does it assume the process is completely stable, but it also assumes it is perfectly centered.
 
J

Jim Jakosh

#17
Cpk vs Ppk

You are not alone in your confusion. I have to explain that very thing to our folks becsue I created electroin X bar and R charts and Capability study charts and they use different calculations.

Here is the scoop I've found.
Cpk for short term capability using the Sq Rt of the sum of the diff's over (n-1) is the sample deviation when YOU DON'T KNOW THE STABILITY from whence you got the samples. They could have common and special causes at work. This is referred to to as Process performance ( Ppk) by the automotive group.

The same formula over (n) is the Capability of the population
when you measure every part in the population ( not just a sample) and you don't know its STABILITY.

Calulcating the Cpk using Rbar/d2 as the std. dev. assumes you have a STABLE population. It is generally used with an X bar and R chart where you can see the pattern and throw out any unstable points and do the calculation.

We distinguish between them as short term and ongoing capability. If the poplualtion from where you drew the short term samples is stable, the two vaules of Cpk ( wiht (ni10 and R bar/d20 should be very close after you measure 100 or more samples.
Thanks, Jim Jakosh
 
C

Chemlab

#18
Not exactly the same topic, but sort of. Have a few questions about setting tolerances and control limits.

1. Our customers often put TBD on the print for physical properties of the material until after 25 batches. For each batch, 5 samples are taken and after 25, we are expected to recommend a specification based on Cpk = 1.33. I have a problem with this that I think is legitimate and trying to make the customer understand. First of all, the samples are not 25 groups of 5 from the same batch of material over time. If 100 samples are taken from the same batch, a nice normal curve is seen. However, calculating Cpk does not take into account sub-group to sub-group variation based on Rbar/d2 - subgroups being different batches. Alot of the variation is a mean shift from batch to batch and the statistics are being done on different populations, different batch of material, thru several independent processes that could affect the measurements. Not only are different batches (from which only 5 samples are taken) being lumped into the equation, but several different setups over time. The result is usually a non-normal distribution. The problem is, given a specification, if I were to sample lots of parts from a particular batch, the capability is fine because 'sigma' is tight, but if treated as if the data came from one batch (population) over the course of 25 batches, then on paper it looks terrible if Ppk is calculated, but so wonderful for Cpk that the specifications are made too tight. I understand that batch-to-batch variation needs to be eliminated, I am just saying that I don't think this is exactly right. We had Chrysler come in some time back, and they argued with our Tier 1 customer that statistical specifications could not be set for this application and that only go-no-go limits could be used.
Anyone know how to properly handle the statistics or do I have it all wrong?

2. Much like #1 above, but with regards to calculating control limits. We have a grinder that, once set up, is VERY capable with the variation taking up so very little of the tolerance. I could sample parts from now to eternity and Rbar would very small. On the next setup up after running a different part, the same capability would be seen. Using R-bar/d2 from the various setups, after the control limits are calculated, they are so tight that the operator has a very hard time just setting up between these limits because the formula doesn't not take into account different setups, which are different populations. However, we can't make new control charts for each new setup because of the short time involved. I've briefly looked at short-term SPC. Is this what I need, something else, or am I totally misunderstanding something?

Thanks.
 
S

sxbalasu

#19
CPK/PPk confusion

As far as my understanding goes CpK is process capability index we get from the data we collect from our control charts on daily basis. Also we use Rbar/d2 to get the sigma value. Basically Ppk is calculated when we do a PPAP. That is when we run 300 components with production tooling and set up and we check random 100 parts from that and calculate sigma with n-1 and this show the preliminary process capability index. What i did when i did PPAP was i got the Pp and Ppk values for the critical characteristics(variable) and if they were below 2.00 then i use a Xbar R control chart and monitor Cp and Cpk on a monthly basis from the data i got from these charts. This also can be used to show continuous improvements onthe process capabilities.
Hope this clears somebody's doubt
 
T

Tim K

#20
Capability Studies

:bigwave:


I agree with the above discussions clarifying Ppk and Cpk.

In the orignal post that started this, the author stated that the data was for individual readings. Since this is the case, Cpk should not have been calculated because it represents data collected as a sub-group.

I am attaching a Capability Study Form I developed. Cpk is calculated from the sigma using R-bar/d2. Ppk is Calculated from the sigma using (n-1). Cpm is calculated from the sigma using (n-1), and it is based off a Taget Value instead of the mean of the tolerance.

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.

Since I already posted this at another site, I guess you need to follow this link:

http://Elsmar.com/Forums/showthread.php?s=&threadid=1994&pagenumber=3

Hope this is helpful :)
 
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