Due to this our customer requesting us to come up with Pp, Ppk figures.
With the data given below can anyone help to figure out the pp,ppk value?

Spec: 107 ± 3 microns
Sample 1 2 3 4 5 6
1) Part A - 108 107 105 108 106 106
2) Part B - 106 107 105 105 104 106
I need to know the formula (not with those code) but the numerical formula using the example above so that in future I can calculate myself.

Please advice. Thanks

Have a look here: http://www.isixsigma.com/library/content/c010806a.asp

I've gone thru that site already and it doesn't have any numerical example shown there.

Anyone here please use the example posted to show me the formula. Thanks.

Attached is the results of a Minitab analysis of the data - numbers & graphs pasted into a word document. Hopefully that points you in the right direction. If you have questions about specific numbers, I should be able to provide a little guidance.

Tim F

Attached is the results of a Minitab analysis of the data - numbers & graphs pasted into a word document. Hopefully that points you in the right direction. If you have questions about specific numbers, I should be able to provide a little guidance.

Tim F
Thanks for your reply. I need to know the numerical formula to get the result.

Please advice. Thanks

You can calculate capability using a scientific calculator.

1) Find mean and standard deviation from the data.
2) Multiply std dev by 6.
3) In your case, tolerance band is +/- 3 or total 6
4) Divide 3) by 2) to get Pp

5) Find smaller of the two absolute values (UCL-Mean) and (LCL-Mean). Use only smaller value.
6) Multiply std dev by 3
7) Ratio of 5) by 6) will give Ppk.

Confidence band using such low sample size is unacceptably wide therefore your calculated values may not mean anything useful in real life. Even with 30 samples, capabilities have tolerance value of +/- 25 %.

Also see these related Cove threads:

Ppk vs Cpk - Good, clear explanation (http://elsmar.com/Forums/showthread.php?t=1994)
Cpk vs. Ppk - Long Term vs. Short Term - Capability vs. Stability (http://elsmar.com/Forums/showthread.php?t=7065)
Cp/Cpk vs Pp/Ppk (Short term using population sigma) - Formulas to use? (http://elsmar.com/Forums/showthread.php?t=4048)

Some Process Capability visuals (http://Elsmar.com/Cp_vs_Cpk.html)

Due to this our customer requesting us to come up with Pp, Ppk figures.
With the data given below can anyone help to figure out the pp,ppk value?

Spec: 107 ± 3 microns
Sample 1 2 3 4 5 6
1) Part A - 108 107 105 108 106 106
2) Part B - 106 107 105 105 104 106
I need to know the formula (not with those code) but the numerical formula using the example above so that in future I can calculate myself.

Please advice. Thanks

There is not enough information here to calculate Pp or Ppk. What is the process. and what does the data represent? The capability analyses that have been provided from dumping this data into a number cruncher may only indicate that the variation you see is from measurement error and perhaps gage error (since a six micron tolerance should be measured with something with a resolution of 600 nanometers at a minimum - and more likely 100 nanometers - not 1 micron resolution), which tends to be normal, and tends to nicely mask the actual process variation. If this was a part from precision machining (the 6 micron tolerance makes me suspicious that it might be), and you both controlled and measured the part correctly, then the capability is (USL-LSL)/UCL-LCL) - not any of the citations listed previously.

See Statistical process control for precision machining (http://elsmar.com/Forums/blog.php?b=79) for more information, if it applies.

You can calculate capability using a scientific calculator.

1) Find mean and standard deviation from the data.
2) Multiply std dev by 6.
3) In your case, tolerance band is +/- 3 or total 6
4) Divide 3) by 2) to get Pp

5) Find smaller of the two absolute values (UCL-Mean) and (LCL-Mean). Use only smaller value.
6) Multiply std dev by 3
7) Ratio of 5) by 6) will give Ppk.


I'm trying to sort out Cpk and Ppk too. So... if I am understanding this correctly, the calculations for Cpk and Ppk are identical.... just use a different sigma.

But that doesn't match my basic understanding ...Cpk is how well curve fits between the control limits and Ppk is how well the curve and limits line up with the specifications. How can the same calculation give two different things. :confused:

You can't go wrong in using minitab. I don't work for minitab, just think it is the greatest tool ever!!! Well worth the time to learn it and use it...my opinion, just sharing the joy!

You can't go wrong in using minitab. I don't work for minitab, just think it is the greatest tool ever!!! Well worth the time to learn it and use it...my opinion, just sharing the joy!

One down side of minitab: GIGO!

Gigo????

Gigo????

garbage in garbage out.

not all distributions are Normal, not all sampling for process capability is correctly done, not all processes are shown to be stable prior to calculating capability, knowledge of the formulas and their intent IS important in interpreting the resutls.


or as Hubert Blalock said: "The manipulation of statistical formulas is no substitute for knowing what one is doing"

I'm trying to sort out Cpk and Ppk too. So... if I am understanding this correctly, the calculations for Cpk and Ppk are identical.... just use a different sigma.

But that doesn't match my basic understanding ...Cpk is how well curve fits between the control limits and Ppk is how well the curve and limits line up with the specifications. How can the same calculation give two different things. :confused:

There are a lot of posts on this very topic here. I would suggest searching for them and then coming back for specific questions. : )

Gigo????

Garbage in - garbage out. It is just a number cruncher. If you do not have a thorough understanding of the source data, it can lead you down a thorny path.

For example: When you calculate a variance (and therefore a standard deviation) of a process, it really represents the total variance. Total variance is a composite of many variances, and they may be of differing distributions - normal, uniform, Weibull - all in differing levels of participation. Making valid decisions likely requires understanding these underlying distributions. The software will not know this, it is not that bright. The user has to ponder these things.

(Yikes...Bev beat me to it!)

I am experiencing that now on the job....non-normal. We are going to take a larger sampling, we are thinking that we didn't get all of the population even though our initial sampling plan was thought to be good.

I am experiencing that now on the job....non-normal. We are going to take a larger sampling, we are thinking that we didn't get all of the population even though our initial sampling plan was thought to be good.

Could be the distribution is truly non-normal! It could happen! Which means your entire population will be non-normal, so your sampling may have been correct.

What is the process?

Blowmolding at this stage, then once that process is stable, the into maching/cutting, welding and then finally assembly. We need to get the blowmolding process stabalized as much as possible in the critical areas first. Yes, it maybe non-normal, but won't know until we actually measure more.

or as Hubert Blalock said: "The manipulation of statistical formulas is no substitute for knowing what one is doing"

I would add to the quote: "...unless you're an SQE for an automotive OEM."

Blowmolding at this stage, then once that process is stable, the into maching/cutting, welding and then finally assembly. We need to get the blowmolding process stabilized as much as possible in the critical areas first. Yes, it maybe non-normal, but won't know until we actually measure more.

I could see a blow molded dimension being non-normal - maybe a Weibull or such. Perhaps similar to a unilateral tolerance, but based on physical limitations (such as the part can be no larger than the mold, but it can shrink smaller...)

Just a thought...

Thanks Bev, but I've already searched and read and read and read and read and read....
And it is still as clear as mud. I think "How can one calculation give you two different things (results or concepts)?" is a relatively specific question.

Thanks Bev, but I've already searched and read and read and read and read and read....
And it is still as clear as mud. I think "How can one calculation give you two different things (results or concepts)?" is a relatively specific question.

This explanation is a tad oversimplified, but it should serve to explain the distinction for you.

Cpk is based on the sample standard deviation and Ppk is based on the population standard deviation. The former is used, as its name suggests, when calculations are based on sampling, rather than measuring all of the individuals. The population standard deviation, on the other hand is used when all of the measurement data for individuals is available.

If your population (all of the things that have been produced, e.g.) is comprised of 100 individuals (for example) and you measure all of them, you would use the population standard deviation. On the other hand, if you have the same population but you've measured them by sampling in subgroups as production is running, you use the sample standard deviation, which, if done properly and you have a normal distribution, will give you an estimate of the population standard deviation.

Over time, given a stable process, the difference between the sample and standard deviations will become negligible.

Thanks, Jim. So... would it be safe to say that an excel sheet that I found and am using should probably only have the Cpk stats as the data input is based on repeated sample sets of 4 each? And that deleting the Ppk portion to avoid confusion would be wise?

Thanks, Jim. So... would it be safe to say that an excel sheet that I found and am using should probably only have the Cpk stats as the data input is based on repeated sample sets of 4 each? And that deleting the Ppk portion to avoid confusion would be wise?

no it may not be 'safe'. it depends on what you are intending to do...or what your customer is actually asking for and wihtout seeing your actual data we cannot say that it is safe.


unfortunately many papers and customers use the term Cpk when they actually want long term capability (the index that uses the total standard deviation). This can be very confusing becauae as Jim stated Cpk uses only the within subgroup standard deviation which will understate actual variation. (IF your process is statistically in control AND you have a relatively independent Normal process stream then Cpk won't be much less than Ppk but it will ALWAYS be less than Ppk.)

so the real question is: what are going to use the index for?

But that doesn't match my basic understanding ...Cpk is how well curve fits between the control limits and Ppk is how well the curve and limits line up with the specifications. How can the same calculation give two different things. :confused:

This is another point of your confusion: Cpk is a comparison of the within subgroup variation to the specification limits NOT the control limits.

Ppk is a comparison of the total variation (within subgroup and between subgroup) to the specification limits.

This is another point of your confusion: Cpk is a comparison of the within subgroup variation to the specification limits NOT the control limits.

Ppk is a comparison of the total variation (within subgroup and between subgroup) to the specification limits.

OK... I think that makes sense. When we say "long term study" - how long? We have no customer requesting any info as yet, but in order to get our TS cert we will need to produce at least one complete PPAP package which includes statistical analysis.

Most of this line (Power Ring Capicitors) is 'specially designed for each customer, and they are ordering 1-10 of them. With no two orders identical the only "long term" data I can produce is % yield and Customer Satisfaction (inferred from lack of complaints and repeat orders). The largest single order I have is 50 pieces for which we have cap and diameter data.

I am struggling with how to turn such limited data into meaningful statistics.

After we have our TS cert there is a good chance that we will have a contract that produces a few thousand pieces per month, but that doesn't help me now.

We do (finally!) have the "blue books" on order :read:and I am hopeful that there will be considerable help in there for this weird little scenario.

:rolleyes:

We do (finally!) have the "blue books" on order :read:and I am hopeful that there will be considerable help in there for this weird little scenario.

:agree1: Good to have the rules of the road. The SPC book is handy, but geared toward larger volumes.

I am struggling with how to turn such limited data into meaningful statistics.


One of the first problems with PPAP data is the expectation of a minimum run size - which would give you a more data to work with. 2.2.11.2 Quality Indices (in the PPAP book) which appears to be you biggest tripping point, states "When not enough data are available (<100 samples) or there are unknown sources of variation, contact the authorized customer representative to develop a suitable plan"

Ah, the typical AIAG "out". At least they give you one. They are learning. Maybe the best thing to do is insert an attribute chart into the PPAP package for your statistical analysis, and use the above statement to cover it.