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Minitab Capability of the Population (no sampling)

#1
Hello!

I've a question about dealing with capability studies on a population (no samples).

In Minitab, when we're doing a Capability Study in a Normal fitted Population, what's the meaning of the subgroup and the CpK? This example, is about a population of several thousand parts analysed within less than an hour in a final testing machine. Being a final test, it's the sum of the previous processes and all of its common and special causes. We're doing a subgroup of 1 but, in this kind of analysis, the only important thing would be Pp and Performance? Or am I wrong on this? The Cp is doing its analysis through the moving average between only 2 parts. If I make the test of doing the subgroup of 1/4 or 1/2 of the parts, the Cp obviously starts to be very close to the Pp values. This several thousand parts are related to each batch of material from several ones along the day (without being the issue in this post, as info, for the intra batch we're using the Between/Within Capability analysis and the subgroup is the batch).



This example is from the Electronic Industry but, I've the same issue in the Injection Molding industry.

What are your advices with this exemples? Is Cp (short term analysis) helpful in this kind of situations?


Many thanks for your replies
 
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Jim Wynne

Staff member
Admin
#2
In order for a capability study to be any kind of useful, the time element is indispensable. Without sampling in chronological order, you have nothing insofar as process capability studies are concerned. This isn't to say that useful information can't be derived from sampling a population, however.
 
#3
Hello!

Thank you for your reply.

All parts of the population are in chronological order. It's a serial production with every part after the previous one. Every part follows all the processes in a row from start to the testing and inspection machines. All of the processes comprise in-line cutting, pressing, electrolyte and other chemical processes and heat treatment.

The capability is a requirement from the costumer. They're doing it in all good parts or, in other words, the entire population. My doubt in my previous question was, if we should use Pp and if Cp (short term) is of any use?

Many thanks for the the advices
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#4
Both Pp and Cp “apply”. But more on that later.

The real question is regarding the ‘sampling’: do you actually test every single part made? Or do you only test every single part made for a specific Customer? What do you consider a ‘batch’? You should never ‘play around’ with the subgrouping. If you are indeed testing every single part made (in the time order in which it is made) then your subgroup size is 2 (sequential parts) period.
 
#5
Both Pp and Cp “apply”. But more on that later.

The real question is regarding the ‘sampling’: do you actually test every single part made? Or do you only test every single part made for a specific Customer? What do you consider a ‘batch’? You should never ‘play around’ with the subgrouping. If you are indeed testing every single part made (in the time order in which it is made) then your subgroup size is 2 (sequential parts) period.

Hello again!


Thank you very much for your reply.


Yes. Every part is tested. 100%. The whole population and for every costumer. It's an in-line real-time testing workbench. The natural subgroup is 2 just like your advice. We can divide it in other natural groups ranging from, material batch as well as other common causes when we're regarding process control and process improvement. We have all of that data but, when the OEM Automotive manufacturer demands the capability study of the bought parts, does it make any sense to show him the Cpk?

- He wants the capability study for all the parts he buys;
- If we send him the CpK (Within) the value will be close to 2.5 and the PpK (Overall) will be no more than 1.1;
- The real process yield is around 97%!!!;
- In my point of view, the short term Cp is the target of possible and profitable progressive process improvements of the Pp, for the same 4M's baseline;
- I believe they're asking for the Pp based on the Sigma of the population and, not the estimate regarding the short term moving average of a subgroup of 2 and its CpK;
- My question arose because I see people who are used to ask for the capability but, in the eyes of the costumer, what he probably wants and is not asking correctly, is the Ppk. I believe is only trying to have something that can guarantee his processes;
- He doesn't even care about any batch of material. He demands to have every batch of material coded and separated but, he wants the capability of all the batches he bought together into one;
- I'm only now working in the company and there's a high risk on this information. We can be delivering parts for several years with the wrong data and, with the costumer also asking it wrongly. When I'm with my colleagues and with the costumer, I see myself as a clear advanced Minitab user compared to them. I & we believe that we need to take real care addressing this subject;

What are your thoughts on this subject?

Thank you in advance for any replies,

Miguel Ribeiro
 
#6
Hello again,

following the last post, if we measure everything, why does the costumer wants the capability? Like you said, we're not sampling. The only thing crossing my mind is that he wants to have more tools regarding any problematic background on our side or, from any other supplier!

In the contest of the last post and the note on this one, what are your thoughts and advices on this issue?

Many thanks for your replies,

Miguel
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#7
This is always a difficult situation. In general, my experience is that the Customer doesn't know what they are asking for. They are simply and blindly applying their 'standard' request. There will be no thought given - they will just check a box saying that you submitted the data requested and be done with it.

Neither Cpk or Ppk have any use for individual shipments/lots/batches. There may be some inference that could be made if you were sampling, and you knew the distribution and you were not concerned with the outer 1s tail(s). All predictions of defects beyond the inner +2s is fraught with over estimating the defect level as distributions simply don’t have infinite tails in reality. The way statistical coverage of distributions work is that at least Y% of the distribution lies within +Xs of the mean. too often people misinterpret this to mean that Y% of the data must lie beyond +Xs of the mean – this is how they predict defect rates with Cpk/Ppk. And it is wrong. Of course if you have tested unit then you actually know how many defects exist. Applying Cpk/Ppk to predict the defect rate is quite frankly nonsensical. Crudely put it is stupid.

There is one clarifying question I have: are you only calculating Cpk/Ppk on yielded product?

Are you sure your Customer is actually asking for short term capability? Some companies ask for Cpk but the formula they use is for Ppk.

There are two considerations here that might be a tad useful for you.

First: all capability indices are basically useless as – well as useless as the most useless thing you can think of. Especially when they conflate defect rates with the index. But we are stuck with them as long as people refuse to engage their brains and THINK. Once you accept that you will be better able to argue against it or just supply their misguided request with something that keeps everyone calm.

Second: there is great intrinsic value in understanding the components of variation of your process: piece to piece, batch to batch, raw material lot to lot, etc. They can help focus you on the best areas to improve your product performance. But you don’t need Cpk or Ppk to understand this a simple multi-vari chart will tell you what you need to know.
 
#8
This is always a difficult situation. In general, my experience is that the Customer doesn't know what they are asking for. They are simply and blindly applying their 'standard' request. There will be no thought given - they will just check a box saying that you submitted the data requested and be done with it.

Neither Cpk or Ppk have any use for individual shipments/lots/batches. There may be some inference that could be made if you were sampling, and you knew the distribution and you were not concerned with the outer 1s tail(s). All predictions of defects beyond the inner +2s is fraught with over estimating the defect level as distributions simply don’t have infinite tails in reality. The way statistical coverage of distributions work is that at least Y% of the distribution lies within +Xs of the mean. too often people misinterpret this to mean that Y% of the data must lie beyond +Xs of the mean – this is how they predict defect rates with Cpk/Ppk. And it is wrong. Of course if you have tested unit then you actually know how many defects exist. Applying Cpk/Ppk to predict the defect rate is quite frankly nonsensical. Crudely put it is stupid.

There is one clarifying question I have: are you only calculating Cpk/Ppk on yielded product?

Are you sure your Customer is actually asking for short term capability? Some companies ask for Cpk but the formula they use is for Ppk.

There are two considerations here that might be a tad useful for you.

First: all capability indices are basically useless as – well as useless as the most useless thing you can think of. Especially when they conflate defect rates with the index. But we are stuck with them as long as people refuse to engage their brains and THINK. Once you accept that you will be better able to argue against it or just supply their misguided request with something that keeps everyone calm.

Second: there is great intrinsic value in understanding the components of variation of your process: piece to piece, batch to batch, raw material lot to lot, etc. They can help focus you on the best areas to improve your product performance. But you don’t need Cpk or Ppk to understand this a simple multi-vari chart will tell you what you need to know.
Hello!

First of all, thank you for your reply!

Your first paragraph and your first observation are aligned into what I also believe: they're probably following a "standard, and the "thinking" part doesn't exist. I also believe that who's asking for it has no power to question anything about it: centrally decided. It's probably a standard to all suppliers independently if they're sampling or not: "blind pre-requisite." We'll try to figure out what are the formulas behind they're capability calculations. They're probably using the Pp and PpK ones! I'll see internally if we have any possibility or context to discuss this point with the costumer.

About the predictions of defects beyond the inner plus or minus 2s, I usually say that it's "up to" and never " it is". The way you said it will correct my approach from now on to "...statistical coverage of distributions work is that at least Y% of the distribution lies within +Xs of the mean."

We send several batches assembled into one weekly capability study. For me, I'm trying to take advantage of the testing machines and go backwards into the processes trying to link it back to the local SPC (I believe that I also need to see it better with the process owners). We're also tracking it mainly to the special causes within the 4M's approach (material batches, shifts and setups) and I'll bring into to the "...piece to piece, batch to batch, raw material lot to lot, etc.". The idea is to go into improvement the product and decrease waste by understanding the "....great intrinsic value in understanding the components of variation..."

I didn't post your clarifying question because while on my mind, I thought that it could divert people from the main subject. You went right into the point: "are you only calculating Cpk/Ppk on yielded product?"

I don't like the awnser I'm going to write but, while writing it, I want you to know that we're deeply concerned in correcting this approach. In the past we were brushing the data out from all the points. The criteria were about taking out the points "we know" that are bad readings, machines errors or any known subjects. I've asked how sustainable it is this selection with all the thousands of parts and 15 to 20 batches every week. SOP or any other thing? What we've found is that the completely "stupid" readings, are clearly well taken off. The others usually are bad products, dragging also off a considerable percentage of good points (all of them are out of control (<LCL; >UPL)) . We're having several discussions because we now know that we can't do a taylored "VOP". For us to improve we need to know were are the problems. Doing this will mislead us in our internal improvements efforts. The testing machine guarantees the good parts for the costumer but, doesn't solve our problems. On the costumer side, we have about 1,6 PpK but internally the values are trending to an Overall of 1-1,2 PpK. Do you have any advice on all of this process?

*I've also asked if the error of the system can bring in a part as "good" In the same way the error says it's "bad"!

Thank you in advance for any replies!
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#9
One purpose of the Ppk calculation has been posited that it gives an idea of YIELD and therefore cost reduction opportunity as well as understanding risk of making on-time deliveries. This does require that all results are included not just the passing results or the shipped product (after rework or repair). Of course simply plotting your yields in time sequence does this much better without cumbersome math. Plotting your data in time sequence also provides really good clues as to the causes or areas to look for improvement. To ignore the failures is to fool yourself. It would also be a violation of Customer requirements that could be observed in an audit.

The only data that should be censored (even when using outlier detection math) is that which is clearly invalid. A testing error or data entry error. Everything else counts - even the data that is out of statistical control.


And you should definitely perform a MSA for pass/fail. That is step ONE in SPC (step 2) and process capability (step 3)
 
#10
One purpose of the Ppk calculation has been posited that it gives an idea of YIELD and therefore cost reduction opportunity as well as understanding risk of making on-time deliveries. This does require that all results are included not just the passing results or the shipped product (after rework or repair). Of course simply plotting your yields in time sequence does this much better without cumbersome math. Plotting your data in time sequence also provides really good clues as to the causes or areas to look for improvement. To ignore the failures is to fool yourself. It would also be a violation of Customer requirements that could be observed in an audit.

The only data that should be censored (even when using outlier detection math) is that which is clearly invalid. A testing error or data entry error. Everything else counts - even the data that is out of statistical control.


And you should definitely perform a MSA for pass/fail. That is step ONE in SPC (step 2) and process capability (step 3)
Hello!

Thank you for the reply!

Recently, due to all of this subject I've developed a internal training starting by what everybody wanted to hear, Capability! After that, I've directed to all of the 3 steps you've mentioned and also that is important to have processes under control: several info from Dr. Deming and Dr. Juran. Now we're analysing processes and discussing the sampling procedure and size for the MSA! Our latest discussions are how to do the MSA across all production lines! We're doing this analysis supported by the AIAG Manuals, the books "Mastering Statiscal Process Control, Tim Stapenhurst - Elsevier", "The Certified Six Sigma Green Belt Handbook - ASQ", "The Certified Six Sigma Black Belt Handbook-ASQ" and the Minitab Quality manual.

This does require that all results are included not just the passing results or the shipped product (after rework or repair).

Another amazing thing I forgot to say: the costumer only wants the capability of the parts we're sending!!! We're doing it the best we can but what is this for?

Internally, when I've started to ask the questions you saw in the last posts, the resistance was huge and the ideas were fare from welcome. At this moment, things are changing and here I am! We now have most of the leaders on the boat trying to find ways to improve. We're trying to bring in the costumers but, it's not being easy to do it. We've zero complaints.

We'll follow your advices regarding the costumers approach and the efforts to improve the internal processes. I hope these ideas can go fast enough and I, that started to make the questions, won't being killed in the process: "It is difficult to get a man to understand something, when his salary depends upon his not understanding it. - Upton Sinclair".

I'll keep in touch. Any more advices are welcome! Many thanks for your help until now.

PS: I've enjoyed your "Statistical Alchemy" post and attachment.

Miguel
 
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