Determining Control Limits from a desired Cpk

Bev D

Heretical Statistician
Staff member
Super Moderator
#11
not sure what you mean by "prevent any rejected parts"...are you asking for a sampling plan that will only accept the lot when there are no defects in the lot?

in any case you must give us at least the defect rate you want to ACCEPT 95% of the time (or some other confidence level, 95% is typical). This is the AQL. If your Cpk value is OK with you you might want to use this as your AQL level...this means you will accept most lots made at this defect rate.

On the other hand if you want to ensure that you REJECT a certain defect rate 95% of the time, you are stipulating a RQL.

so....we need you to stipulate either an AQL, RQL or even both.
 
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M

Mr.Happy

#12
Hi Bev,
Let me give some more information:
We took 30 parts (history from CMM) and calculated the Cpk value from dimension 46 +0 / -0,1 the Cpk found is 0,78.
Now we want to prevent that out of spec. parts go out to our customer.
This means that we most increase the measuring freq. now it is 1:20 but we don?t want to go as hi as 1:1.
And now my question:
Can I from this Cpk 0,78 calculate the check freq. for the production 1:?
(Confidence Level 95%)
Thanks for your input..
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#13
Well if I take a traditional lot acceptance sampling plan (which doesn't take into account the lot size) and I use your defect rate based on the Cpk value as the RQL and I use a c=0 plan then your sample size 311 ramdomly selected units. (p=.00964)

However, I might advise a different approach. a sample of 30 parts to determine your Cpk is almost useless. Can you post the raw data from your study?

We can devise a better plan if we understand how your process actually varies and this involves plotting your results in time sequence for awhile. this is a fairly low failure rate - how frequently do you see out of spec parts? waht volumes are you running? (how many parts produced in a day, an hour? off of how many machines?). Can you tell us what the characteristic is? hwo is it measured? have you completed a Gage R&R? (if so can you post this data?)

I would advise measuring 3 sequential parts every hour or two for the next several days. then post this data. in this way we can develop a more targeted plan that will have much smaller sample sizes...
 
S

Surehawk

#14
Hmm, this should have it's own thread, but oh well.

a Cp of 0,78 is what I would call a seriously unstable process. It is to early to do math for me right now, but when you have a Cpk of .67 it is 45500 ppm outside your tolerancelevel, but this is only as long as the machine stays stable, and you don't have to be far of target to have a Cpk of .67 when having your Cp value.

I have been doing some research in using the Cp-level to determine a samplingplan, and what I have come up so far is that I have yet to find a process that stays that stable. with a Cp>1.33 it would not be needed a sampling plan if I could trust the process to just stay, then I could just aim at the middle value and then leave the machine never to be measured again.

BUT, with a Cp of .78 I would say you need to do a six sigma project or some other improvementwork on the machine til you get a value at least a little higher then 1, until then I would suggest measuring every single product if you want to avoid sending bad products to your customer.
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#15
a Cp of 0,78 is what I would call a seriously unstable process.
One clarification - a process can be perfectly stable and predictable, but be predictably bad with the Cp of 0.78. That is why it is so important to do the SPC along with the Cp calculations so if you know if the process is stable and not capable, or unstable and sometimes capable, sometimes not capable.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#16
To reiterate what Steve said - I've seen a lot of processes in a lot of industries that were perfectly stable and horribly incapable.


a 0.78 Ppk yields a 9,642 ppm. not all that horrible.
remember that the Z score to ppm convertion is logarithmic
(Z score = 3*Ppk)
 
S

Surehawk

#17
My appolegy, you are both absolutly righ, incapable would be the word not unstable.

And I suppose it is depending on the industry if you would call almost 1% of the products in a controlled process outside tolerance ok.

I stand by my opinion, however, that a sampling plan after a Cp value by itself is not a good idea.
 
M

Mr.Happy

#18
Hi Guys,

Some additional information:
parts are machined in 2 steps on one Horizontal milling machine.
One side of the dimension is in step 1 the other side is machined in step 2 an makes the end dimension of 46 +0 /-0,1mm.
Machine is running in 3 shifts and produces about 16 parts per shift.
All the dimensions are stable except for this one, see attached XLS file for the calculations.

Thank you all for your input until now, and if it really need his own topic maybe one of you can help to do so?

Mr.Happy
 

Attachments

Bev D

Heretical Statistician
Staff member
Super Moderator
#19
hmmm. The process in question isn't necessarily unstable - there is no way to tell that without a time series plot of the data.

the histogram suggests that the process isn't homogenous and this would be a very important clue as to what is going on to get at the causal mechanism and allow you to develop a much more effective sample plan to catch the out of spec parts.

but we need to know more:
how did you sample the 30 pieces? were they produced close in time or spread out over many days or weeks or months?
Is more than 1 mill involved? If so are teh resutls from different mills mixed into this data?
can the characteristic be measured in more than place along the length? is the CMM result an average of several measurements or a single reading in a set location?


If you have historical data from your 1:20 CMM measurements can you get a time ordered output of the results for the last 4 weeks?

by the way 9,000ppm is 0.1% (not 1%) and you have NO out of spec parts...
 
B

boyan

#20
hmmm. The process in question isn't necessarily unstable - there is no way to tell that without a time series plot of the data.

the histogram suggests that the process isn't homogenous and this would be a very important clue as to what is going on to get at the causal mechanism and allow you to develop a much more effective sample plan to catch the out of spec parts.

but we need to know more:
how did you sample the 30 pieces? were they produced close in time or spread out over many days or weeks or months?
Is more than 1 mill involved? If so are teh resutls from different mills mixed into this data?
can the characteristic be measured in more than place along the length? is the CMM result an average of several measurements or a single reading in a set location?


If you have historical data from your 1:20 CMM measurements can you get a time ordered output of the results for the last 4 weeks?

by the way 9,000ppm is 0.1% (not 1%) and you have NO out of spec parts...
I am net to this forum and I have to say hats off to you man... I wish one day I reach your level! lol
 
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