Sample Size for Capability Calculation

P

Palt88

#1
Hi all,

Sorry I have browse a little bit in the forum, but not able to find something relevant...

If You want to calculate the capability (Cpk or PpK) of a batch, and only this, we do know that a representative sample of minimum 32 parts is required to get a correct calculation.

But when you have large batch of 500 000+ parts, what sample size would you take to have a reliable result? is there any clue for large batch size?

Just to explain you what we are doing:
We are manufacturing batch which are between 500 000 and 1 000 000 parts (approx this is done in 3 days).

At each determined frequency we are taking some samples => at the end of the batch we have collected let's say 300 samples.

=> The capability is calculated (continous dimensional datas). According our customer the result must be over 1.00

Is there any rational or clue to write to say that 100 samples or 50 or whatever instead of 300 are enough to make the capability calculation?

Thanks
Fred
 
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bobdoering

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#2
Re: Sampling size for capability calculation

Before even attempting to answer this, it would be good to identify what the process that produces the batch is - to get an idea of how homogeneous the batch process is as a starting point. Is this a batch you control, or would this be incoming receiving of a batch of product from outside your control?
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#3
Re: Sampling size for capability calculation

The accuracy of a sample size is not related to lot size* (population).
The important characteristics are the standard deviation of the lot and the representativeness of the sample. As stated in your other post the sample size of 32 is an arbitrary seelction for your company and is not a universal standard...

Yes, Minitab's sample size tool will help you calculate a sample size that is appropriate for the accuracy you want given the standard deviation of your process and how 'confident' you want to be in your estimate.


*The only exception to this is when the lot you are sampling from is relatively small and then a finite population adjsutment can be made. However, most industrial appplicaitons don't need this...
 

bobdoering

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#4
Re: Sampling size for capability calculation

...and the representativeness of the sample.
This is the key point my questions are trying to address - and may be the toughest to ensure - especially without an understanding of the process. If it is one big vat that is poured off into individual containers, then it may be very homogeneous and the sampling will work fine. But, if it is actually from a "batch" (as in one set-up) of a continuous process that can vary over time - all bets (as in probability) - are off.
 
P

Palt88

#5
Thanks Guys for your help,

Sorry I'm little bit confused. I don't know if the things you are asking have any influence in my question?

To clarify if it can helps : we have an internal production of moulded components and, for example within a produced batch of 800 000 pcs, 300 samples are taken to be QC measured and then Cpk'ed.

About the process: the samples are representative...and the process is stable and is six sigma capable since years.

But...my question is strictly based on the sampling size required FOR A CAPABILITY CALCULATION (I insist :)): what I learned since years is that we need 30 or 32 samples minimum in any cases, not less.
But then...when you have large batch is this still enough for the calculation?

Is there any existing formulas or table or should I go a complete different way? (I'm thinking of comparing capabilities calculated with 300 parts and capabilities calculated with for example 60 parts and compare if there is significant difference between these 2 results issued from a same population) :confused:

Thanks
 

Phil Huber

Inactive Registered Visitor
#6
Considering your statement that this process has already demonstrated stability and capability, my Six Sigma workbook suggests a minimum sample size of 40 pcs to construct a histogram which could then be used to calculate sigma and process capability.

Hope this helps.
 

Phil Huber

Inactive Registered Visitor
#7
One other thought came to me. If you wish to perform this capability study a number of times over some period, you could perform an F-Test to see if these populations vary with any statistical significant difference.
 
C

CristianoP

#8
[...] my question is strictly based on the sampling size required FOR A CAPABILITY CALCULATION [...]
You need to know the distribution of the variable for which you are calculating the Cpk, then you can calculate the confidence intervals for the mean and for the standard deviation.

If your variable is normally distributed, you can take a look at the NIST's handbook chap. 1.3.5.2 or 7.2.2.1 (for the mean) and 7.2.3.1 for the standard deviation.

Cristiano
 

bobdoering

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#9
You need to know the distribution of the variable for which you are calculating the Cpk...
That's the key point. Incorrect sampling (sampling error) will lead to an erroneous assumption as to what the distribution is, further compounding errors in subsequent calculations. That is why a sample size taken with sufficient frequency and sufficient size to establish the correct distribution is necessary - and a good basis for the question. Is a sample every 26,000 parts (30 pc sample) adequate to accurately describe the distribution? Best answer: it depends. It may be if 800,000 parts are made with no adjustments or material changes. It seems very likely that the variation would be normal if that is the case.
 
C

CristianoP

#10
Is a sample every 26,000 parts (30 pc sample) adequate to accurately describe the distribution? Best answer: it depends.
I totally agree.

It may be if 800,000 parts are made with no adjustments or material changes. It seems very likely that the variation would be normal if that is the case.
Agreed this too. :)
In case of adjustments or material changes, it is likely that the distribution would be multi-modal. In that case, the calculation of the confidence interval could be very difficult and the Cpk would be meaningless.

Cristiano
 
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