DISCUSSION
AQL (Acceptable Quality Level) assumes no knowledge of the capability of the process that produced the part being sampled. What if the underlying performance capability is known? What if the capability is Cpk = 2.0 (or 6 sigma or 3.4 defects per million opportunities). Does it still make sense to continue to test with a specified AQL Level? Sample size and the decision to Reject or Fail to Reject the lot is based upon Percent Defective (or Binomial Distribution) with the null hypothesis (Ho) being, % defective is not greater than 1% (for an 1.0 AQL) and the alternate hypothesis (Ha) being greater than 1% defective. A 1.0 AQL is 10,000 DPMO or 3.83 sigma.

Or asked another way, if our customers wished a 5.5 sigma performance, or 100 DPMO, then this would be a 0.01AQL. What would the sample size be for that? 100%?

QUESTION 1
Is the sample size the same between parts/features with both known and unknown capability? Or stated differently, what is the right sample size for parts with known performance capability (Cpk and/or Ppk)?

QUESTION 2
Is there a specification/method that defines a reduced sample size for processes with known capability. The purpose of the sample would be to ensure that the process is stable (SPC might be a method to ensure this).

DISCUSSION
AQL (Acceptable Quality Level) assumes no knowledge of the capability of the process that produced the part being sampled. What if the underlying performance capability is known? What if the capability is Cpk = 2.0 (or 6 sigma or 3.4 defects per million opportunities). Does it still make sense to continue to test with a specified AQL Level? Sample size and the decision to Reject or Fail to Reject the lot is based upon Percent Defective (or Binomial Distribution) with the null hypothesis (Ho) being, % defective is not greater than 1% (for an 1.0 AQL) and the alternate hypothesis (Ha) being greater than 1% defective. A 1.0 AQL is 10,000 DPMO or 3.83 sigma.

Or asked another way, if our customers wished a 5.5 sigma performance, or 100 DPMO, then this would be a 0.01AQL. What would the sample size be for that? 100%?

QUESTION 1
Is the sample size the same between parts/features with both known and unknown capability? Or stated differently, what is the right sample size for parts with known performance capability (Cpk and/or Ppk)?

QUESTION 2
Is there a specification/method that defines a reduced sample size for processes with known capability. The purpose of the sample would be to ensure that the process is stable (SPC might be a method to ensure this).



Mike - Welcome to the cove. :bigwave: You are in the right place to get a logical answer to your questions. You may want to consider the use of skip lot inspection / sampling method once your process has been proven to be statistically capable. We employed this technique in our receiving inspection of incoming components and it worked very well for us.

O.k.

So what drives the decision to skip a lot (or many lots and how many)?

Guess I'm not looking for a black and white answer, but a general line of logic that would pass a litmus test for those "locked-in" to a current line of thinking. I can do the sales pitch, just need some help putting the pitch (argument) together.

Mike

When you are dealing with very small PPM levels, sampling of any kind is ineffective.

You have two basic choices. Either 100% inspect to attempt to detect the small number of defects, or trust in your Cpk = 2 capability, control your process with SPC to ensure that it does not drift, and do not inspect at all.

Miner,

You make a good point.

What should be the sample size for the SPC? 1? 2? Depends on the Cpk? First, middle, last piece?

Ultimately I'm trying to reduce the Appraisal COQ without increasing risk of failure.

Thanks,

Mike

The subgroup size and frequency should be based on the process. Read up on Rational Subgroups to help determine this. I cannot really advise you without knowing a lot more about your process.

Thank you. That is helpful.

Dear all,

I would like to continue the post because I have a similar problem that maybe link to that.

What I'm used to do is:
- validate a process (check process capabilities)
- choose an AQL in regards of the process capability

I was used to used the following table:



Cpk < 1.0 100%


Cpk >= 1.0 AQL 1.0


Cpk >= 1.33 AQL 2.5


Cpk >= 1.66 AQL 4.0


Cpk >= 2.0 No sampling





This table is of course not from me, but from a medical company and is stated as a guideline.

But my question is: HOW THE LINKS IS MADE BETWEEN CpK and AQL ???

Is there any calculation, curves, tables or whatever that is here to explain a little bit this guidlines?

Thanks for any helps

Up!

It is understood that with a 6 sigma capabiltiy sampling is inefective, but question 1 is still open.

Does somebody is able to explain what method they use to select an AQL against a CpK ? Does someone is using the same exemple of table shown above?

Does somebody knows any rational behind this table?

Thanks

Cpk < 1.0 100%


Cpk >= 1.0 AQL 1.0


Cpk >= 1.33 AQL 2.5


Cpk >= 1.66 AQL 4.0


Cpk >= 2.0 No sampling


This table does not make sense to me!
AQL (Acceptable Quality Limit) is essentially the % of defective material which could be found in a lot before the lot is rejected. This table is saying that as your capability improves and therefore the % defective within the population decreases then it is OK to accept a lot with more defects.

The Cpk and AQL are contradicting each other.

Hi prototyper,

I'm afraid not to really understand you.
The table is saying that more the process is capable, less samples will be taken to inspect it.

Could you then explain me (us) how you determine your inspection level in respect of the Capability level?

Hi prototyper,

Maybe I forget to mention, this exemple applies to the C=0 table which is different from the ISO2859, that maybe you are talking about.

In the C=0 more the AQL value is big, less the sampling qty is.

For example:
Lot size: 1000pcs
Aql 1.0: n=34 pcs
Aql 4.0: n=15 pcs
0 defect accepted in any cases.

So more the process is capable, more your AQL value will be high to get lower sampling size.

In the ISO2859 in the same case you will have always the same sample size (80pcs), but more the AQL level is high, more you will accept defect pieces. 2pcs for AQL 1.0, 7 pcs for AQL4.0

I assume the misunderstanding is coming from that.


Keep going...

Hi prototyper,

Maybe I forget to mention, this exemple applies to the C=0 table which is different from the ISO2859, that maybe you are talking about.

In the C=0 more the AQL value is big, less the sampling qty is.

For example:
Lot size: 1000pcs
Aql 1.0: n=34 pcs
Aql 4.0: n=15 pcs
0 defect accepted in any cases.

So more the process is capable, more your AQL value will be high to get lower sampling size.

In the ISO2859 in the same case you will have always the same sample size (80pcs), but more the AQL level is high, more you will accept defect pieces. 2pcs for AQL 1.0, 7 pcs for AQL4.0

I assume the misunderstanding is coming from that.


Keep going...

Whilst I agree that if your process has a higher Cpk you may wish to reduce the amount of inspection or even stop inspection completely, what you are describing is not the way sample inspection works.

Sampling is about the probability of finding defects. If you want to ensure a higher Cpk you are making the hypothesis that there is less chance of finding defects in the population and therefore you will need to take a larger sample size to have the required confidence level that this is the case.

What you describe is not a valid sample plan. It is a plan to reduce inspection based on what you know of your process from independent measurement.

I agree that you are wasting your time conducting sample inspection on a population which you know has a high Cpk, but there is no valid statistical basis for the "Plan" you describe.