Using SPC Control Charts to Reduce AQL Sample Size

Bev D

Heretical Statistician
Staff member
Super Moderator
#11
Hi, I read the statement "if Cpk> 1,33 then the AQL reduces to 2,5%." :confused:Can you explain how you get to this. I would expect that a Cpk has only 66 pppm defective which would be an AQL of 0,0066%

By the way does anybody knows how to design a sampling plan to guarantee a Cpk of 1,33, rather than quaranteeing an AQL of say 1%?

:thanx:
ABSOLUTELY: the sample size is 45,390 pieces. However, that only "guarantees" the lot will be 66ppm defective or better it doesn't guarantee the process spread. Additionally, there is a 5% chance that you might accept the lot if it slightly worse than 66ppm.

I used a RQL plan without modifying for a small lot size. An RQL plan will REJECT the lot if it is 66ppm or worse defective. (AQL plans are based on the quality level you will allow to be accepted.) I used a 95% probability of rejecting the lot. If I were to use a 99% probability of rejecting the sample size would be: 69,776.

all sarcasm aside, obviously no attribute (pass/fail) sample plan can 'guarantee' such low defect rates unless the sample is very very large.

You might consider using a variables sample plan such as ANSI Z1.9-2008 However, the best approach is to utilize SPC, mistake proofign and positive process controls to ensure a stable capable process...
 
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bobdoering

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#12
3. Make a new sampling plan - I want something that is statistically valid and easy to use. I'm thinking that quality could receive a lot of parts and a report with the control chart from the lot and the cpk.
- If there were any special causes of variation with a data point out of spec, quality would inspect 100%.
- If there were special causes of variation within spec limits, quality would inspect at a heightened level which they could look up on a simple chart.
- If the process is in control and the cpk is < 1.33 and > 1, inspect at normal level
- If process is in control and cpk >1.33, inspect at reduced level.

Has anyone ever used a plan like I outlined in option 3?
Yes, I did this to ensure that final inspection would have a significantly higher throughput.

Here is a little detail you need to consider:
You can not use "data point out of spec, quality would inspect 100%" - because if you wait until you have a data point out of spec, it may be too late and you will already have out of spec parts. This can occur before it is detected, due to sampling and measurement error. You need to start 100% inspection at a point before that - maybe somewhere between 75-90% of the spec - depending on the resolution of your sampling frequency and gaging system. Conversely, "there were special causes of variation within spec limits," not sure if that has any impact on sorting for that particular characteristic. There are many clues that an out of control characteristic provide about the process that are not directly related to it being incapable.
 
N

New to Quality

#13
Thanks for the response. And thank you for correcting some of my details, those are very important points that I missed.

Now that I know the concept is plausible, do you know of an existing sampling plan with heightened/reduced sample sizes based on process capability?

Thanks!
 
S

statuser

#14
Thanks a lot for the response

The measurements we do are continuous variables on steel wires such tensile strengths, diameter, etc). The customers are asking for CpK levels of > 1,33, which yields 66 ppm non-conformities based on the normal probability curve.
We try to use the MIL 414 or ISO 3951 standard for variables (not the ones for attributes), but these sampling plans do not cover these low levels of non-conforming 66 ppm for a Cpk of 1,33, (for a Cpk =1 process 2700 ppm non conforming)
I have several questions:
1.How can we calculate sampling plans for variables using the MIL 414 or ISO standard for these low levels of non conformities?
2. Why are the MIL and ISO standards not covering AQL < 0,01? Many companies have to prove lower levels than 100 ppm!
3. Can we use the Operating Curve method to calculate sample size? ( for instance CPk 1,33 is AQL 0,0066 with alfa risk of 0,05 and CpK 1 would be RQL 0,27 with beta risk of 0,1, ),
4. Why does the Operating Curve method not take into account the lot size to calculate the sample size ( or maybe why do the MIL and ISO standards use the lot size to calculate the sample size? ). Apparently MIL 414 standard and OC methods are based on the same statistics but both approach the problem from a totally different angle.

I appreciate your response
 

Mike S.

Happy to be Alive
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#15
I agree. Use the switching Procedures found in ANSI/ASQ Z1.4-2003. If things go poorly then you increase inspections if they go well you loosen them.



Hope this is helpful,
Mark
You can also switch to a C=0 sampling plan and significantly reduce the number of samples required for a given AQL.
 

bobdoering

Stop X-bar/R Madness!!
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#17
Hi again,

What plan did you follow to do this?

Thanks!
It was precision machining, so we used SPC on the shop floor (X hi/lo-R charts), and for those dimensions that were not charted, we utilized 75% tolerance gaging on the shop floor. One should never use 100% tolerance gages on the shop floor anyway - it ignores the total variance equation, which is why things may look good on the shop floor but fail final. We used a c=0 inspection both before and after implementation of these controls. The efficiency of not failing final inspection, by not having to remake or rework and re-final inspect was the first huge benefit. After that, the problem is dealing with special causes (for example, in machining broken tools.)
 
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