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Application of AQL (Acceptable Quality Level) Concept

W

wintay

#1
Hi,

I would like to clarify the understanding of the application of AQL concept in the production line. If the production line only manufactures one type product of only 200 units, can I still apply the AQL concept?
Reason is the definition of AQL is the quality level that is worst tolerable process average when a continuing series of lots is submitted for acceptance sampling. Can we still consider the above mentioned as continuing series of lots since the production only produced 200 units?

Please help to clarify my doubt.

Million Thanks.
 
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Bev D

Heretical Statistician
Staff member
Super Moderator
#3
Hi,

The definition of AQL is the quality level that is worst tolerable process average when a continuing series of lots is submitted for acceptance sampling. Can we still consider the above mentioned as continuing series of lots since the production only produced 200 units?
Yes. The definition is intended to focus on a continuing stream of LOTS not Units and keep us from using it one time for a single lot.
 
D

DrM2u

#4
I agree with the other responses. My suggestion is to set your own AQL and use a (customer specified or accepted) sampling plan for part inspection. There are a few sampling plans floating around that you can choose from, or develop your own.
 
W

wintay

#5
If the lot production is only 200 units, can I use the Limiting Quality Table? I am trying to understand the concept of applying AQL. To be honest, I still do not understand fully the meaning of AQL in layman term. For example, can I relate AQL to the reliability figure?

Thanks.
 

Statistical Steven

Statistician
Staff member
Super Moderator
#6
If the lot production is only 200 units, can I use the Limiting Quality Table? I am trying to understand the concept of applying AQL. To be honest, I still do not understand fully the meaning of AQL in layman term. For example, can I relate AQL to the reliability figure?

Thanks.
In laymans terms, every sampling plan has two risks, called Type I and Type II risks. The Type I risk is the probability of rejecting a good lot and the Type II risk is the probability of accepting a bad lot. The Type I risk, also called the producers risk is related to AQL. We define the AQL as the maximum percent defective that our sampling plan would accept 95% of the time. In other words, a process with a percent defective equal to the AQL would be accepted 95% of the time. That same sampling plan will accept lots with higher percent defectives in the lot, just at a lower probability of acceptance. We define the Type II error as the consumer risk, and is the maximum percent defective that our sampling plan would accept 10% of the time. In other words, a process with a percent defective equal to the LQ would be accepted 10% of the time.

If I have a sampling plan of 30 with a acc/rej of 0/1, the AQL is 0.17% with an LQ of 7.4%. You could also have a sample size of 211 with acc/rej of 1/2 that gives an AQL of 0.17% but the LQ for this plan is 1.8%. Then there is the sampling plan of 125 units with acc/rej of 0/1 that has a AQL of 0.031% but the LQ is 1.8%.

So, as you can see there is NOT only one sampling plan that defines the AQL or LQ.
 

Statistical Steven

Statistician
Staff member
Super Moderator
#7
Just a follow up to my last post.....

I calculated LQ @ 5% probability of acceptance instead of 10%.
Which sampling plan would you pick and why?

Accept Number Sample Size AQL LQ (@5%)
0 20 0.3% 13.9%
1 141 0.3% 3.4%
2 319 0.3% 2.0%
3 531 0.3% 1.5%
4 766 0.3% 1.2%

0 20 0.3% 13.9%
1 33 1.1% 13.9%
2 43 1.9% 13.9%
3 54 2.6% 13.9%
4 64 3.2% 13.9%
 
A

AndrewNOConnor

#8
Steven, just to clarify your explanation.

For single (isolated) lot its easy, you just use the confidence levels on the p value from a Binomial/Hypergeometric distribution (however you choose to calculate it) and you can calculate both producer and consumer risk.

I thought the concept of AQL for multiple lots from a single process, took into account the fact that relaxation and more stringent inspection regimes were triggered based on switching rules depending on the performance of previous lots. Hence the AQL provides an asymptomatic quality level or 'process average' and relies on many lots to allow the affect of the switching rules to be enacted.

I'm not certain in this view of AQL or specifically how the values are calculated (I could only think of a simulation study), nor how AQL relates to consumer and producer risk (I found the standards vague) but its at odds of your definition of AQL which was defined as only producer risk and for isolated lots.

Thoughts?

Cheers

Andrew
 

Statistical Steven

Statistician
Staff member
Super Moderator
#9
The switching rules are different than the AQL. The AQL and the tables in Z1.4 are based on the binomial. AQL is a process average and not a lot specific rate, but if the process average equals the AQL level you will accept lots 95% of the time with the sampling plan.


Steven, just to clarify your explanation.

For single (isolated) lot its easy, you just use the confidence levels on the p value from a Binomial/Hypergeometric distribution (however you choose to calculate it) and you can calculate both producer and consumer risk.

I thought the concept of AQL for multiple lots from a single process, took into account the fact that relaxation and more stringent inspection regimes were triggered based on switching rules depending on the performance of previous lots. Hence the AQL provides an asymptomatic quality level or 'process average' and relies on many lots to allow the affect of the switching rules to be enacted.

I'm not certain in this view of AQL or specifically how the values are calculated (I could only think of a simulation study), nor how AQL relates to consumer and producer risk (I found the standards vague) but its at odds of your definition of AQL which was defined as only producer risk and for isolated lots.

Thoughts?

Cheers

Andrew
 
N

norbus

#10
If I have a sampling plan of 30 with a acc/rej of 0/1, the AQL is 0.17% with an LQ of 7.4%. You could also have a sample size of 211 with acc/rej of 1/2 that gives an AQL of 0.17% but the LQ for this plan is 1.8%. Then there is the sampling plan of 125 units with acc/rej of 0/1 that has a AQL of 0.031% but the LQ is 1.8%.

So, as you can see there is NOT only one sampling plan that defines the AQL or LQ.
Hello, Steven.
Please explain what formulas need to be used (or what algorithms) to get 0.17 % of AQL, having N=30 and Ac/Re=0/1 (like in example described above in your post). The same question is about evaluation of LQ value.
 
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