# AQL – more than 100 in Sampling Plan Standards

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• #31564

Vetri
Member

While referring to the Standards available for Design of Sampling Plans for Attributes / Count of Defects,
in the existing standards,  IS 2500 : Part 1 (Indian Standards) or MIL-STD-105D,
we find that against the AQL’s we find values upto 1000 – How can AQL’s be more than 100?
Help Sought in Clarifying this.

Thanks & Regards,

Vetri

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#84212

Vetri
Member

Thnx & Rgds,
Vetri

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#84221

T I
Member

I thought by definition that AQL ranged from 0 to 100 percent. Where are your values of 1000 percent located again? Can you be more descriptive of how you are experiencing the number?

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#84225

Vetri
Member

If you may kindly refer to IS 2500 : Part 1 (Indian Standard) / ISO 2859-1 / MIL-STD-105D/E, in these Tables under the AQLs we have values ranging from 0.010 to 1000 along the Horizontal Axis for which the various combinations of Accept & Reject Numbers are given.

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#84254

Gabriel
Participant

I don’t remember very well and I don’t have this standard available now. So please check the following.
I think that in the expalanotry pages before the tables, you will find something like that the tables are based on the Binomial deistribution for AQLs lwer than a certain value, and Poisson distribution for higher AQLs.
Binomial distribution is related with defective count. But Poisson distribution is related to defects count. You can never have more than 100 defective parts in 100 parts, but you can have more than 100 defects in 100 parts.
Can you check in your standars if what I am saying is correct, please?

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#84372

Vetri
Member

A copy (Image) of the Standard has been enclosed and the entity 1000 encircled in Red

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#84375

Ropp
Participant

In ANSI Z1.4 which is an updated 105-E it explains that AQL is specified as per cent to AQL of 10 and as non conformities per hundred units thereafter.Don’t have a copy here, but  I’m sure that MIL 105 will have a similar explaination if you will take the time to read it.
Gabriel is correct in that the model changes from binomial to the computationally easier Poisson at the 10 % point.

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#84385

walden
Participant

The last couple of previous posts are correct. Per ANSI/ASQC Z1.4-1993:
“AQL values of 10.0 or less may be expressed either in percent nonconforming or in nonconformities per hundred units; those over 10.0 shall be expressed in nonconformities per hundred units only”.

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#84462

Vetri
Member

Thanks a lot Friends!
Continuing on the same subject,
What are the alpha and beta values that have been used in these tables?

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#84520

Vetri
Member

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#84527

abasu
Participant

alpha or producer risk is the risk of having a good part rejected by the customer.
beta or consumer risk is the risk of accepting a bad part by the consumer.

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#84531

walden
Participant

Abasu did a nice job of defining the risks for you, but I think you were looking for the numerical risks in the plans.
The producer risk is between 5 and 10% and the consumer risk is 10%. If you have a copy of MIL-STD-105 or ANSI/ASQC Z1.4, look at the Operating Characteristic curves and tables for any given simple sampling plan at the end the the standards.
There are also tables/matrices for Average Outgoing Quality (AOQ) and Limiting Quality (LQ) at Pa=10%.

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#84542

Gabriel
Participant

Chris, could you clarify?
The curves you mention gives, for each sampling plan, the probability to accept (or reject = 100% – P(accept)) a batch if function of the quality level (QL) of the batch.
So, when you say “producer risk is between 5 and 10%” I understand that the probability to reject a lot with a QL = AQL is 5 to 10%. Is this correct?
Now, when you say “the consumer risk is 10%” it means that the probability to accept a batch is 10%. For which QL?. Not QL=AQL, because the probability to accept such a batch is 90 to 95%.
For the same AQL you have different sampling plans (different letters), and as the sample size increases the probability to reject a batch with QL=AQL remains 5 to 10%, while the probability to accept a batch with a given QL>AQL is reduced. So what does it mean that the consumer risk is 10%?
[WARNING: Delirium starts here!]
In an hypothesis, the alfa risk is the probabilty to reject Ho when it was true, and the betta risk is the probability to fail to reject Ho when Ha was true, but in this case you must say how far is the parameter from what was supposed in Ho.
For example, you suspect that a coin is not fair because ir delivers few faces, but you want to be sure before “condemning” it. If you want to test if the coin delivers a face 50% of the times (Ho), with the alternative being that it delivers in fact less than that (Ha), you can make a test that would be to throw the coin n times and accept Ha (and then rejec Ho) only if you get an X% (somewhere between 0 and 50%) or less of faces. Of course, there is a risk that the coin was fair but you got X% or less just by chance. This is the alfa risk. Typically, you first choose that risk and then use a proper X% to get it. Also of course, there is arisk that you get more than X% of faces and then you don’t reject Ho, but really the coin delivers less than 50% of the faces, so Ha was true and Ho not. Which is the risk of that? I would say it is 100%. You may fail to detect the difference, but I doubt that there is a single coin in the world that delivers EXACTLY 50% of faces. Ok, you don’t care if it is 49.99% instead of 50%, so let’s ask: Which difference would be big enough to concern? Let’s say that if the coin delivers more than 45% of faces you don’t care about that being too few faces. Then we can refrase the question and ask: Which is the probability to fail to get, in n trials, X% or less faces from a coin that in fact delivers 45% of faces? This is the betta risk, and it will be different if, instead of using 45%, we used for example 49%.
Note that the sample size is very important here. If you throw the coin 50 times, you need to find 40% or less faces to say that this result would come from a fair coin only 10% of the times, and then you reject that possibility and state that the coin delivers less than 50% of faces with an alpha risk of 10%. But even if the coin delivered actually 45% of faces, you will yet fail to get 40% or less faces 71% of the times (betta risk = 71%). To lower the betta risk to 50% keeping 50 trials you must be willing to say that the coin delivers less than 50% of faces when you find 44% or less faces. But this will happen by chance with a fair coin 24% of the times (increased the alfa risk to 24%). So, when you improve one risk, you worsen the other one. The only way to improve both risks at the same time, or to improve one without worsening the other, is to increase the sample size. For example, throwing a fair coin 500 times you will get 47% or less faces  only 10% of the times, so if you get that you can say that the coin is not fair and delivers less than 50% of faces with an alpha risk of 10%. And a coin that delivers 45% of faces will deliver more than 47% in 500 trials only in 17% of the times, so your betta risk to miss such a coin is 17%.
I don’t know if the following is correct, but for these sampling plans I would state the test as follows:
Ho: QL = AQL
Ha: QL > AQL
If you reject the batch (find more than c defectives in the sample) then you take Ha as true and reject Ho. But 5 to 10 % of the times you would anyway reject, just by chance, batches with QL=AQL.
If you fail to reject the batch (find c or less defectives in the sample), then you still have a chance that Ha is true. Of course that it will be harder to make this mistake if the QL is by far > than the AQL, and if the QL is “just above” the AQL you will most probably make the mistake of accepting the batch. Then the betta risk requiers another question: By how much is QL > AQL? Then you can say “batches with QL > AQL by this much (example: QL = AQL + 10%) will be still accepted ‘betta’% of the times”.
Let’s try an example (I am using Binomial because I don’t have the standard now)
n   c   P(acc) (QL=10%)   P(rej) (QL=20%)    QL for P(rej)=90%
8    2           96%                          20%                            54%
50  8           94%                          69%                             25%
These could be sampling plans for AQL=10%. For both cases, a batch with QL=AQL will be accepted about 95% of the times, and then the producer risk is the remaining 5%.
Now, batches with a QL=AQL+10%=20% will be rejected only 20% of the times with the first plan and 69% of the times with the second plan. Then the betta risk for QL=20% is 80% and 31%.
You will be 90% sure that you will reject batches with a QL=54% using the first plan and with QL=25% using the second plan. For those QL the betta risk would be 10%.
Both plans have the same risk to wrongly reject a batch (alpha risk), but the second has more “power” (less betta risk) to detect batches that are a given amount over the AQL.
Well, I got pretty confused by now… Does what I am saying have any sence? Any clarification is welcomed.

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#84591

walden
Participant

Gabiel,
Wow, you said a mouthful.
I was merely trying to answer the original query in simple terms without getting in too deep with the background statistics and implications.
Producer’s (alpha) risk is the probability that a “good” lot will be rejected by the sampling plan. This risk is associated with a defined level of “good” quality, typically the AQL.
Consumer’s (beta) risk is the probability that a “bad” lot will be accepted by the sampling plan. This risk is associated with a defined level of “bad” quality, such as the Lot Tolerance Percent Defective (LTPD). The LTPD is defined as the lot quality which has a probability of acceptance of 0.10. Traditionally, a consumer’s risk of 10% was common in acceptance sampling plans. Of course, for plans with small sample sizes the LTPD can be large, as shown in your example.
If you desire to limit the percent of nonconforming units (or nonconformities per 100 units) to a particular quality level, a minimum sample size can be determined by using the LQ tables for Pa’s of 5 or 10% and a given AQL.
Chris

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#84612

Gabriel
Participant

Chris:
So, to my question:
“The consumer risk is 10%” means that the probability to accept a batch is 10%. For which QL?
For the QL that would be accepted 10% of the times!
I would prefer to answer to the original post saying that the Alpha risk for a “good qulity level” = AQL is 5 to 10% and that the Betta risk deppends on the level of “poor quality” he is willing to accept, and that for that level it still depends on the sampling plan.
By the way, What is “mouthful”? I don’t know whetehr I should be glad or angry.

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#84613

walden
Participant

Gabriel,
Be glad, there was no insult intended. I just meant you had a lot of detail in your response. Well done.
Cheers,
Chris

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#84626

Leon mz zhang
Participant

pls refer to
http://www.samplingplans.com
there are valueable information .

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#84642

walden
Participant

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#86293

Wagh
Participant

Hi  Dave
I think the key words are
a) For an AQL of 0 to 10   :      it is the count of ‘defective’ parts
b) For an AQL > 10           :      it is the count of  ‘defects’
Thanks Vetri for raising the doubt I had too.
Gabriel –  Spot on once again – Thanks a million

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#86297

Wagh
Participant

Hi Leon ,
Excellent link. Have saved it and will revert  for clarifications

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#103556

Johnny Chua
Participant

Hi Gabriel,
CAn

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#103557

Johnny Chua
Participant

Hi Gabriel,
From you, I learnt that Binomial Dist is Pa= (c,n,p TRUE) using excel. What about Poisson Dist? What data is needed?
Pls help.
Johnny Chua

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#103588

Gabriel
Participant

What is the probability to accept a lot with a defectives rate p (# defective parts in the lot / # parts in the lot) if the sample size is n parts and the acceptance criteria is “no more than c defective parts in the sample?”
Pa=BINOMDIST(c,n,p,TRUE)
What is the probability to acept a lot with a defects rate is u (# defects in the lot / # units in the lot) if the sample size is n units and the acceptance criteria is “no more than c defects in the sample”?
Pa=POISSON(c,u*n,TRUE)
Notes:
“Units” is not necesarily “parts”. A unit can be a pound of grease, a box of 100 screws, a feet of wire,… (also “parts” such as a bearing, a screw, an o-ring…. quailfy as “uinits”)
The important thing is to be consistent: I received a lot of  “boxes” of 100 screws each, the sample size is 8 “boxes” (n) and I will accept the lot if I find no more than 4 defects (c) in the wole sample. What is the probability to accept a lot with a defects rate of 0.75 defects per “box”?
=POISSON(4,0.75*8,true)=0.28=28%
The “0.75*8” (i.e. u*n) is to make the “units” consistent inside the formula. The formula requiers you to enter the number of events within a given unit and the average number of events per unit. In this case, we have 4 “defects in the sample” and an average of “0.75 defects per box”, so they are not comparable. It can be proven that if the average of A (A is any variable with any distribution) is µ, the average of k*A is k*µ. So the average of defects in 8 boxes (the sample size) is the 8 times the average of defects per box. So we have 4 “defects in 8 boxes” and an average of 0.75*8=6 “defects per 8 boxes”. So, for the formula the “unit” is “8 boxes”. Now we can compare.
Note that “defects” can be of different kind. For example in this example the screw can have “thread not ok” or “head not ok”. If you find in the sample one screw with the thread not ok, another screw with the head not ok, and another screw with both defects, then you found 4 defects in the sample (that would have been counted as 3 defectives for the binomial distribution).

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#103681

Johnny Chua
Participant

Thanks Gabriel, you’re really a great help…..appreciate your patient guidance.

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#103683

mman
Participant

Great Answer (Contribution).Should be bench-marked and considered as an example .regards

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#184806

Pai
Participant

Hi! Gabriel,
Your knowledge seems to be extraordinary, as you explain with lot of details.
My Introduction:
I have done 3 years Diploma in Electronics Engg. I am also in the field of QA. I have not done any kind of Studies, Degrees or certifications in QA. And I am Just TimePassing in this line from 4yrs. But I have a strong Learning attitude and interest in QA. So will you PLEASE GUIDE ME FOR MY BEST CARRIER PROSPECT:
I have some questions from your side:
1) In which area of Quality I make myself strong?
2) From where I start and like…. that till finish?
3) How can I achieve success in this field?
4) What is the main demand of Organisations from QA?
I am Married and I have not done any serious professional skills please HELP me in some common learning skills.
I have full time Internet available in my office. So I can see what you tell me to see on the net.
Regards,
Rajesh Sharma

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#184807

Severino
Participant

The truth is you cannot be successful in this field because you responded to a 6 year old post which shows you do not pay attention to detail.  Assuming you won’t listen to sound advice, why don’t you start by clicking on the links on the left hand side of this website and exploring the tools and concepts already presented to you.

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