# Determining the Total Sample Size using AQL - AQL Lot Quantity question

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#### shivan

Hi all,

I had a question regarding whether there are any rules defining what is considered a "lot" when you are trying to determine the total sample size using AQL.

For example, if I have 500 units of product x and 700 units of product y, can I combine them and consider it one lot when determining sampling size or do I have to determine the sample size separately since its two different products?

In another example, if I have one batch of product x that is made at one point in time, and another batch of product x that is made at another point in time, can this be combined into the same lot or does it need to be separately evaluated as well?

I assumed that the production environment and process must be similar to determine the lot quantity. Hence, in both examples above, I assumed they must be evaluated separately. If this is not the case, can you also help me understand why my reasoning is not sound?

Thanks!

#### mdurivage

##### Quite Involved in Discussions
Re: AQL lot quantity question

By definition:
1) a lot is a group of products manufactured or processed under substantially the same condition
2) a quanity of product accumulated under conditions uniform for sampling purposes

source: Quality Dictionary by Tracy Omdahl

#### Statistical Steven

##### Statistician
Super Moderator
Re: AQL lot quantity question

Hi all,

I had a question regarding whether there are any rules defining what is considered a "lot" when you are trying to determine the total sample size using AQL.

For example, if I have 500 units of product x and 700 units of product y, can I combine them and consider it one lot when determining sampling size or do I have to determine the sample size separately since its two different products?

In another example, if I have one batch of product x that is made at one point in time, and another batch of product x that is made at another point in time, can this be combined into the same lot or does it need to be separately evaluated as well?

I assumed that the production environment and process must be similar to determine the lot quantity. Hence, in both examples above, I assumed they must be evaluated separately. If this is not the case, can you also help me understand why my reasoning is not sound?

Thanks!
Just so you know, lot size has no bearing on the AQL value. The calculation of AQL and LTPD are a function of sample size and acceptable defects.

In your situation you have to decide how you "accept" product. If you want to accept both lots with one sample, you should make sure that the sample you inspect is representative of both lots.

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#### shivan

Re: AQL lot quantity question

Sorry, I was using the definitions to loosely. I guess what I am asking is if you hold the inspection level (used to determine sample size based on lot) and AQL number constant, is it acceptable to combine 2 different products or 1 products made at different times into one lot in order to determine the sample size?

Assuming G2 with a AQL of 1.0, product A with 500 units and product B with 800 units, can you....

option A: sample 125 units (based on the sum of product A and B using G2) for both products
option B: sample 50 units for product A (based on G2 for 500 units) and 80 units for product B (based on G2 for 800 units)

I noted that the total sample size is different here (as well as defect threshold), hence my question. Please let me know if that makes sense.

#### Statistical Steven

##### Statistician
Super Moderator
Re: AQL lot quantity question

Sorry, I was using the definitions to loosely. I guess what I am asking is if you hold the inspection level (used to determine sample size based on lot) and AQL number constant, is it acceptable to combine 2 different products or 1 products made at different times into one lot in order to determine the sample size?

Assuming G2 with a AQL of 1.0, product A with 500 units and product B with 800 units, can you....

option A: sample 125 units (based on the sum of product A and B using G2) for both products
option B: sample 50 units for product A (based on G2 for 500 units) and 80 units for product B (based on G2 for 800 units)

I noted that the total sample size is different here (as well as defect threshold), hence my question. Please let me know if that makes sense.
If you use option A, you will be accepting both lots or rejecting both lots. The sample of 125 would consist of 77 from Product B and 48 from Product A. These numbers are pretty close to Option B, so there is NO advantage to combining products.

Of course, there is NO logic to this sampling, but if you want to mix products that if your choice.

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#### shivan

Re: AQL lot quantity question

Hi Steven,

So based on what you are saying both option A and option B are feasible? You mentioned that if you use option A you must fail both products or pass both products, is thie below true assuming the same example as the previous post?

Product A defects found: 0
Product B defects found: 5
Defect threshold for 125 samples: 3

Fail both A and B and NOT just B?

#### Statistical Steven

##### Statistician
Super Moderator
Re: AQL lot quantity question

Hi Steven,

So based on what you are saying both option A and option B are feasible? You mentioned that if you use option A you must fail both products or pass both products, is thie below true assuming the same example as the previous post?

Product A defects found: 0
Product B defects found: 5
Defect threshold for 125 samples: 3

Fail both A and B and NOT just B?
When you combine the two lots, you create a "super-lot". Each individual lot loses its identity. If you want to keep lot identification, then you must use two different sampling plans as outlined in Option B.