# % on the population based on % of the sampling

#### Aline_Ev

##### New Member
Hello Everyone

My question concern Quality control. I would like to estimate the number of defectives pieces on the total quantity of my order based on the result of defectives pieces on my sampling. Sampling size is based on the "Acceptance Quality Limit" (AQL Level II).

Example 1:
Quantity of my order : 40.000 pieces
Sampling (according to AQL Level II) : 500 pieces (to inspect)
Number of defectives pieces in my sampling : 60 pieces
Estimated number of defectives pieces in my order (so on the 40K pcs) : ??

Example 2 :
Quantity of my order : 80.000 pieces
Sampling (according to AQL Level II) : 500 pieces (to inspect)
Number of defectives pieces in my sampling : 60 pieces
Estimated number of defectives pieces in my order (so on the 80K pcs) : ??

As you can see, the sampling size is the same for both batches however one is double than the other. I am afraid that the answer is going to be "your sampling doesn't represent your total quantity so we can't do a conclusion on the whole batch" but I really need an estimation.

For those who don't know the AQL table, below are few examples of how the sampling size is chosen (according to AQL Level II) :
281-500 order qty --> sampling size 50 pieces
501-1200 order qty --> sampling size 80 pieces
1201-3200 order qty --> sampling size 125 pieces
3201-10.000 order qty --> sampling size 200 pieces
10.001-35.000 order qty --> sampling size 315 pieces
35.001-150.000 order qty --> sampling size 500 pieces
150.001-500.000 order qty --> sampling size 800 pieces
500.000 and more order qty --> sampling size 1250 pieces

#### Miner

##### TS Contributor
I recommend that you post this in a quality forum as you will get better response. The two best forums are:
I think you are misunderstanding the use and purpose of AQL tables. You correctly used them to determine the sample size, but the next step is to determine The Acceptance number and Rejection number based on an AQL that your company has deemed appropriate. The largest Rejection number is 22, so your 60 defectives would cause you to reject the lot.

An estimate of the order would simply be 60/500 = 0.12. The 95% confidence interval is: 0.09 - 0.15. This is completely independent of AQL tables.

#### Aline_Ev

##### New Member
Thanks a lot, @Miner
You are right about the interpretation of the AQL table but my friend would like to do the inspection not to reject/accept the whole batch but to agree with the supplier on a number of extra pcs that will be added with the shipment after the inspection (based on an estimated number of defects on the whole batch). So the AQL table, in this case, is only used to select the sampling size. Therefore I thought it becomes more of a statistical problem on how to bring back a % from sampling to the whole qty.

Understood that in this case 12% for the sampling will become for the total qty from 9,5% to 14,5% (with CI 95%) but I was wondering if the fact that only 0,62% of pcs have been inspected (for 80K) compared to 1,25% (for 40K) will affect the result (need to be taken into consideration).

Thanks for the Quality forum I will check and post on those ;-)

#### Miner

##### TS Contributor
The level of uncertainty (i.e., width of the confidence intervals) is based on the sample size, not the population size or the percent of the population inspected. This assumes that defectives are homogeneously distributed throughout the lot and the sample was truly random. Otherwise, all bets are off.

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#### Aline_Ev

##### New Member
OK, well noted, thank for your feedback