# % of defects on the whole batch based on result from inspection under AQL Level II

#### Aline

##### Registered
Hello Everyone,

I know that this is not the way to read the AQL table however a friend of mine would like to estimate the number of defectives pcs in the whole batch based on the result of defectives pcs from an inspection done under AQL Level II ?

For example :
Ordered qty : 40.000 pcs
Sampling (according to AQL Level II) : 500 pcs
Number of defectives pieces in my sampling: 30 pieces (so 6%)
Estimated number of defectives pcs in my order (so on the 40K pcs) : ??

I know that AQL is to after accept/reject the order based on the number of defects and the acceptance level but my friend doesn't want to do the inspection to reject or accept the batch but to get an agreement with the supplier on the number of pcs that will be added extra to the ordered qty (based on this estimated number of defectives pcs on the whole batch).

If anyone has a sort of answer for this I will be very happy
I have been looking on the statistical websites for some formulas but as the sampling size is chosen by AQL and the same for 40K or 150K, it's not really a representative sampling of the whole batch.

#### Jim Wynne

Staff member
There seems to be some confusion here over the purpose and methods of sampling inspection, but let's start with the basics. In the original sampling of 500 pieces, was sampling done randomly? Note that "randomly" in this context means that each of the 40,000 pieces had an equal chance of being selected. If your response is "yes," please describe how this was accomplished.

#### Aline

##### Registered
Thanks for the reply, yes sorry this is pretty confusing as I understand that this is not the purpose of AQL table… But yes all pcs are randomly selected. The whole order is ready and the inspector is choosing randomly cartons among and will check few pieces per each carton and so on until 500 pcs is reached.

#### Jim Wynne

Staff member
Thanks for the reply, yes sorry this is pretty confusing as I understand that this is not the purpose of AQL table… But yes all pcs are randomly selected. The whole order is ready and the inspector is choosing randomly cartons among and will check few pieces per each carton and so on until 500 pcs is reached.
What I said was that each of the 40,000 pieces had to have an equal chance of being chosen, not each of x cartons. The point is that there is probably no practical way to conduct a random sampling of a 40,000-piece lot, and unless the sampling is random, all bets are off as to how well the sample represents the population.

#### Aline

##### Registered
In theory, one pc can be checked in 500 different cartons and this will make it random (all the 40.000 pcs have the same chance to be chosen) but unfortunatly in reality I have doubt that the inspector will open 500 cartons :s

#### Jim Wynne

Staff member
In theory, one pc can be checked in 500 different cartons and this will make it random (all the 40.000 pcs have the same chance to be chosen) but unfortunatly in reality I have doubt that the inspector will open 500 cartons :s
Each piece in each of the 500 cartons would have to have an equal chance to be chosen. As I said, there's probably no practical way to do it. What you should probably do is (a) tell the customer what you've found and agree on a number of extra pieces, and (b) do a better job of process control.

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