Here is a little story about misinterpretation of sampling outputs.

A company was given instruction to collect 8 samples and approve the batch if there was only one defect part within the sample.

The smart reader quickly calculated that they were now allowed to produce 12.5% defect parts as one in eight is 12.5%.

Unfortunately this is not how it works. Comparing the sample of 8 and acceptance number 1 with the tables in ISO 2859-1 one will see that it matched an AQL of 6.5.

What does that mean in plain English?

To explain it in a very simplified way; If the defect ratio is 6,5% there is a good chance that you will only find one defect in the sample but if the defect ratio is higher it is likely that you will find more. So a sample of 8 where you accept one defect actually represents only a 6.5% ratio.

But why is one in eight not 12.5% ?

The short answer is the “Binomial Distribution”.

Imagine a box with red and blue balls. If you take 10 balls from the box and find one red, are you then sure that there will be exactly 10% red balls in the box?

No, you wouldn’t would you? Because at another ratio you might also have found just one red ball in your sample.

Actually there is 28% chance to find one red ball if the ratio is 5%, 38% if it is 10% and 34% chance to find one red ball if the box contains 20% red balls.

The graph below illustrated the chance of finding one red ball by collecting samples of 1-10 balls at different ratios of red balls.

Stayed tuned for more interesting statistical advice.

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