Using AQL to get true random sampling using General Inspection Level II

[Shasta Ell]

OK, say I have 20000 pieces in an order, and if I'm using General Inspection Level II, I will need to inspect 315 pcs.

Now, say those pieces are in boxes of 50. So there are 400 boxes. How many boxes would I sample to get a good random sample and representation of the shipment? Could I use an GI Level II again? Which would mean I would have to open 50 boxes.

[Jim Wynne]

Originally Posted by Shasta Ell

OK, say I have 20000 pieces in an order, and if I'm using General Inspection Level II, I will need to inspect 315 pcs.

Now, say those pieces are in boxes of 50. So there are 400 boxes. How many boxes would I sample to get a good random sample and representation of the shipment? Could I use an GI Level II again? Which would mean I would have to open 50 boxes.

It's not that easy. For the sample to be truly random, each member of the population must have an equal chance of being selected. The situation you describe is the reason that actual random sampling is rarely done, but the integrity of the sampling plan is out the window unless randomness is assured.

[Tim Folkerts]

I just checked the expected results if the sample was truly random. In that case, you would expect to check (approximately):

• 0 items in 180 of the boxes
• 1 item in 145 of the boxes
• 2 items in 57 of the boxes
• 3 items in 15 boxes
• 4 items in 3 boxes

This would say that a truly random sample would require opening (about) 220 of the 500 boxes.


Tim F

[Jim Wynne]

Originally Posted by Tim Folkerts

This would say that a truly random sample would require opening (about) 220 of the 500 boxes.

But you can't work backwards in the actual sampling process (i.e., you can't assume that if you open 220 boxes that you've done random sampling).

An actual random sample might require all 500 boxes to be opened, or some (random) number equal to 500 - x. Unless you're prepared to uniquely identify each part and use a random-number table, you're not doing random sampling.

[Statistical Steven]

Boxes are not usually random, as they usually represent time order of the process. If you need to sample 315 pieces, I would create a random number generator that gives me 315 numbers between 1 and 500. If you allow for replicates, you might sample more than 1 part in a given box.

You can never get a true random sample, so you have to assume you get the best representative sample.