On 30 Jan 2013 08:09, Bill Reger wrote:
We would like to audit 10% of the Cases that flow down the shipping
conveyor - checking that the contents of the Case matched what was
(supposedly) packed.

Now obviously we could count each Case and pull every 10th Case for
audit. But it would not take long for someone to figure this out -
and if they were so inclined - only short Cases other than the 10th
in line.

Is there an algorithm/logic that we could employ to randomly pull
Cases that would equate to 10% over the course of a day but not be
every 10th Case? (My logic brain is on strike today and I can't think
of a way to design this.)

Instead of "obviously...", but almost the same as that, just adding a random number for which case to audit:

Before the start of each group of ten cases counted [the first and each successive group of ten consecutive cases], randomly choose a number N between one and ten; inclusive. That number N defines which of the next 10 cases is audited; the Nth case.

This method is also very simple, very uniform to prevent a /random/ occurrence of auditing more than two cases consecutively, maintains almost exactly the 10% ratio [except with small numbers, an almost imperceptible skew for a partial group at the tail], not always the same Nth [e.g. not always the 10th] case for every group of ten cases, and no need to know in advance what makes-up each group of ten.

That last point is very important. Trying to delay the decision of which case to audit is where the greatest difficulties lie. Knowing in advance that the 5th case is to be audited, but only three of a group make it to the audit station, then that group can be completed whenever the next seven cases come down the conveyor. Those first three cases can pass-by the audit station regardless of how long the other seven take to arrive. That eventual arrival could even be upon starting up the conveyor the next day, such that the last random number from one day carries over to the next; this of course allows for a larger skew for the percentage [less perceptible with larger numbers of cases processed], because with that, a partial group can be at both the head and the tail in a day.

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