A couple of weeks ago there was a thread which discussed how many rounds of defence ammo one needs to fire in order to be confident that ones gun will feed it reliably. Since I have just purchased a new carry gun I decided to investigate the statistical theory involved and come up with a reasoned answer. Unfortunately space prevents me from detailing the maths involved, but anyone interested should read up on binomial distributions.
There is no one "correct" test. Rather you start with a specification of upper and lower bounds and confidence levels, and an optimality criterion,and can then find the best test for these specifications.
The specification I adopted was that the test should have a 95% chance of rejecting candidates which misfeed more than one round in a hundred, and a 95% chance of accepting candidates which misfeed less than one round in a thousand. The optimality criterion is that it should minimize the average number of rounds required to accept a candidate which misfeeds exactly one round in a thousand.
The resulting test is as follows:
Fire 320 rounds. If you have no feed failures, the candidate passes with no further testing. If you had one or two failures, then fire another 280 rounds. If you have had only one feed failure in all 600 rounds fired (320+280) so far, candidate passes without further testing. If you have had two failures, then fire a further 280 rounds. If you still have only two failures in all 880 rounds fired (320+280+280) then the candidate passes. If at any stage of the test you reach a total of three misfeeds over all rounds fired, then the candidate fails.
This test has a 95% chance of rejecting any candidate which has a probability of misfeeding of 1.00% (one round in a hundred) or more. It has a 95% chance of accepting a candidate which has a probability of misfeeding of 0.11% or less. The average number of rounds required to accept a candidate which has a probabil of misfeeding of exactly 0.10% is 405.
I intend to try it out on my new carry gun (a Taurus PT-908) as soon as I get my license for it (we have a waiting period of 6-8 weeks for each new gun here in South Africa, talk about antici... PATION!). This test is not intended to be the ultimate reliability test, but rather an initial minimum which will give me confidence to carry it. After it passes (I hope) I will continue to fire defence ammo on a regular basis, log the results and update my reliability statistics accordingly.