harrygunner
Member
- Joined
- Mar 23, 2006
- Messages
- 1,045
Noticed the numbers posted. This lead me to look at the Poisson distribution equation to calculate the probability of no failures given an observed number on flawless shots.
The Poisson distribution is: p(k) = (l^k)/(k!)(e^l)
p(k) is the probability of 'k' occurring given 'l' being observed.
For this issue, k = 0 (no malfunctions) and l = 1/(number of shots with no malfunctions).
(For small rates of occurrence, calculations using the correct Poisson estimates reduce to what many may be using to select numbers.)
Bottom line:
Those using 500 flawless rounds accept a .998 probability of no malfunctions. i.e. if one can shoot 500 flawless rounds through a gun, the probability of no malfunctions is 99.8%
And -
100 <-> 99.0%
250 <-> 99.6%
1000 <-> 99.9%
Looking at the way the distribution curves are shaped, after the first 500 rounds, the second 500 rounds are in the noise compared to all the other things that can go wrong during a shootout. If 500 rounds cost $300, the second $300 expenditure may be unnecessary.
Questions of the type asked by the OP have been addressed mathematically a long time ago. If the probability of an event over an interval is proportional to the length of the interval, then Poisson statistics apply.
Those numbers above are lower bounds on the probability the gun is reliable given the number of successive successful firings. In other words, the gun is probably at least that reliable, but it's possible it's more reliable.
Shooting a couple of magazines or a fifty round box leaves around a 2% to 5% chance that gun is unreliable. Carrying the gun in this case is relying on the reputation of the manufacturer (it's a Glock) or the type of gun (it's a revolver).
The Poisson distribution is: p(k) = (l^k)/(k!)(e^l)
p(k) is the probability of 'k' occurring given 'l' being observed.
For this issue, k = 0 (no malfunctions) and l = 1/(number of shots with no malfunctions).
(For small rates of occurrence, calculations using the correct Poisson estimates reduce to what many may be using to select numbers.)
Bottom line:
Those using 500 flawless rounds accept a .998 probability of no malfunctions. i.e. if one can shoot 500 flawless rounds through a gun, the probability of no malfunctions is 99.8%
And -
100 <-> 99.0%
250 <-> 99.6%
1000 <-> 99.9%
Looking at the way the distribution curves are shaped, after the first 500 rounds, the second 500 rounds are in the noise compared to all the other things that can go wrong during a shootout. If 500 rounds cost $300, the second $300 expenditure may be unnecessary.
Questions of the type asked by the OP have been addressed mathematically a long time ago. If the probability of an event over an interval is proportional to the length of the interval, then Poisson statistics apply.
Those numbers above are lower bounds on the probability the gun is reliable given the number of successive successful firings. In other words, the gun is probably at least that reliable, but it's possible it's more reliable.
Shooting a couple of magazines or a fifty round box leaves around a 2% to 5% chance that gun is unreliable. Carrying the gun in this case is relying on the reputation of the manufacturer (it's a Glock) or the type of gun (it's a revolver).
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