How to Calculate Mean Rounds Between Failures?

[M1Rifle30-06]

Kind of an amateur question, but can anyone familiar with the concept of Mean Rounds Between Failures (MRBF) confirm for me how exactly it's calculated?

I have a Glock 19 Gen 4 with 3,080 rounds through it. It has had one stoppage on an extended magazine.

Do you stick the stoppage in the middle of the round count? In that case it'd be dividing 3,080 by 2, which would be 1,540.

Or (and this is what I'm leaning towards being correct), do you divide the total number of rounds fired by the number of stoppages? In this case, it'd be a MRBF of 3,080 since it was 1 stoppage. The wording of FBI handgun reliability requirements mentions it must have "no more than 1 stoppage in 2000 rounds, or 2000 MRBF", which sounds like this formula.

Could someone more mathematically inclined than I confirm one way or the other for me? Thanks.

[Jim Watson]

Hard to have a mean without multiple values to average out.
Shoot 30000 and call back tomorrow.

Otherwise you can call it 3080 or you can call it a fluke due to trick magazine.

[TunnelRat]

Yeah you need more than one failure.

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[Bartholomew Roberts]

“Stoppage” and “Failure” mean different things usually. A stoppage is typically something you can clear without tools immediately. A failure is a more serious issue that takes the weapon out of service temporarily. So MRBS and MRBF measure different things.

[M1Rifle30-06]

“Stoppage” and “Failure” mean different things usually. A stoppage is typically something you can clear without tools immediately. A failure is a more serious issue that takes the weapon out of service temporarily. So MRBS and MRBF measure different things.

Oh, I see. Well, in this instance I'm more concerned with stoppages rather than failures.

[44 AMP]

I have a Glock 19 Gen 4 with 3,080 rounds through it. It has had one stoppage on an extended magazine.

and when did that stoppage occur? At what round count? Was it at #3,080? or somewhere else?

No matter what round # it happened at, it is ONE stoppage. (so far) you can't calculate anything BETWEEN unless you have at least TWO data points.
And, one set of points isn't enough to determine any kind of "mean average".


AND there is also the point about the cause of the stoppage. For example, if a gun jams because you fed it a bad round, you can't blame the gun.

[RickB]

Yeah, right now you have one stoppage per 3080, and a year from now, it might be one per 6160.

I bought a new gun last Spring, put 1000 trouble-free rounds through it, then had four stoppages, of two different kinds, in the span of 100 rounds.
I looked at it as four in 100, not four in 1100 (who cares what happened in the past, if it's now going to malfunction every 25 rounds?), but the mean would be one per 275.

[T. O'Heir]

There's no such formula. Mathematical or otherwise.
Any standard the FBI invents is 100% arbitrary. The FBI is not now nor have they ever been the authoritative body on anything firearm related either.
"...mean different things usually..." And is the same thing at the same time. The 7th Round Stoppage issue with the M1 Rifle, for instance, kept the rifle out of service temporarily because it failed to cycle properly. It was caused by a manufacturing error and was temporarily fixed by how one loaded clips, but math had nothing to do with it or its fix.

[TunnelRat]

I'd disagree that MRBF/MRBS is completely arbitrary.

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[RickB]

The FBI is not now nor have they ever been the authoritative body on anything firearm related either.

That may be true, but police departments and ammo makers treated the FBI's ammo testing protocols as the gospel for decades, if not still.

[TunnelRat]

Even a broken clock is right twice a day, and I'd argue the FBI is better than a broken clock. I don't think I'd label the FBI as the penultimate authority, and they've certainly changed their minds over the years, but I don't think all of their findings are completely out of left field. I do think there is some effort to get consistent results and to try to quantify what many times are typically qualitative measures. Does understanding change over time? Yes it does, and sometimes the FBI is behind the curve. That said I'd say there is a lot more challenge in reporting/predicting the effectiveness of handgun calibers against humanity targets than there is measuring the number of rounds between failures.

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[Lohman446]

Mean is the arithmetic average. If you had one failure and it happened after 2400 rounds then the mean rounds between failure is 2400. If however the next failure happened 10 rounds later the mean rounds between failure is 1205

2400 (before first failure) + 10 (before second) / 2 (number of failures)

There is a danger when dealing with small sample sizes in noting there is a major difference with just adding one more value to the sample. Its also dangerous to do with a single pistol because a flaw in that pistol that is not common to the model could throw off the entire perception.

[TunnelRat]

Is it that simple? I'd almost thing you'd keep track of the number of rounds between each failure and then average those numbers rather than simply dividing total round count by number of failures. But then again the method I just described would be very skewwd by outliers, so I'm not sure.

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[fastbolt]

This sort of thing is something that both firearm company engineers and some independent scientific labs who test firearms can determine for themselves and apply over time and a lot of rounds fired.

For the rest of us those numbers aren't all that meaningful when applied to one particular gun we may use and shoot.

Many instances of "testing" for large contract/bid, and NIJ duty pistol testing recommendations, includes language which allows for a maximum number of stoppages not related to the ammunition or shooter-induced (meaning determined to be directly attributable to the pistol of magazine), and that might mean 2-5 assorted stoppages out of 600 rounds fired might not necessarily "fail" a make/model/caliber pistol submitted for testing. Other testing might go farther/longer and have different requirements.

I can think of one major state agency who randomly selected 2 production pistols which were then used to fire several thousand rounds through each in the course of a day, only pausing when the guns were too hot to touch, and the 3 (combined) stoppages observed were determined to have been caused by faulty ammunition (mix of duty and green training ammo) and pressure from a gloved thumb of one of the test shooters. The guns passed inspection and testing and the contract was adopted.

I can think of another major gov test where one of the submitted pistols had the recoil spring assembly guide rod and the pistol's dustcover distort and go out-of-spec due to the heat of extended firing. Due to NDA's signed, the results didn't become public.

I can think of another fed agency testing where some different caliber plastic models from a couple of gun makers were used to fire 10K rounds each over a 2-day period, and when the guns from the 2 manufacturers passed, one was selected for issue (less costly) and the other was accepted for optional/personal purchase and use (at individual expense).

I can think of some other tests with which I've become familiar over the years, too.

None of those tests involved calculating some "mean rounds fired between failures", according to what I was told by people familiar, monitoring or participating in them at the time, but any stoppages or parts failures were considered against the totality of the testing circumstances.

[JohnKSa]

A 'mean' is an average, and to have a meaningful average you need more than one event of interest.

The point already made about the difference between stoppages and failures is a good one.

Anyway, to determine 'Mean Rounds Between Stoppages/Malfunctions', you would need enough rounds fired to get a significant number of stoppage/malfunctions. And you would need to keep track of the point at which each of the failures occurred.

As pointed out, it's not really the kind of thing most individuals have the resources to determine.

There's no such formula. Mathematical or otherwise.

That's incorrect. There's a simple formula and it can be found on line.

[M1Rifle30-06]

and when did that stoppage occur? At what round count? Was it at #3,080? or somewhere else?

The stoppage was at about 1500 rounds using a Glock factory 33 round magazine. It has now been shot for a total of 3,030 rounds with no stoppages since then.

Mean is the arithmetic average. If you had one failure and it happened after 2400 rounds then the mean rounds between failure is 2400. If however the next failure happened 10 rounds later the mean rounds between failure is 1205

2400 (before first failure) + 10 (before second) / 2 (number of failures)

I think this is what I understand it to be. However, as others have pointed out, I have no other stoppages to have an additional data point. Does that mean, if there has only been one stoppage, the formula is 3030 (total number of rounds fired) / 1 (number of stoppages) for a MRBS of 3030?

Again, the stoppage occurred around the 1500 round mark.

There's no such formula. Mathematical or otherwise.
Any standard the FBI invents is 100% arbitrary. The FBI is not now nor have they ever been the authoritative body on anything firearm related either.

The FBI is far from the only organization that uses this method of determining reliability, and I don't believe they necessarily invented it. It's pretty standard across LEO agencies and militaries across the world. A weapon's track record of reliability is something that can be objectively measured.

[44 AMP]

While we all like to play with numbers and be able to throw around impressive round counts between "stoppages", what does it really mean??

Not a lot.
Because first off, you aren't testing just one thing. You are testing two, and possibly more things. The main things are the gun, and its ammunition. Fine to say "this gun went x thousand rounds between stoppages" but you have to also remember that the ammo went x number of rounds without malfunction at the same time. We all want perfect ammo, we hope for perfect ammo, for what we pay, we expect perfect ammo, but we don't always get it.

how do you count the failure rate of the gun, if the failure isn't actually the gun, but the ammo??

If you had one failure and it happened after 2400 rounds then the mean rounds between failure is 2400. If however the next failure happened 10 rounds later the mean rounds between failure is 1205

this is a good example. The math is right, as math, but the conclusion is flawed.

The stoppage was at about 1500 rounds using a Glock factory 33 round magazine. It has now been shot for a total of 3,030 rounds with no stoppages since then.

Well, then, brother, by the math, you're DUE!!

This is another problem with straight math vs. the real world. Along with flawless ammo, the math assumes consistency. And our real world is very consistent about being inconsistent especially at inconvenient times.

Lets say, for example you got a stoppage at 1500rnds (and it was the gun at fault, not a bad round or the shooter limp wristing it) then you go another 1500 without a stoppage, and then another 756 rounds and you get a stoppage. Then 127 rounds after that you get a stoppage, then you go a wonderful 2750 without a stoppage. Do the math, get an average, a "mean" number. It will be solid math, but it won't be what actually happened, and its not any kind of solid predictor of what will happen in the future.

[ballardw]

I would think that the first step is to define what constitutes a "failure" before starting the whole analyis.
If you do not know what you will be counting the whole process gets a bit wishy-washy.

[CockNBama]

M1 is confusing an index, MRBF, with measurement. Indices such as MRBF or MTBF are indices that are applicable to fleets, and predictors, by extension, of individual articles.

What M1 is doing is measuring. Such records could contribute to an index of performance, if there were LOTS of other pistols in the measurement group.

As it is, MTBF is meaningless for his pistol.

Next up is the Conditional Probility of a failure on his next round...

[RKG]

Originally Posted by RickB

That may be true, but police departments and ammo makers treated the FBI's ammo testing protocols as the gospel for decades, if not still.

True. And one time the notion that the Earth was flat was also gospel.

[Double Naught Spy]

That may be true, but police departments and ammo makers treated the FBI's ammo testing protocols as the gospel for decades, if not still.

Blind leading the blind? Remember when the FBI abandoned 9mm and other lesser calibers for the almighty 10mm and then abandoned it for the .40 and now have readopted the 9mm?

It bugs me when people/government agencies fail to think for themselves. I understand that nobody wants to re-invent the wheel, but when basing a decision on the research of others, you need to evaluate the research yourself to see if it is 1) valid and 2) valid for your needs.

The same goes for quantitative assessments for firearms performance. So you have X number of failures given Y number of rounds. Is it safe to assume there is a relationship between the number of rounds fired or are there other parameters involved? 44Amp touched on this. For example, different ammo, different magazines, maintenance, etc.