humans DO have a “bathtub curve…” – deaths per 100,000 per year.
There is a reason the first bit of the bathtub curve is called “infant mortality”…
Peter wrote:
so we can expect to see the usual great contributions on EuroGA from Maoraigh until I am around 71
Depends on how much foggy flying he does 
The probability of reaching time, t, when MTBF is know is R(t) = e^(-t/MTBF)
MTBF is 10k hours (from above). Let’s say 50 hours per year, and 5 of those are over fog. 50 hours of foggy flying.
R = 0.995 = 99.5 % chance of surviving those 50 hours over fog.
Hmm, that was much better than I expected. I guess it’s safe to say that even with lots of foggy flying, we still can expect to to see the usual great contributions on EuroGA from Maoraigh for at least another 10 years
From here
Peter wrote:
The 50k is the MTBF. It doesn’t relate to how long the engine will run for.
I know that. With MTBF of 50000 there is a 50% chance that it will run (without failure) to about 35000 hours. This still is a whole lot, and nothing like we see in the real world for engine failure (due to any cause). If the MTBF was 5000, that number would still be 3500 h, which still is a lot, but closer to what we actually see.
Just to put a perspective on this. Let’s say everyone fly 50 h each year. This will require 700 pilots flying 50h each year, and on average only one person experience an engine failure every second year. Remember that engine failures can be caused by a whole lot other than the engine itself.
We probably could find a better number if someone went through investigation reports and counted all propulsion failure related accidents. This number would still be way too high though, because incidents where the engine fails, but it ends well (for any reason whatsoever, the engine could simply start again), aren’t in any accident report.
@LeSving, the fraction of engine failures among all accidents is very different from specific engine reliability.
An illustration to the difference between the two: imagine that 80% accidents are caused by sober drivers and 20% by drunk ones; furthermore, 80% accidents happen at low speeds and 20% at high speeds. If you want to improve safety, would you recommend driving drunk and very fast?
With MTBF of 50000 there is a 50% chance that it will run (without failure) to about 35000 hours
Not usually. MTBF calculation is potentially complex and subject to varying definitions especially on repairable systems such as our engines. It also doesn’t work on systems which are subject to an “end of life” factor – e.g. human MTBF has been calculated at 800 years which merely means that during a normal lifetime humans very rarely suddenly die, and the human lifetime cannot be extrapolated from it.
Similarly a piston engine will never make 50k hrs; one would need to replace almost every moving part in it at various points to achieve that (the serial number plate would make 50k ok ). Crankshafts tend to make of the order of 10k hrs before reaching the limit for undersize bearings, crankcases can be skimmed only so many times, etc.
The MTBF calculation becomes controversial for repairable or precautionary-serviceable systems. For example I had a sticky valve. It was diagnosed and repaired. But if there was no engine instrumentation, and the pilot was a renter who is not familiar with the way the engine sounds and goes for a flight in almost anything on which the engine starts up, he would have eventually got some form of failure. A similar debate takes place with turbo engine owners, who tend to take the view that cracked cylinders are not a failure; cylinders are “consumables”. Only if a cylinder head comes right off during flight would it be an “engine failure”.
I don’t know where the 50k Lyco number comes from. It’s appeared in the aviation press for many years. One data point, found by @cobalt, is above.
I think what people mean about MTBF=50k hours is that the catastrophic failure rate is 1/50,000 per running hour. People often abreviate in an MTBF but as Peter noted, it doesn’t make sense for piston engines.
From my small experience as an engineer in a major aerospace group, is that failure rates/MTBF means nothing except for circuit boards in a precise thermal environment. For mechanical parts, it depends too luc on external factors like corrosion etc….
As for the bathtub curve, it is very theoretical too. From what I see, every equipment has its own failure curve, depending on what is inside.
Not usually
That is exactly what it means, and an aircraft engine is, in theory, the perfect example because it is subjected to overhaul every 2000 h for instance, where parts outside spec are replaced. Theoretically the engine is as good as new every 2000 h
The problem is, the theory doesn’t hold up in real life, and certainly not when it comes to reliability of the entire propulsion system (relevant to the original thread)
Peter wrote:
human MTBF has been calculated at 800 years
According to your link, that’s the MTBF of a 25 year old human, applying the same methods for estimating MTBF as for a manufactured product. That method/calculation falls for the very reason/fallacy explained in the very same article, but which the author then ignores.
[MTBF] It’s the inverse of the annual failure rate if the failure rate is constant.
They key point is that human’s “failure rate” is not constant, 80-year old humans fail much more (often) than 25-year old humans. Taking a look at https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/bulletins/deathsregistrationsummarytables/2018, we see that there were 541,589 deaths in England&Wales in 2018. That’s out of a population of 59,115,809. That’s an annual “failure rate” of 0,92%, an estimated MTBF of 109 years.
This “raw” estimate/calculation still has a problem; it is that the population is not uniform in age. To get the “true” MTBF, you have to take all people born in a year, wait for all of them to die and then you can compute the exact number. All the rest is an estimate.
Obviously, the MTBFs of manufactured stuff is also all estimates :) With more or less “problems” in the estimate :)
Well, yes, I posted the human MTBF to illustrate that heavy assumptions are made there
Humans are fairly unique in that there is a pretty clear reduction in life expectancy as they get older. This doesn’t happen with most machinery, which has a broad spectrum of lifetimes. A random piece of 1970s electronics is highly likely to work when switched on now, or in 100 years’ time, subject to some specific requirements like no corrosion, no electrolytic caps, etc.
MTBF is generally calculated (there is a milspec handbook for that; widely used) but it can be derived from real data. One of my products had this done by a customer, based on a few tens of k units sold, how many came back, etc, and it worked out at 600 years. I am certain the MTBF of an engine cannot be usefully calculated; it has to come from real data.
LeSving wrote:
and nothing like we see in the real world for engine failure (due to any cause).
Peter wrote:
I am certain the MTBF of an engine cannot be usefully calculated; it has to come from real data.
But MTBF calculations don’t have the impact built in of wrench-happy mechanics fiddling with the product. 
