2 Engines and 4 Engines
That would apply if EACH engine had its own individual probability specified. Then the chance would become the sum of the two probalities eg Engine 'A' has a 1:1 000 000 chance of failure, engine 'B' has a 1.5:1 000 000 then overall probability would be 2.5:1 000 000.
However, this is not the case. Within the probability for the FLEET, some fail early, some fail much later but the overall probability remains consistant. This is Ignoring trends from a spate of failures or unusually good reliability. Failure probability is quoted on fleetwide basis which is largely independent of engine location. It's a bell curve that considers ALL engines in operation. A statistic that applies to a population is not capable of supplying a prediction for any particular member of the population.
For any specific airframe, that airframe could have an increased probability of failure IF it is unfortunate enough to be fitted with engines that are each on the unreliable side of the bell curve. However, the airframe could equally have a much reduced probability of failure if it ends up fitted with engines that happen to be all on the more reliable side of the curve.
Changing the number of engines on the airframe doesn't affect this **overall** probability and so that is why there is this seemingly weird 'number of engines doesn't affect reliability' situation. Keep in mind that adding more engines could result in the airframe getting a batch of 'super reliable' ones then the chance of a failure would reduce. Until it received a batch of 'super unreliable' ones when the chance of a failure would increase. Over time, and over a large number of installations, the 'average' chance of failure would tend towards the fleet average.
Oh, why did I get involved in this discussion??
But it is a great debate and I have been following responses very closely, with interest.
Tins is on the money! In a theoretical world, if the demonstrated failure rate were < 1:100,000, when the fleet total exceeds 100,000 hours, it is really irrelevent whether the engine which will fail is on a single engine or multi engine aircraft. For that reason, there should be no greater risk of engine failure on a S/E or M/E aircraft.
However, I accept if one has a four engine aircraft, the risk may be higher that the engine which is going to fail will be on that four engine aircraft and not on the S/E aircraft.
Now I'm completely muddled!
But I still suggest the failed engine is not relevent - it's how many you have left after the failure that counts. Unless of course, the aircraft is a BN2A MKIII Trislander, in which case the two remaining are guaranteed to take you to the scene of the crash!
Woomera
However, this is not the case. Within the probability for the FLEET, some fail early, some fail much later but the overall probability remains consistant. This is Ignoring trends from a spate of failures or unusually good reliability. Failure probability is quoted on fleetwide basis which is largely independent of engine location. It's a bell curve that considers ALL engines in operation. A statistic that applies to a population is not capable of supplying a prediction for any particular member of the population.
For any specific airframe, that airframe could have an increased probability of failure IF it is unfortunate enough to be fitted with engines that are each on the unreliable side of the bell curve. However, the airframe could equally have a much reduced probability of failure if it ends up fitted with engines that happen to be all on the more reliable side of the curve.
Changing the number of engines on the airframe doesn't affect this **overall** probability and so that is why there is this seemingly weird 'number of engines doesn't affect reliability' situation. Keep in mind that adding more engines could result in the airframe getting a batch of 'super reliable' ones then the chance of a failure would reduce. Until it received a batch of 'super unreliable' ones when the chance of a failure would increase. Over time, and over a large number of installations, the 'average' chance of failure would tend towards the fleet average.
Oh, why did I get involved in this discussion??
But it is a great debate and I have been following responses very closely, with interest.
Tins is on the money! In a theoretical world, if the demonstrated failure rate were < 1:100,000, when the fleet total exceeds 100,000 hours, it is really irrelevent whether the engine which will fail is on a single engine or multi engine aircraft. For that reason, there should be no greater risk of engine failure on a S/E or M/E aircraft.
However, I accept if one has a four engine aircraft, the risk may be higher that the engine which is going to fail will be on that four engine aircraft and not on the S/E aircraft.
Now I'm completely muddled!
But I still suggest the failed engine is not relevent - it's how many you have left after the failure that counts. Unless of course, the aircraft is a BN2A MKIII Trislander, in which case the two remaining are guaranteed to take you to the scene of the crash!
Woomera
Last edited by Woomera; 11th Aug 2004 at 01:09.
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You COULD have a situation of very bad luck, where both engines on the 2 engined aircraft failed really early, and the engines on the 4 engined aircraft never failed, just luck. 
However, there MUST be more chance of ONE engine failing at any time on the 4, than ONE engine failing on the 2.
There is however more chance of ALL engines failing on the 2 than the 4.
IF you still don't get it, forget aircraft, it is just logic.
I am about to head off to work now.
During my drive to work in my car, IF a semi trailer was to follow me over the exact same roads, there is (I hope ) MORE chance that he will get ONE flat tyre with his 18 tyres, than I will get ONE in my 4.
Mentioning both failing - the BASI accident report on the Chieftan double engine failure in South Australia is a worthwhile read in relation to piston engine reliability.
Woomera
However, there MUST be more chance of ONE engine failing at any time on the 4, than ONE engine failing on the 2.
There is however more chance of ALL engines failing on the 2 than the 4.
IF you still don't get it, forget aircraft, it is just logic.
I am about to head off to work now.
During my drive to work in my car, IF a semi trailer was to follow me over the exact same roads, there is (I hope
) MORE chance that he will get ONE flat tyre with his 18 tyres, than I will get ONE in my 4. Mentioning both failing - the BASI accident report on the Chieftan double engine failure in South Australia is a worthwhile read in relation to piston engine reliability.
Woomera
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Woomera,
You seem to be having two bob each way.
(QUOTE)
Tins is on the money! In a theoretical world, if the demonstrated failure rate were < 1:100,000, when the fleet total exceeds 100,000 hours, it is really irrelevent whether the engine which will fail is on a single engine or multi engine aircraft. For that reason, there should be no greater risk of engine failure on a S/E or M/E aircraft.
However, I accept if one has a four engine aircraft, the risk may be higher that the engine which is going to fail will be on that four engine aircraft and not on the S/E aircraft.
Now I'm completely muddled!
(ENDQUOTE)
IF you have a certain engine type, just pretend say CFM56, and in the Airline we are both with, it has a failure rate of 1 in 100,000 hours.
You are flying an aircraft with 2 of these CFM56s, and I am flying an (imaginary) aircraft in our fleet with 10 of these CFM56s.
Obviously nobody can be sure which CFM56 will fail next, however surely you believe that the ODDS are ONE of my 10 will fail before ONE of your 2.
Of course I will still have 9 left...........
You seem to be having two bob each way.
(QUOTE)
Tins is on the money! In a theoretical world, if the demonstrated failure rate were < 1:100,000, when the fleet total exceeds 100,000 hours, it is really irrelevent whether the engine which will fail is on a single engine or multi engine aircraft. For that reason, there should be no greater risk of engine failure on a S/E or M/E aircraft.
However, I accept if one has a four engine aircraft, the risk may be higher that the engine which is going to fail will be on that four engine aircraft and not on the S/E aircraft.
Now I'm completely muddled!
(ENDQUOTE)
IF you have a certain engine type, just pretend say CFM56, and in the Airline we are both with, it has a failure rate of 1 in 100,000 hours.
You are flying an aircraft with 2 of these CFM56s, and I am flying an (imaginary) aircraft in our fleet with 10 of these CFM56s.
Obviously nobody can be sure which CFM56 will fail next, however surely you believe that the ODDS are ONE of my 10 will fail before ONE of your 2.
Of course I will still have 9 left...........
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An interesting debate. All based on mathematical concepts and theories.
BUT.
Having spent many years in technical fields (too many?), it is may contention that maths has NOTHING to do with the probability of failure of components. The ONLY law that applies universally is Murphys, which basically states (paraphrased) that:
A component will fail when:
1) It is at its most inconvenient,
2) It will do the most damage,
3) All of the above.
and no mathematical algorythm will ever be able to predict it happening.
Cynical I know, but it works in the majority of cases and if it doesn't at some stage, it's only to cause maximum embarrassment to someone expressing the theory.
BUT.
Having spent many years in technical fields (too many?), it is may contention that maths has NOTHING to do with the probability of failure of components. The ONLY law that applies universally is Murphys, which basically states (paraphrased) that:
A component will fail when:
1) It is at its most inconvenient,
2) It will do the most damage,
3) All of the above.
and no mathematical algorythm will ever be able to predict it happening.
Cynical I know, but it works in the majority of cases and if it doesn't at some stage, it's only to cause maximum embarrassment to someone expressing the theory.
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Now there is a good example.
There is MUCH more chance of losing one engine on any BAe146, than one engine on any 777.
Probably more chance of losing 2 or 3 on the Bring Another Engine before you lose one on the Boeing.......
There is MUCH more chance of losing one engine on any BAe146, than one engine on any 777.
Probably more chance of losing 2 or 3 on the Bring Another Engine before you lose one on the Boeing.......
planemad2,
I like you logic, but it is flawed...
The 146/RJ has been flying for much more time than the 777, basically only AlliedSignal & Lycoming as engine manufacturer for the 146/RJ family, you have multiple for the 777 (GE/PW/RR).
For each flight hour a 146/RJ does, it adds 4 hours to the number of hours the engine type has done in service. Similar, each flight hour a 777 does, it adds 2 hours to the number of hours the engine type for that manufacturer has done in service.
Now the mean time between failure (MTBF) is defined as
MTBF = (flying hours * aircraft quantity)/(number of confirmed failures)
The 777 has had a number of engine failures, can remember high speed rejects, inflight, and even the 777 demostration a/c in south africa have had failures. Its a new engine, has not flown a lot relative to the 146/RJ. A new engine is prone to more teathing problems than a proven engine.
So IMHO the MTBF on a 777 would be higher than that of a 146, purely because the maturity of the 146/RJ fleet, and the 4 times factor per flight hour vs 2 (maybe less if you consider the 3 777 engine manufacturers), the maturity of the engine, and the single engine manufacturer for the aircraft.
However, I do see the 777 MTFB to increase, and the 146/RJ one to stay static or decrease.
I like you logic, but it is flawed...
The 146/RJ has been flying for much more time than the 777, basically only AlliedSignal & Lycoming as engine manufacturer for the 146/RJ family, you have multiple for the 777 (GE/PW/RR).
For each flight hour a 146/RJ does, it adds 4 hours to the number of hours the engine type has done in service. Similar, each flight hour a 777 does, it adds 2 hours to the number of hours the engine type for that manufacturer has done in service.
Now the mean time between failure (MTBF) is defined as
MTBF = (flying hours * aircraft quantity)/(number of confirmed failures)
The 777 has had a number of engine failures, can remember high speed rejects, inflight, and even the 777 demostration a/c in south africa have had failures. Its a new engine, has not flown a lot relative to the 146/RJ. A new engine is prone to more teathing problems than a proven engine.
So IMHO the MTBF on a 777 would be higher than that of a 146, purely because the maturity of the 146/RJ fleet, and the 4 times factor per flight hour vs 2 (maybe less if you consider the 3 777 engine manufacturers), the maturity of the engine, and the single engine manufacturer for the aircraft.
However, I do see the 777 MTFB to increase, and the 146/RJ one to stay static or decrease.
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I didn't bring up about the 146 and 777, that was someone else.
It was a joke.
IF you take one engine type, like I mentioned before the CFM56 as an example, and say just for this discussion it has a failure rate on average of 1 failure in every 100,000 hours.
Now this following example is ridiculous, but I cannot believe that some still don't get it, so it is necessary.
Assume there is one aircraft fitted with 2 of these CFM56s, and another aircraft fitted with 100 of them.
PLEASE PLEASE tell me you agree that there is more chance of ONE engine failing at any given time on the 100 engined aircraft as opposed to the 2 engined aircraft.
Of course there is way more chance of ALL engines failing on the 2 engined aircraft than on the 100 engined aircraft.
It was a joke.
IF you take one engine type, like I mentioned before the CFM56 as an example, and say just for this discussion it has a failure rate on average of 1 failure in every 100,000 hours.
Now this following example is ridiculous, but I cannot believe that some still don't get it, so it is necessary.
Assume there is one aircraft fitted with 2 of these CFM56s, and another aircraft fitted with 100 of them.
PLEASE PLEASE tell me you agree that there is more chance of ONE engine failing at any given time on the 100 engined aircraft as opposed to the 2 engined aircraft.
Of course there is way more chance of ALL engines failing on the 2 engined aircraft than on the 100 engined aircraft.
planemad2,
Using your 100 engines on an aircraft means you have a higher chance of an engine failure train of thought, it would also follow using your logic that if you had one engine installed on the aircraft you would have less chace of an engine failure....or if we narrow it down to talking about entire population of CFM56 engines...are we saying that somewhere out there installed on aircraft x which may have 1, 2, 4, or 100 CFM 56 engines out there we would expect one failure every 100 000 hrs ?
Does it really mean, a MTBF of 1:100 000, that you would expect mathematically an aircraft with 100 engines to fly for 1000 hours without a failure, an aircraft with 2 engines 50 000 hours without a failure, and an aircraft with one engine 100 000 hours without a failure? or is it really saying that out of the total population of engines you would expect a failure after 100 000 hours, but you don’t know when or where ?
What happens to the aircraft with 100 engines when it reaches 1000 hours of flying ? The MTBF for that aircraft has just jumped from 1:100 000 to 1:200 000 after 1000 hrs, and the two engine aircraft the MTBF would go from 1:100 000 to 1:102 000 after 1000 hrs.
Realistically...this maths is just that, maths. If you can tell me which aircraft if going to have the next engine failure, you are doing better than anyone else out there in industry.
The real reason for the number of engines installed on an aircraft is to do with design parameters, not predicted engine failure rates, when the 747 was designed, you could not get two or three engines big enough to power it, even now the A380 has a limited payload as the 4 large engines it has cannot produce the thrust required for the full design load. Give it time, engine technology will improve, and target thrust ratings will be achieved.
This might actually surprise you....the original 747 layout
Tri jets were designed also to meet design parameters. Before ETOPS you could not fly greater than 60 minutes from a suitable aerodrome in a twin, now with ETOPS introduced, you can do the Atlantic in a twin with ETOPS concessions, so there is no longer a requirement for Trijets.
Why has Airbus gone for the long range quads...could it be as simple as there is not enough ground clearance to put a 777 size engine on the wing without redesigning the landing gear ? You know the aircraft would have ground clearance to put 4 A330 size engines out there….without a big redesign, which is simpler, quicker to bring to the market, cheaper to design, and easier to manufacture ? And of course…lots of punters still like 4 engines…
Using your 100 engines on an aircraft means you have a higher chance of an engine failure train of thought, it would also follow using your logic that if you had one engine installed on the aircraft you would have less chace of an engine failure....or if we narrow it down to talking about entire population of CFM56 engines...are we saying that somewhere out there installed on aircraft x which may have 1, 2, 4, or 100 CFM 56 engines out there we would expect one failure every 100 000 hrs ?
Does it really mean, a MTBF of 1:100 000, that you would expect mathematically an aircraft with 100 engines to fly for 1000 hours without a failure, an aircraft with 2 engines 50 000 hours without a failure, and an aircraft with one engine 100 000 hours without a failure? or is it really saying that out of the total population of engines you would expect a failure after 100 000 hours, but you don’t know when or where ?
What happens to the aircraft with 100 engines when it reaches 1000 hours of flying ? The MTBF for that aircraft has just jumped from 1:100 000 to 1:200 000 after 1000 hrs, and the two engine aircraft the MTBF would go from 1:100 000 to 1:102 000 after 1000 hrs.
Realistically...this maths is just that, maths. If you can tell me which aircraft if going to have the next engine failure, you are doing better than anyone else out there in industry.
The real reason for the number of engines installed on an aircraft is to do with design parameters, not predicted engine failure rates, when the 747 was designed, you could not get two or three engines big enough to power it, even now the A380 has a limited payload as the 4 large engines it has cannot produce the thrust required for the full design load. Give it time, engine technology will improve, and target thrust ratings will be achieved.
This might actually surprise you....the original 747 layout
Tri jets were designed also to meet design parameters. Before ETOPS you could not fly greater than 60 minutes from a suitable aerodrome in a twin, now with ETOPS introduced, you can do the Atlantic in a twin with ETOPS concessions, so there is no longer a requirement for Trijets.
Why has Airbus gone for the long range quads...could it be as simple as there is not enough ground clearance to put a 777 size engine on the wing without redesigning the landing gear ? You know the aircraft would have ground clearance to put 4 A330 size engines out there….without a big redesign, which is simpler, quicker to bring to the market, cheaper to design, and easier to manufacture ? And of course…lots of punters still like 4 engines…
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I give up trying to explain it.........
BTW, yes you would have less chance of having ONE engine failure on your single engined CFM56 aircraft, than on a similar CFM56 twin, but I don't want to be on it thanks.
Okay, one last try.
Forget engines, let's look at hydraulic pumps.
Say each engine has 2 hydraulic pumps, so on a 2 engined aircraft there are 4 engine driven hydraulic pumps, and on the 4 engined aircraft there are 8 pumps.
Now the 4 engined aircaft is probably safer, but there MUST be more chance of ONE hydraulic pump failing on the 4 than the 2.
But LESS chance of losing ALL pumps on the 4.
BTW, yes you would have less chance of having ONE engine failure on your single engined CFM56 aircraft, than on a similar CFM56 twin, but I don't want to be on it thanks.
Okay, one last try.
Forget engines, let's look at hydraulic pumps.
Say each engine has 2 hydraulic pumps, so on a 2 engined aircraft there are 4 engine driven hydraulic pumps, and on the 4 engined aircraft there are 8 pumps.
Now the 4 engined aircaft is probably safer, but there MUST be more chance of ONE hydraulic pump failing on the 4 than the 2.
But LESS chance of losing ALL pumps on the 4.
This MTBF stuff is all very interesting, but if we are talking about theoretical aircraft all powered by engine x (with a certain MTBF), then that MTBF is a constant, and therfore not really relevant.
My maths is a bit dodgy these days, but being a bit of a gambling man, I found this formula:
log(1 - DC)
N = ----------------
log(1 - p)
N=number of trials (in this case number of engines)
DC= degree of certainty
p= probability (in this case MTBF)
So swh, plug in whatever MTBF and number of engines you want into your scientific calculator and let me know what you come up with.
My maths is a bit dodgy these days, but being a bit of a gambling man, I found this formula:
log(1 - DC)
N = ----------------
log(1 - p)
N=number of trials (in this case number of engines)
DC= degree of certainty
p= probability (in this case MTBF)
So swh, plug in whatever MTBF and number of engines you want into your scientific calculator and let me know what you come up with.
ok lets look at it this way.... if an aircraft has an MTBF of 1:100 000, if you have 2 engine sthere is more chance of that engine being on your aircraft. For example lets consider say a lycoming O-360 example as a whole... quite a popular make of engine on both singles and twin engine aircraft alike...... who has the greatest chance of that engine being on their aircraft? true of however only slight. 
Secondly, if an aircraft operates on four engines with a set MTBF.. does that mean because you clock up 4 engine hours per flight hour and if you compare it to an aircraft with two engines (both engine types having simliar MTBF's) that per flight hour the chance of an engine failing on the 4 engines aircraft if increased because the engine logs more hours over a shorter period of time....... hence greater the engine, greater the chance... even using that MTBF formula i saw before.....
Secondly, if an aircraft operates on four engines with a set MTBF.. does that mean because you clock up 4 engine hours per flight hour and if you compare it to an aircraft with two engines (both engine types having simliar MTBF's) that per flight hour the chance of an engine failing on the 4 engines aircraft if increased because the engine logs more hours over a shorter period of time....... hence greater the engine, greater the chance... even using that MTBF formula i saw before.....
G,
At design phase there is a theoretical constant MTBF, this is how Boeing was able to get the 777 ETOPS approved "off the plan" without flying for the normal surveillance period. Previous to the 777 ETOPS approval from the FAA required operators to establish the systems and documentation for a period of time and report any failures during that period.
The MTBF in real life varies as engine trend monitoring equipment and trip logs are collected, either manually or via some electronic means like ACARS, quick access recorders etc, and is used to build a statistical picture.
The actual MTBF is not a constant, and varies between operators, we can see here in Australia that VB do not have automatic rights to the same ETOPS planning as what QF does for their 737's. Does this mean a VB 737 is more likely to have an engine failure than a QF one, no. However QF has a more substantial set of historical statistical data they can draw on, and hence a lower MTBF, this is due to flying more hours with the engine type.
What really determines the MTBF is the number of hours the engine flies, a 4 engine aircraft build this statistical picture up quicker than a 2 engine aircraft, and generally also fly longer routes, with less cycles, which all aids in reducing the actual MTBF.
The formula you have illustrated fails to take in account that the actual MTBF is not a constant, it can only be used to look at a snapshot of data. It was however a nice twist to a dull discussion.
P.S. you must be a gambling man...your formula looks a lot like the \'Fundamental Formula of Gambling\' (FFG): N = log(1 – DC) / log(1 - p).......
At design phase there is a theoretical constant MTBF, this is how Boeing was able to get the 777 ETOPS approved "off the plan" without flying for the normal surveillance period. Previous to the 777 ETOPS approval from the FAA required operators to establish the systems and documentation for a period of time and report any failures during that period.
The MTBF in real life varies as engine trend monitoring equipment and trip logs are collected, either manually or via some electronic means like ACARS, quick access recorders etc, and is used to build a statistical picture.
The actual MTBF is not a constant, and varies between operators, we can see here in Australia that VB do not have automatic rights to the same ETOPS planning as what QF does for their 737's. Does this mean a VB 737 is more likely to have an engine failure than a QF one, no. However QF has a more substantial set of historical statistical data they can draw on, and hence a lower MTBF, this is due to flying more hours with the engine type.
What really determines the MTBF is the number of hours the engine flies, a 4 engine aircraft build this statistical picture up quicker than a 2 engine aircraft, and generally also fly longer routes, with less cycles, which all aids in reducing the actual MTBF.
The formula you have illustrated fails to take in account that the actual MTBF is not a constant, it can only be used to look at a snapshot of data. It was however a nice twist to a dull discussion.
P.S. you must be a gambling man...your formula looks a lot like the \'Fundamental Formula of Gambling\' (FFG): N = log(1 – DC) / log(1 - p).......
swh,
So what is the actual MTBF formula, because the one you posted obviously does not support your idea that VB didn't get the same ETOPs rights as QF because of their MTBF? What a load of
Regardless, when we compare apples with apples, the MTBF doesn't matter.
ok so lets take another theoretical scenario, similar to what we have heard but taken further for the purpose of this kinda silly discussion.
2 aircraft; A is fitted with every single engine x (all direct from the factory - no statistical data available, blah blah - SAME, all same!) in the world bar 1, which is fitted to aircraft B. If they both take off at exactly the same time, which of these is more likely to have AN engine failure?
So what is the actual MTBF formula, because the one you posted obviously does not support your idea that VB didn't get the same ETOPs rights as QF because of their MTBF? What a load of
Regardless, when we compare apples with apples, the MTBF doesn't matter.
ok so lets take another theoretical scenario, similar to what we have heard but taken further for the purpose of this kinda silly discussion.
2 aircraft; A is fitted with every single engine x (all direct from the factory - no statistical data available, blah blah - SAME, all same!) in the world bar 1, which is fitted to aircraft B. If they both take off at exactly the same time, which of these is more likely to have AN engine failure?
G,
Your so so easy to get a rise from !
To answer your questions ....
MTBF = (flying hours * aircraft quantity)/(number of confirmed failures)
More flying hours you do, the more engines you have, the bigger the number ontop gets, MTBF increases.
The silly theoretical scenario question...
Mathematically their would be no chance of an engine failure, as giving your start conditions, their is no failure record, so there can be no mean time between failures, and no hours flown, the MTBF is zero, and last time I did maths anything multiplied by zero is still zero.
You were right it was a silly theoretical scenario...
Edit : made an error, fixed it
Your so so easy to get a rise from !
To answer your questions ....
MTBF = (flying hours * aircraft quantity)/(number of confirmed failures)
More flying hours you do, the more engines you have, the bigger the number ontop gets, MTBF increases.
The silly theoretical scenario question...
Mathematically their would be no chance of an engine failure, as giving your start conditions, their is no failure record, so there can be no mean time between failures, and no hours flown, the MTBF is zero, and last time I did maths anything multiplied by zero is still zero.
You were right it was a silly theoretical scenario...
Edit : made an error, fixed it
Last edited by swh; 17th Aug 2004 at 01:02.
swh, thanks as always for your informative and practical reply, in this case a yr6 maths lesson.
So I design a new engine and put it onto a new aircraft, I should be able to get ETOPs, because the MTBF would be zero until the engine failed (as you cleverly pointed out, anything multiplied by zero is zero )
But didn't you say;
so then, in your own words, these engines x would have a MTBF other than zero, so do the maths again using any number other than zero for the silly scenario.
Now a serious question on the MTBF formula;
I don't pretend to know much about it, but could you clarify it for me. From what you're saying different operators must have different MTBF's. Is the following then correct?
MTBF = (flying hours*aircraft quantity)(of that operator)/(number of confirmed failures)(of that engine worldwide)
So I design a new engine and put it onto a new aircraft, I should be able to get ETOPs, because the MTBF would be zero until the engine failed (as you cleverly pointed out, anything multiplied by zero is zero
)But didn't you say;
At design phase there is a theoretical constant MTBF
Now a serious question on the MTBF formula;
I don't pretend to know much about it, but could you clarify it for me. From what you're saying different operators must have different MTBF's. Is the following then correct?
MTBF = (flying hours*aircraft quantity)(of that operator)/(number of confirmed failures)(of that engine worldwide)
G,
The operators would have their own MTBF for only their fleet, its representative of how they operate and maintain their fleet, which may be better than or worse than the average worldwide.
The regulator will look more at a worldwide MTBF figure to benchmark an operator when considering granting approvals. A manufacturer will look at a worldwide MTBF, but will classify the results according to overall usage, and defined stage lengths, areas of operation etc.
The MTBF number derived at design phase normally comes from the reliability engineers who look at results of wear oil consumption etc from engine strip back during development testing. They come up with a plethora of numbers that are used for maintenance planning, parts replacement, overhaul periods etc.
Some snippets from NPRM AC 121-03(0): ETOPS Approval which may help ...
To establish whether a particular airframe-engine combination has satisfied the propulsion systems reliability requirements for extended range operation, an assessment will be made by CASA, using all pertinent propulsion system data. To accomplish the assessment, CASA will need world fleet data, and data from various sources (the operator, the engine manufacturer and the aeroplane manufacturer) which should be extensive enough and of sufficient maturity to enable CASA to assess with a high level of confidence, using engineering and operational judgement and standard statistical methods where appropriate, that the risk of total power loss from independent causes is sufficiently low. CASA will state whether or not the current propulsion system reliability of a particular airframe-engine combination satisfies the relevant criteria. Included in the statement, if the operation is approved, will be the engine build standard, propulsion system configuration, operating condition and limitations required to qualify the propulsion system as suitable for extended range operation.
...
There is justification for the view that modern propulsion systems achieve a stable reliability level by 100,000 hours for new types and 50,000 hours for derivatives. 3000 to 4000 hours is considered to be the necessary time in service for a specific unit to indicate problem areas.
Normally, the service experience will be:
(1) For new propulsion systems: 100,000 hours and 12 months service. Where experience on another aeroplane is applicable, a significant portion of the 100,000 hours should normally be obtained on the candidate aeroplane. On a case-by-case, relevant test and design experience, and maximum diversion time
requested, could be taken into account when arriving at the in-service experience required.
(2) For derivative propulsion systems: 50,000 hours and 12 months service. These values may vary according to the degree of commonality. To this end in determining the derivative status of a propulsion system, consideration should be given to technical criteria referring to the commonality with previous ETOPS-rated engines.
Prime areas of concern include:
a) Turbomachinery
b) Controls and accessories and control logic
c) Configuration hardware (piping, cables etc.)
d) Aircraft to engine interfaces and interaction (fire, thrust reverser, avionics etc.)
...
Considerations would be made on a case-by-case basis and would need to provide a demonstrated level of propulsion system reliability in terms of in flight shut down IFSD rate of the order of 0.05 per 1000-hours, as is necessary also for new propulsion systems.
...
When considering safety targets, an accepted practice is to allocate appropriate portions of the total to the various potential contributing factors. By applying this practice to the overall target of 0.3 x 10-6 per flying hour, in the proportions previously considered appropriate, the probability of a catastrophic accident due to complete loss of thrust from independent causes must be no worse than 0.3 x 10-6 per flying hour.
...
A family of ETOPS products with a high degree of similarity is considered as mature once:
(a) the product family has accumulated at least 250,000 flight hours for an aircraft family or 500,000 operating hours for an engine family;
(b) the product family has accumulated service experience covering a comprehensive spectrum of operating conditions (e.g. cold, hot, humid,);
(c) each ETOPS approved model or variant in the family has achieved the reliability objectives for ETOPS and has remained stable at or below the objectives fleet-wide for at least two years. New models or significant design changes may not be considered mature until they have individually satisfied the condition of sub-section (a).
...
An analysis will be made on a case-by-case basis, of all significant failures, defects and malfunctions experienced in service (or during testing) for the particular airframe/ engine combination. Significant failures are principally those causing or resulting in in-flight shutdown or flameout of the engine(s), but may also include unusual ground failures and/or unscheduled removal of engines. In making the assessment, consideration will be given to the following:
a) the type of propulsion system, previous experience, whether the power-unit is new or a derivative of an existing model, and the operating thrust level to be used after one engine shutdown.
b) the trends in the cumulative twelve month rolling average, updated quarterly, of inflight shutdown rates versus propulsion system flight hours and cycles.
c) the demonstrated effect of corrective modifications, maintenance, etc. on the possible future reliability of the propulsion system.
d) maintenance actions recommended and performance and their effect on propulsion system and APU failure rates.
e) the accumulation of operational experience which covers the range of environmental conditions likely to be encountered.
f) intended maximum flight duration, and maximum diversion in the ETOPS segment, used in the extended range operation under consideration.
(3) Engineering judgement will be used in the analysis of the above such that the potential improvement in reliability, following the introduction of corrective actions identified during the analysis, can be quantified.
(4) The resultant predicted reliability level and the criteria developed in accordance with section 1.c will together be used to determine the maximum diversion time for which the particular airframe-engine combination qualifies.
...
Statistical indicators (MTBF/MTBUR) and engineering judgement applied to the individual events must be used to evaluate the maturity and the reliability of all ETOPS significant systems.
The operators would have their own MTBF for only their fleet, its representative of how they operate and maintain their fleet, which may be better than or worse than the average worldwide.
The regulator will look more at a worldwide MTBF figure to benchmark an operator when considering granting approvals. A manufacturer will look at a worldwide MTBF, but will classify the results according to overall usage, and defined stage lengths, areas of operation etc.
The MTBF number derived at design phase normally comes from the reliability engineers who look at results of wear oil consumption etc from engine strip back during development testing. They come up with a plethora of numbers that are used for maintenance planning, parts replacement, overhaul periods etc.
Some snippets from NPRM AC 121-03(0): ETOPS Approval which may help ...
To establish whether a particular airframe-engine combination has satisfied the propulsion systems reliability requirements for extended range operation, an assessment will be made by CASA, using all pertinent propulsion system data. To accomplish the assessment, CASA will need world fleet data, and data from various sources (the operator, the engine manufacturer and the aeroplane manufacturer) which should be extensive enough and of sufficient maturity to enable CASA to assess with a high level of confidence, using engineering and operational judgement and standard statistical methods where appropriate, that the risk of total power loss from independent causes is sufficiently low. CASA will state whether or not the current propulsion system reliability of a particular airframe-engine combination satisfies the relevant criteria. Included in the statement, if the operation is approved, will be the engine build standard, propulsion system configuration, operating condition and limitations required to qualify the propulsion system as suitable for extended range operation.
...
There is justification for the view that modern propulsion systems achieve a stable reliability level by 100,000 hours for new types and 50,000 hours for derivatives. 3000 to 4000 hours is considered to be the necessary time in service for a specific unit to indicate problem areas.
Normally, the service experience will be:
(1) For new propulsion systems: 100,000 hours and 12 months service. Where experience on another aeroplane is applicable, a significant portion of the 100,000 hours should normally be obtained on the candidate aeroplane. On a case-by-case, relevant test and design experience, and maximum diversion time
requested, could be taken into account when arriving at the in-service experience required.
(2) For derivative propulsion systems: 50,000 hours and 12 months service. These values may vary according to the degree of commonality. To this end in determining the derivative status of a propulsion system, consideration should be given to technical criteria referring to the commonality with previous ETOPS-rated engines.
Prime areas of concern include:
a) Turbomachinery
b) Controls and accessories and control logic
c) Configuration hardware (piping, cables etc.)
d) Aircraft to engine interfaces and interaction (fire, thrust reverser, avionics etc.)
...
Considerations would be made on a case-by-case basis and would need to provide a demonstrated level of propulsion system reliability in terms of in flight shut down IFSD rate of the order of 0.05 per 1000-hours, as is necessary also for new propulsion systems.
...
When considering safety targets, an accepted practice is to allocate appropriate portions of the total to the various potential contributing factors. By applying this practice to the overall target of 0.3 x 10-6 per flying hour, in the proportions previously considered appropriate, the probability of a catastrophic accident due to complete loss of thrust from independent causes must be no worse than 0.3 x 10-6 per flying hour.
...
A family of ETOPS products with a high degree of similarity is considered as mature once:
(a) the product family has accumulated at least 250,000 flight hours for an aircraft family or 500,000 operating hours for an engine family;
(b) the product family has accumulated service experience covering a comprehensive spectrum of operating conditions (e.g. cold, hot, humid,);
(c) each ETOPS approved model or variant in the family has achieved the reliability objectives for ETOPS and has remained stable at or below the objectives fleet-wide for at least two years. New models or significant design changes may not be considered mature until they have individually satisfied the condition of sub-section (a).
...
An analysis will be made on a case-by-case basis, of all significant failures, defects and malfunctions experienced in service (or during testing) for the particular airframe/ engine combination. Significant failures are principally those causing or resulting in in-flight shutdown or flameout of the engine(s), but may also include unusual ground failures and/or unscheduled removal of engines. In making the assessment, consideration will be given to the following:
a) the type of propulsion system, previous experience, whether the power-unit is new or a derivative of an existing model, and the operating thrust level to be used after one engine shutdown.
b) the trends in the cumulative twelve month rolling average, updated quarterly, of inflight shutdown rates versus propulsion system flight hours and cycles.
c) the demonstrated effect of corrective modifications, maintenance, etc. on the possible future reliability of the propulsion system.
d) maintenance actions recommended and performance and their effect on propulsion system and APU failure rates.
e) the accumulation of operational experience which covers the range of environmental conditions likely to be encountered.
f) intended maximum flight duration, and maximum diversion in the ETOPS segment, used in the extended range operation under consideration.
(3) Engineering judgement will be used in the analysis of the above such that the potential improvement in reliability, following the introduction of corrective actions identified during the analysis, can be quantified.
(4) The resultant predicted reliability level and the criteria developed in accordance with section 1.c will together be used to determine the maximum diversion time for which the particular airframe-engine combination qualifies.
...
Statistical indicators (MTBF/MTBUR) and engineering judgement applied to the individual events must be used to evaluate the maturity and the reliability of all ETOPS significant systems.