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Crash LPCS (also engine failure probability on a twin)

RobertL18C wrote:

Actually it’s slightly more than twice, as you may have a double engine failure in a twin.

Errr….actually…

It’s slightly less than twice (making some assumptions such as the probability of failure being identical for both engines). To illustrate, let’s imagine we have a batch of horribly unreliable engines, which have a 1-in-10 chance of quitting on takeoff as this keeps the numbers within the realm of mental arithmetic.

For a single engine aircraft, it’s simple: we have a 1-in-10 chance of taking off and having it quit.

But for a twin we don’t have a 2-in-10 chance of taking off and having at least one quit, the probability is slightly lower. We have a 1-(9/10)^2 chance of having at least one engine quit. Calculating, this becomes a 1 – (81/100) chance of having at least one quit on takeoff, which is a 19/100ths chance of having at least one quit (which is a slightly lower probability than 2 in 10. That isn’t to say that “double the chance of failure in a twin” isn’t a fair approximation, of course!)

Similarly if we had a 10 engined aircraft with these 1-in-10 chance of quitting engines, many would assume this means you’re certain to suffer at least one failure on takeoff, after all, 1 in 10 chance and ten engines… but this isn’t so. The probability of at least one stopping on takeoff is only around 63% (and indeed you can prove that for any given 1 in X chance where you have X independent events (and each engine on the plane here is considered an independent event), as X approaches infinity the chance of at least one in whatever event it is happening will be around 63%. To prove this calculate lim x→infinity 1-(1/x)^x. Indeed for any probability smaller than 1 in 5, for a 1 in x chance and attempting x times, the probability will be between 68% and 63%, tending towards 63% as x gets larger.

Last Edited by alioth at 20 Apr 13:39
Andreas IOM

I think the engine failures are not idependent, and likely have some reasonable amount of positive correlation:
- bad maintenance
- design issue
- maintenance not done
- wrong fuel
- not enough fuel
- bird flock

and so on

DELETED.
I wrote nonsense :-)

Last Edited by Coolhand at 20 Apr 15:19
LECU - Madrid, Spain

DELETED (no longer relevant)

Last Edited by Noe at 20 Apr 15:24

@Coolhand,

Not so. Following your logic, if you have a 50% chance (1/2) of an engine failing, you would have an engine failure EVERY take-off (1/2 + 1/2 = 1).

The probability of AT LEAST one engine failing really is 1 – (1/2)^2 = 1 – 1/4 = 75% in that case. Basic statistics.

25% – all goes well
50% – a single engine fails
25% – both engines fail

Biggin Hill

Ok, ok, you were faster replying than me deleting

LECU - Madrid, Spain

@Coolhand,

too late… si tacuisses…

:-D

Mind you, a few days ago I used ^2, not ^3 to calculate the mass of a scale model spitfire, an error of similar entertainment value.

Last Edited by Cobalt at 20 Apr 15:24
Biggin Hill

…it takes the unique community of the forum to introduce Boethius to GA

Oxford (EGTK)

172driver wrote:

Agreed, but it has happened on type before – here

The Navahoe is an Avgas type however…. I’d be hard pressed to find a condition when Jet A1 blows up like that.

LSZH, Switzerland

Mooney_Driver wrote:

I’d be hard pressed to find a condition when Jet A1 blows up like that.

There is one single case I am aware of, where an inflight explosion was most probably caused by an air-fuel mixture in an empty tank ignited by sparks from a defective cable: https://en.wikipedia.org/wiki/TWA_Flight_800

EDDS - Stuttgart
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