Re: A3XX vs B747-600 (was: Airbus lawsuit coming?)

Date:         13 Nov 96 02:41:21 
From:         Bard.Venas@termo.unit.no
Organization: The Norwegian University of Science and Technology
References:   1 2 3 4 5 6
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In <airliners.1996.2345@ohare.Chicago.COM>, Patrick.Petit@cern.ch (Patrick PETIT) writes:
>In article <airliners.1996.2257@ohare.Chicago.COM>, rickydik@ix.netcom.com
>says...
>>There may be more A320's built than Comets, but the A320 may still have
>>a worse accident record, which at one time was the worst since the
>>beginning of the jet age.
>
>Statistics from Boeing:
>
>Accidents rate (per million of flights between 1958 and 1993)
>
>Comet  9.63
>B707  6.14
>DC8  5.49
>Trident 5.00
>DC10 2.67
>A320 2.50
>B747 -1/2/300 1.71
>DC9 1.18
>B737 -1/200 1.15
>A300 .98
>B727 .87
>A310 .64
>

It would have been interesting to know the actual number of flights the
statistics are based on also. I have some basic engineering knowledge of
statistics and this made me try to figure out how significant the
differences cited above really are.

Say the probability of an accident is one in a million (P=1e-6).
This leads to a probability of s number of accidents during N flights
to be described by a "binominal distribution"

Prob{accidents=s) = P^s * exp(-P*N) * N^s / s!

as long as N is much larger than s  :-). s! is the faculty
of s (=1*2*...*s).

The Boeing home page says that the 737 has some 60million flights,
the distribution above then leeds it to be 90% probable that the
number of accidents should have been between 50 and 70 if the
accident rate in fact is one to a million - leading to an accident
rate between 0.83 and 1.16. Thus a rather uncertain number even
after 60 million flights!

I don't know how many flights e.g. the A320 had in 1993, but
to show the point say a relatively new aircraft has 800.000 flights
and the same probability of accident (P=1e-6) it would then be

36% likelihood of 0 accidents                0 per million
36% likelihood of 1 accidents                1.25 per million
14% likelihood of 2 accidents                2.5 per million
14% likelihood of more than 2 accidents     .....

This isn't ment to be a pro or con anything, only to say that when
discussing 'very low probability events' such as airliner accidents
one may need some more caution than simply dividing the number
who falls down by the number that went up ...

Regards

Bard Venas
Department of Mechanics, Thermo and Fluid Dynamics
Norwegian University of Science and Technology
N-7034 Trondheim-NTNU, Norway