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Old 31st Dec 2007, 14:09
  #44 (permalink)  
PBL
 
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Well, let's try some *very* crude estimates to give people an idea of what they can conclude without even leaving the armchair to look up the systems. And let me estimate without leaving *my* armchair to go look anything up.

Malinge told the CPI that the A320 family had accumulated about 60 million flight hours.

There have been dual hydraulic failures. Let's suppose there have been 60 of them to make the arithmetic easy. That makes one dual-failure in 1 million flight hours.

Suppose in each of these cases the two systems failed independently. We can take the posterior reliability of each, the MTBF to be 1,000 hours (1,000 x 1,000 = 1 million).

So what is the expected MTBF for three systems? 1,000 x 1,000 x 1,000 = 10^9 hours. So we can expect another
940 million flight hours to go before seeing one.

60 million under the belt, 940 million to go. How many hours a year does an A320 fly, and how many of them are
there? Well, they have been in service 19 years. Let us assume a constant rate of production, x aircraft per year, and that all of them carry on flying for ever at identical levels, say y hours per year. Then there will be xy hours
flown in the first year, 2xy in the second year, 3xy in the
third year, and so on. And we know
xy + 2xy + 3xy + ..... + 19xy = 60 million.

xy + 2xy + ..... +19xy = xy(1 + 2 + 3 + ... + 19) = xy.190 = 60 million

So xy = about 316,000.

Now we want to know how many years it is going to be before the fleet accumulates 1 billion hours. We want to
solve for n in
316,000(1 + 2 + 3 + .... + n) = 1,000,000,000

That is, (1 + 2 + .... + n) = about 3,165.

Now, (1 + 2 + .... + n) = n.(n+1)/2 so we want to solve for
n where n.(n+1) = 6,330. Now, n.(n+1) is a little over n^2, so let's just take the square root of 6,330, say of 6,400, which is about 80 (since 8^2 = 64). So we are round about 80 years of service life before we expect to see a triple failure, and we have had 20 years already, so we can expect another 60 years without one. Don't explain that plane to be flying in line service in 60 years.

All that without leaving the armchair to get a calculator!

Now, about those dual failures. There are, as has been mentioned, dual failures with common cause, namely concerning the PTU. The third system is independent of this common cause, so assuming all failures (including dual failures) are independent is a conservative assumption.

The only non-conservative assumption I see in this is that A320 family aircraft are not produced at a constant rate per year since service intro, but at an increasing rate. However, look at one of the other assumptions. Is is *really* true that one loses one hydraulic system every one thousand flight hours in an A320? I don't think so, I think it is *much, much* more rarely than this. That more than makes up for any increased production rate.

As NoD and T-t-o have said, don't expect the sim, even the Iron Bird, to accurately portray what's going to happen for real in this scenario, for the reasons they have mentioned.

PBL
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