[kharms]

We have some idea of a crash rate for safe airplanes. Something like: P(Crash|Miles Flow & Hull Age)

If we assume this airplane is safe, we can apply that probability to it and then ask P(2 Crashes|N Miles & 350 New Planes).

You would then have a probability for this just being bad luck, and compare that against your prior that this is a safe plane.

I haven’t done the math, but my gut says it would point to grounding the plane.

[bjourne]

According to https://en.wikipedia.org/wiki/Aviation_safety#Evolution the fatal accidents per million flights were 0.39 in 2018.

The MAX8 fleet has been operational for about six months. Assuming 3 flights per day: 350 * 6 * 30 * 3 = 0.189 million flights.

To estimate the probability of two accidents, we can use a Poisson distribution with x = 2 and μ = 0.189 * 0.39 = 0.0737

P(x=2) = e^(-μ)μ^x / x! = 0.25%

I.e your gut feeling is correct (if my math is correct, that is). If one uses the estimate from a sibling comment of 1 crash in 11 million fights, the probability decreases further to 0.01% Actually the correct calculation is:

1 - P(x=0) - P(x=1) = 0.26%

since we are looking for the probability of there being more than one plane crash -- not just the probability of there being exactly two plane crashes.

[DuskStar]

Might also be worth considering P(2 Crashes | N Miles across 350 planes where at least one operator has incompetent maintenance), because that might not be all that different from P(1 crash | N Miles across 350 planes where all operators properly maintain their planes)

Look at things like Alaska Airlines Flight 261 [0] - safe airframe, deficient maintenance, plane loses all pitch control and impacts ocean. Yes, this still means that Boeing needs to improve things - single points of failures are never OK on a plane - but it also doesn't (IMO) mean the plane is fundamentally unsafe without those fixes.

0: https://en.wikipedia.org/wiki/Alaska_Airlines_Flight_261

[wikiwawa]

The mean of a Beta Distribution (2, 348) (https://www.wolframalpha.com/input/?i=beta+distribution+(2,+...) is roughly half a percent, much higher than the 1 in 11 million across all flights (https://www.quora.com/What-is-the-probability-for-an-airplan...).

(You can pretty much always make statistical inference, with uncertainty going up with the lack of data)

[DuskStar]

I highly doubt there have been 11 million airliners manufactured, though - and that's what the 348 number is.

If we assume that the average MAX 8 has been in service for a year (first delivery was a little less than 2 years ago), and conducts 4 flights a day, we get this [0] - a mean of 1/250000. Still worse than 1/11000000, but only by a factor of 50 instead of 50 thousand.

0: https://www.wolframalpha.com/input/?x=0&y=0&i=beta+distribut...

[wikiwawa]

Good point, I was wondering why I was off orders of magnitude.

[Retric]

Depends on your assumptions, but safe aircraft will crash making the first data point meaningless as you are choosing it at the starting point. Second, you are not just running one trial on one design but many trails on many designs.

I suggest you try the math as the odds are reasonably high.

This changes if you start talking about crashes since the first commercial flight, but those are again different numbers.

[hexane360]

>I haven’t done the math, but my gut says it would point to grounding the plane.

"Guts" are notoriously good at statistical inference