On: Satellite burns up following SpaceX rocket glitch

[aeontech]

You are mixing your terms I think. (2/4)^3 is the chances of the next launch also having a single engine failure.

The chances of a single engine failing in a launch based on these four launches should be 2/36, two engines failed out of 36 fired total.

So, assuming that a single engine failure does not increase failure chance of nearby engines (which is not true probably), and assuming past performance is indicator of future performance, and discounting all the test fires that they have done with the rocket, the formula should look more like the following:

Chances of any given 3 engines failing is the inverse of the chances of at least two engines failing at the same time.

Chances of at least two engines failing equals no engines failing + 1 engine failing + 2 engines failing

Based on current engine failure rate, that's (17/18)^9 + (1/18)^8 + C(9,2) * (1/18)^2 * (17/18)^7

where C(9,2) = 9!/(2! 7!) = 36

So that looks more like 98.88% chance of two or fewer engines failing, the converse of which is about 0.02% chance of a triple or more failure.

(math is not my strong suit, please correct me if I'm wrong, but #math on IRC thought this looked correct).

[ordinary → aeontech]

> Based on current engine failure rate, that's (17/18)^9 + (1/18)^8 + C(9,2) * (1/18)^2 * (17/18)^7

I think the second part of that calculation is incorrect. I'm getting:

  P(0 engine fail) = (17/18)^9 ~= 0.5978
  P(1 engine fail) = (17/18)^8 * (1/18) * C(9,1) ~= 0.3165
  P(2 engine fail) = (17/18)^7 * (1/18)^2 * C(9,2) ~= 0.0745

Adding those together gives:

  P(<=2 engine fail) = (17/18)^9  +  (17/18)^8 / 2  +  (17/18)^7 / 9 ~= 0.9888

That's the same answer you came up with, so I guess you have the correct calculation written down somewhere. Moving to 3 or more engine fails then gives:

  P(>=3 engine fail) = 1 - P(<=2 engine fail) ~= 0.0112

[aeontech → ordinary]

you're absolutely right, i was doing the final subtraction in my head and not paying attention...

[dbaupp → aeontech]

Not commenting on the correctness or otherwise of the rest, but 98.88 + 0.02 != 100. (You probably want 1.12% chance of triple or more failure.)

[aeontech → dbaupp]

d'oh! thanks :)

[codex → aeontech]

I believe this is correct. I had too few digits of precision in my original calculation; rounding is bad!