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Is it known whether probabilities of success vs failure (and specifically fatal failures) were estimated at the time for the Apollo XI mission? Or perhaps some current estimates?

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    $\begingroup$ My best current estimate for success of Apollo 11 is 100%. My second-best current estimate for success of Apollo 11 is 85.7%. I'm defining success as moon landing and return with no fatalities. $\endgroup$ – Russell Borogove Dec 12 '14 at 18:13
  • $\begingroup$ I got it. But, of course, by "current estimate" I mean the best "objective" estimation we would compute today based on all the data/facts available to a person before July 16, 1969. $\endgroup$ – leonbloy Dec 12 '14 at 20:19
  • $\begingroup$ It could have been done. MTBF for all components could have been estimated, and aggregated to provide an MTBF for the complete vehicle. I believe there was a statement that no single failure should compromise the mission, no two failures should compromise crew safety. That would have required an MTBF analysis to ensure mission goals could be met. A probability of success would fall out of that analysis. $\endgroup$ – Anthony X May 22 '17 at 1:21
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Neil Armstrong thought they had a 90% chance of survival, but only a 50-50 chance of landing on the first attempt. I've seen one source that says Aldrin was less optimistic, estimating 2/3 chance of survival and 1/3 chance of success. At that time, Apollo spacecraft had flown several missions safely, including two lunar orbit missions, so presumably he was worried about the landing proper.

I've seen multiple references to a "three nines" goal per mission for crew safety, and either 90% or 99% for mission success. Presumably they got to those reliability estimates "on paper" by the time Apollo 11 flew.

Both those numbers seem pretty optimistic to me. In the end, the Apollo flights from 11 on had a 100% safety rate and 85.7% mission success rate, and Apollo 11 was probably the riskiest of that series.

Here's an early-1965 QA report giving the then-current probabilities of success as 0.73 and safety as 0.96, and presumably they got those numbers up over the next four years.

However, the individual failures experienced on the actual Apollo missions generally fell into the "unknown unknowns" category of interactions between individually-reliable subsystems, so I feel like the actual chances could have been quite a bit worse than what the analysts might have calculated.

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    $\begingroup$ "Three nines" denoted extremely high quality in the 1960s. Nowadays, that's rather subpar. The modern standard is 99.99966% reliability (3.4 defective parts per million), the so-called six sigma level. (That's actually 4.5 sigma, not six. There's a reason for the downgrade from six to 4.5. Things fail as they age.) Complex systems that comprise many thousands of parts need that level of component reliability to have an overall system reliability that is anywhere close to what modern customers expect. $\endgroup$ – David Hammen Dec 13 '14 at 8:25
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    $\begingroup$ Well, it's important to keep in mind whether we're talking about reliability of parts, of subsystems, or of a complete craft. If your individual welds are six sigma, but a single weld failure out of ten thousand kills your crew, you're looking at only 97% safety. The huge number of components in a Saturn/Apollo mission had to individually be of high quality, and a lot of redundancy and fall-back capability was designed in. $\endgroup$ – Russell Borogove Dec 13 '14 at 19:22
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    $\begingroup$ One thing we learned about NASA from the investigation into the Challenger disaster is that, by the 1980s at least, they were making ridiculously optimistic assumptions about reliablity. Feynman's appendix to the Rogers Commission report points out that NASA management believed the shuttle had only a 1-in-100,000 failure probability, corresponding to launching one shuttle every day for 300 years and only losing one. So I'd definitely take the 73%/96% claim in the NASA tech report with a pinch of salt. $\endgroup$ – David Richerby Dec 14 '14 at 12:53
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    $\begingroup$ Feynman says that at the time of Challenger, working engineers estimated the shuttle as 99% safe while management underrated that risk by a factor of 1000. If you take Armstrong as a "working engineer" estimating Apollo 11 as 90% safe, and management underrates that risk by a factor of 100, you get the three-nines safety estimate. In the end, 2 of 135 shuttle flights were safety failures, for a 98.5% safety record - essentially the "working engineer" estimate. So it seems like management's "optimism factor" got 10 times worse between the Apollo era and Challenger. $\endgroup$ – Russell Borogove Dec 14 '14 at 17:42
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    $\begingroup$ 100% safety is defined as "all crew got home alive", not "all crew got home alive in all possible worlds." A13 was somewhat less crazy improvisation than it's been portrayed; LM as lifeboat had been explicitly planned for, for example. $\endgroup$ – Russell Borogove May 22 '17 at 15:07
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If the manufactured parts for the Apollo spacecraft had a .1% failure rate the mission would have certainly failed. There were over 6,000,000 parts used. At .1% failure rate 600 individual parts would have failed.

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    $\begingroup$ If this is a comment on the accepted answer's mention of "three nines", it is a) misplaced (answers need to answer the question, rather than engaging in back-and-forth with other answers) and b) based on a misunderstanding of the stated figure, which refers to the overall reliability, not that of any individual parts. $\endgroup$ – Nathan Tuggy May 22 '17 at 4:05

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