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Where Did That Number Come From?

I hadn't seen this before. Mike Griffin is claiming that extending Shuttle will dramatically reduce its reliability:

In April this year, he told a Senate panel: "If one were to do as some have suggested and fly the shuttle for an additional five years -- say, two missions a year -- the risk would be about one in 12 that we would lose another crew. That's a high risk ..... [one] I would not choose to accept on behalf of our astronauts."

So he's saying that each of those flights has a probability of success of 99.1% (about one in a hundred chance of losing the vehicle). That's the number that, when taken to the tenth power (the number of flights) comes out to a 92% probability of not losing a vehicle. 99% is slightly better than historical record, based on the two losses of Challenger and Columbia, but I would expect after all the money they spent on resolving foam and other issues that they should have a much safer vehicle now (probably the safest it's ever been). Is he assuming some kind of reduction in reliability as the system ages or we can't replace parts over that fiveyear period? I'm curious to know how they came up with it.

bbbeard wrote:

I would wager that someone has calculated for him the operating curve for the (2, 123) sampling plan [there having been 2 failures out of 123 flights]. And he is taking the best possible (minimum) failure rate based on historical experience, with a constraint of having no more than 10% producer risk. [psst... a lot of Constellation requirements are written in this kind of language, using consumer risk instead of producer risk.]

Try this: open Excel and type in the following formula:

=BINOMDIST(2,123,0.9%,TRUE)

and you should get a return value of 90%. The 90% is the complement of the producer risk.

So, using just flight experience as a guide, it is unlikely that the reliability of the shuttle is better than an 0.9% failure rate. As you figured out, that adds up to trouble over a number of years.

And that's being optimistic. The 10% consumer risk estimate of the failure rate is 4.27% per flight.

From his standpoint, this argument is sound. He's not assuming reliability degradation -- he's assuming that 2 failures out of 123 flights is a sample. Which it is, albeit with a broad 10-90 confidence band. OTOH, what you are suggesting is that the numbers be fudged to reflect some kind of golden wisdom we've achieved over the years now that we've solved the foam and O-ring problems. Although I'm mildly sympathetic, I wouldn't be able to defend your logic in front of an inquisitor.

Edward Wright wrote:

From his standpoint, this argument is sound. He's not assuming reliability degradation -- he's assuming that 2 failures out of 123 flights is a sample. Which it is, albeit with a broad 10-90 confidence band.

Except that Griffin considered that risk perfectly acceptable up to now -- otherwise, he would not have been flying the Shuttle up to now. If the risk hasn't increased, how has it suddenly become "unacceptably" high?

Also, there's the fact that Orion is not likely to be significantly safer than the Shuttle. In fact, the program risk will be much greater. Unlike ISS, the Moon program won't have Progress, Soyuz, etc. as a backup. If there's a failure of any one component -- Ares, Orion, the lunar transfer stage, the lunar lander -- the whole program will come crashing down like a house of cards.

Yet, the man who says it would be "irresponsible" to allow private enterprise in "the critical path" (since private enterprise is allegedly so much less reliable than socialist enterprise) sees nothing wrong with accepting those risks in his program.

bbbeard wrote:

Ed W wrote:

Except that Griffin considered that risk perfectly acceptable up to now -- otherwise, he would not have been flying the Shuttle up to now. If the risk hasn't increased, how has it suddenly become "unacceptably" high?

I would guess for the same reason that accident rates for fighter aircraft in the 1950's became unacceptable by the 1970's -- and wholly out of line by the 1980's. Yet we still let ANG units fly Thuds until enough F-16s could come off the assembly line to replace them.

And I dispute your characterization of the Ares I/Orion reliability.

BBB

Edward Wright wrote:

I would guess for the same reason that accident rates for fighter aircraft in the 1950's became unacceptable by the 1970's -- and wholly out of line by the 1980's. Yet we still let ANG units fly Thuds until enough F-16s could come off the assembly line to replace them.

That argument might make sense if Griffin were talking about replacing the Shuttle with a more modern design, but he isn't.

Fighter aircraft in 1950's were not remotely as dangerous as Apollo/Shuttle/Orion. To find comparable accident rates for aircraft you need to go back before 1908.

We tolerated the risks because the USAF helps protect the national security of the United States. ISS does nothing to protect the United States, no matter what Griffin says.

Besides, the F-105 was retired to replace it with a better aircraft -- not to build a "Brewster Buffalo on Steroids." If someone had proposed replacing the F-105 with a less capable aircraft that was at least as dangerous and more expensive to operate, they wouldn't have bothered.

And I dispute your characterization of the Ares I/Orion reliability.

You can dispute gravity, too. The facts don't change just because the Keep Space Expensive crowd disputes them.

The US, Russia, China, ESA, etc. have spent hundreds of billions on expendable rockets. None of them have ever been safer than the Shuttle. It's naive to assume that the next one will.

bbbeard wrote:

Ed W wrote:

You can dispute gravity, too. The facts don't change just because the Keep Space Expensive crowd disputes them.

Well, opinions are why we have horse races and elections, I guess. Nonetheless, I know a bit about gravity and a bit about Ares, having worked on both, so I feel confident in ignoring you.

Edward Wright wrote:

Nonetheless, I know a bit about gravity and a bit about Ares, having worked on both

You worked on gravity?

That makes you what, 17 billion years old? :-)

I can believe you worked on Ares, given your Alfred E. Neuman attitude toward safety. That's the scary thing. I think some of you guys actually believe your marketing hype.

bbbeard wrote:

Ed W wrote:

You worked on gravity? That makes you what, 17 billion years old? :-)

No, silly ;-)

It means I took classical field theory in grad school. So I know my way around a Christoffel symbol.

BBB

Karl Hallowell wrote:

BBB, no offense, but my take is that there's not enough experience in the world much less NASA to promise loss of mission (LOM) numbers better than the Space Shuttle (OTOH, loss of crew (LOC) can be made significantly better, at least for launch). The ESAS LOM numbers are a moderate fantasy.

As I see it, any rocket produced by NASA, or for that matter any other collection of rocketry and relevant manufacture experts on the planet will product rockets that fail on the order of 1/N (a crude approximation) where N is the number of launches of the vehicle in question over its lifetime. For Ares I, N is somewhere around 100. That puts LOM at around 1 in 100 just like the Shuttle. I wouldn't be surprised, if the thrust oscillation mitigation effort weakens that safety number a little too.

bbbeard wrote:

KH wrote:

As I see it, any rocket produced by NASA, or for that matter any other collection of rocketry and relevant manufacture experts on the planet will product rockets that fail on the order of 1/N (a crude approximation) where N is the number of launches of the vehicle in question over its lifetime.

I'd like to say that's provably wrong, but on second thought, it is merely incoherent. Consider Blue Streak, an early British ICBM that went three strikes and then out, i.e. its failure rate was N/N=1, not 1/N [its successor, Europa, was also a miserable performer]. Consider SpaceX's Falcon I. At this point its failure rate is also N/N=1, not 1/N. Consider the Atlas family. In its first 300 launches, there were 256 successes and 44 failures, so the failure rate was 44/300, not 1/300.

So frankly, your reasoning is impaired.

G2G-MDR [got to go - must design rocket]