From an interview with Ed Mango, head of NASA’s commercial crew program, in which he discusses safety requirements for commercial entities who want to subcontract flights to the ISS from NASA.

Chaikin: And the probability of “loss of crew” has to be better than 1 in 1000?

Mango: Yes and no. What we’ve done is we’ve separated those into what you need for ascent and what you need for entry. For ascent it’s 1 in 500, and independently for entry it’s 1 in 500. We don’t want industry … to [interpret the 1-in-1,000 requirement] to say, “We’ve got a great ascent; we don’t need as much descent protection.” In reality we’ve got to protect the life of the crew all the time.

Now [the probability for] the mission itself is 1 in 270. That is an overall number. That’s loss of crew for the entire mission profile, including ascent, on-orbit, and entry. The thing that drives the 1 in 270 is really micrometeorites and orbital debris … whatever things that are in space that you can collide with. So that’s what drops that number down, because you’ve got to look at the 210 days, the fact that your heat shield or something might be exposed to whatever that debris is for that period of time. NASA looks at Loss of Vehicle the same as Loss of Crew. If the vehicle is damaged and it may not be detected prior to de-orbit, then you have loss of crew.

What does “yes” mean in the “yes and no” answer? Also, with a 1/500 probability of accident at takeoff and an independent 1/500 probability of accident at landing, we are already at a 1/250.2 probability of accident, so how do we get to 1/270 after adding accidents in mid-flight?

In not entirely unrelated news, a member of the board of Florida’s 3rd district took, and failed, the Florida Comprehensive Assessment Test (FCAT), a standardized test, as documented in two posts on the Washington Post blog.

Relevant quote:

“I won’t beat around the bush. The math section had 60 questions. I knew the answers to none of them, but managed to guess ten out of the 60 correctly. On the reading test, I got 62% . In our system, that’s a ‘D,’ and would get me a mandatory assignment to a double block of reading instruction.

“It seems to me something is seriously wrong. I have a bachelor of science degree, two masters degrees, and 15 credit hours toward a doctorate. I help oversee an organization with 22,000 employees and a $3 billion operations and capital budget, and am able to make sense of complex data related to those responsibilities….

Here is a sample of the math portion of the 10th grade FCAT, the most advanced one. Sample question: “An electrician charges a $45 fee to make a house call plus an hourly rate for labor. If the electrician works at one house for 3 hours and charges $145.50 for the job, what is the electrician’s hourly rate?” You can use a calculator.

I am not sure how appropriate “probability” is for measuring the risk of an event such “loss of crew”. It’s unlikely its a frequentist probability, or the fraction of times crew loss happens when a certain kind of space flight takes off, the frequency being measured over many experiments.

If its a Bayesian probability or a belief, then it is very dependent on the model, the prior and so on, and the numbers may change a lot depending on how you set the parameters. Without knowing the details, it is hard to say what is reasonable and what is not.

I think the easiest explanation for Mango’s flub is that he is trying to divide by two and just failing on the spot. He meant to say 1 in 2000 for ascent and 1 in 2000 for descent. The bizarre thing is his concern that industry will say “We’ve got a great ascent; we don’t need as much descent protection.”

As if having a 100% chance of ascending safely, and a 0% chance of descending safely would give you… a 50% chance of survival?

I love the “Independently for entry” part of this. I am not sure how you get independent events if the probability of the union of the two events is 0. (Unless somehow one can “lose” the crew twice!)

Paul, there is a perfectly sane way to think about them as independent events. One can certainly lose a crew twice–there is more than one spacecraft.

It would make sense to take the frequentist view, as the inverse of the mean time between accidents. A 1/270 probability of accident is rather low; the space shuttle had two accidents in 135 flights, on the 26th and 113th flight, suggesting a risk well above 1%.

There are (at least) two possible explanations for that board member failing the test.

a) The test is meaningless/too hard.

b) US academic degrees are worthless.

Choose your favorite.