Thursday, June 7, 2007

The probabilities of shuttle launches

Running the numbers, NASA cleared the Shuttle Atlantis for launch tomorrow, subject to weather and unexpected delays of course. But the same facts told different ways tell different stories. For example, forecasters predict favorable weather with 70% probability, as there is a 30% chance of thunderstorms. These two pieces of information fit together well but paint very different pictures in one’s mind. Seventy percent favorable weather? A sunny day with some puffy clouds. Thirty percent thunderstorms? Quick, get indoors to avoid getting hit by lightning or hail!

Twenty-one years ago, on January 28, 1986, the Shuttle Challenger exploded just seventy-three seconds after takeoff, killing the entire crew. Subsequent analysis showed that when making their launch decision, Morton Thiokol and NASA engineers looked at the right numbers but came up with the wrong story. The engineers correctly chose to analyze a scatter diagram of O-ring failure frequencies by temperature. But their analysis was flawed: They performed a regression test on the data and found no statistical basis for unacceptable O-ring failure rates at 29 degrees Fahrenheit, the expected O-ring temperature at launch. If they instead had looked at the Bayesian probability of O-ring failure below 59 degrees, they would have realized there had been a 100% O-ring failure rate in past flights and thus would have decided not to launch.

Math is more than just the numbers. And a shuttle launch is more than just another flight. A lot is riding on it. I just hope that NASA has both its numbers and its stories right tomorrow.

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