Monday, June 15, 2015

Validating the Strategy for Securing Oxygen Masks

I was on a 13 hour flight from Washington DC to Dubai UAE. The pre-flight speech included the standard line:

"In the event that the plane loses cabin pressure while at altitude, the oxygen masks will fall from the ceiling. If you are traveling with a child or someone who requires assistance, secure your oxygen mask first before helping others."

So I decided to take a few minutes out of the next 13 hours to determine if this advice would hold up under a mathematical analysis. The following table summarizes my findings.

Assumptions (for the purpose of this analysis)
1. The plane ultimately lands safely
2. Everyone who gets the mask on correctly will survive, and everyone who doesn't will die
3. There is one child seated next to you who needs assistance
4. Once someone starts working on a mask, they continue until success or failure of securing that mask
5. Without oxygen, you and the child will lose consciousness after the same amount of time
6. You have a 90% chance of getting your own mask on successfully
7. The child has a 10% chance of getting a mask on successfully
8. You have an 80% chance of getting the child's mask on successfully (either if you are already wearing a mask or not)

We can calculate the expected number of survivors using the probabilities shown above:

E[S] | You First = 2(.73) +1(.01) +1(.17) + 0(.09) = 1.64 survivors
E[S] | Assist Child First = 2(.72) +1(.08) +1(0.0) + 0(.20) = 1.52 survivors

So the advice they give you is correct, unless you value the child's life significantly more than your own.


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