Monday, August 25, 2014

Mathematical Bummers and the American Canyon/Napa Earthquake

As Northern California cleans up from the American Canyon/Napa Earthquake of August 24th, 2014, I am reminded of a mathematical exercise I was asked to perform in my early years as an engineer with my former employer.

napa american canyon quake

The question posed by upper management was this:

Given estimated probabilities of an earthquake, grass fire, flood, etc... what is the probability in any given year that any of the natural disasters hit the factory.  For example, suppose estimates from the U.S. Geological Survey for the probability of natural disasters in any given year were as follows:

pearthquake = 5%
pgrass fire = 10%
pflood = 2%

What is the probability that any of these hit?

Well, if you multiplied the probabilities, you'd simply get the chance that all 3 of these natural disasters happen in the same year... so 5% * 10% * 2% is 1 in 1,000.

But that was not, "What is the probability that all of these hit in the same year?"  The question is what is the probability that any of them hit in the same year?

To get to the bottom of this, you simply ask yourself, "What is the probability that none of these things happen in any given year?"

the probability that no earthquake hits is 95%.
the probability that no grass fire hits is 90%.
the probability that no flood happens is 98%.

So the probability that none of these things happen is 95% * 90% * 98% = 83.8%

What's the probability that any one of these things happen? 16.2% a.k.a 1 in 6.

So we handed this answer into upper management and I wasn't in the room, but I was told that my director got scoffed at for presenting this figure.

It's been 13 or 14-years since I handed in that calculation and they've been rolling that dice every year.  Now that it's happened (I slept through it, "shaken, not stirred"), I feel a bit vindicated.

Why does this matter to Zymergi or our customers?  Well, it's the basics of bioreactor contamination probabilities.

If you add up the probabilities of your sterile envelope failures as well as your sterile operations failures, you end up with an N-sided dice that you roll each time you put up a production culture.  And if you've done the math, you realize it doesn't take that many low probability vulnerabilities before they add up.