Legion World Forums LEGION OUTPOST Mission Monitor Board Tamper Lad Geeks Out

So I read a Reuters story about Engineers calculating the chance of tsunami damaging the Fukushima Nuclear plant being 10%.

http://www.reuters.com/article/2011/03/29/us-japa-nuclear-risks-idUSTRE72S2UA20110329

I was chatting with a pro-nuclear colleague who scoffed at such a high probability, because "tsunamis only happen once every 1000 years". After all this was the biggest ever recorded earthquake in Japan.

Intuitively the number seemed correct based on what I remember of Stats classes. So I typed a few numbers into Excel to show it.

Let's assume:
1.Tsunami big enough to go over the breakwaters and damage the power plant happen every 500 years.
2.The waiting times for tsunami is well modelled by the Poisson Distribution http://en.wikipedia.org/wiki/Poisson_process
3.The lifetime of the powerplant is 50 years

So given that information, we have lambda = 1/500 = 0.002

We want to find the probability that exactly no tsunamis P(0) occur in a given year. We substitute this into the Poisson Distribution Equation:

P(x) = lambda * x! / e^-(lambda)

or in English

The probability of x occurrances = lambda multiplied by x occurrances factorial all divided by Euler's number raised to the power of negative lambda.

So in our case, the probability that no tsunamis big enough to damage the plant happen in any given year is:

P(0) = 0.002 * 0! / e^ -0.002

= 99.8002%

So the chance of no disaster in a given year is 99.8002%. Inversely the chance of one or more tsunami in a year is 0.1998%.

Small right????

Seems like it, but we have to remember that the plant has a lifetime of 50 years. So for a disaster free nuclear plant lifetime we need no occurrances in all 50 years.

This is calculated using the binomial distribution subsituting for a series of 50 trials. Where we want the Probability of 0 disasters, the P(disaster) in each trial is 0.1998%. http://en.wikipedia.org/wiki/Binomial_distribution

Plugging the numbers into the spreadsheet function, Excel spits out a probability that over the life of the plant we have a 90.4837% chance of having no tsunami hits. Once again subtracting this value from 100% gives us the probability of one or more tsunami hitting the plant over 50 years.

So the chance we have a once every 500 year tsunami hit and damage a plant on the seaside in Fukushima is indeed 9.5163% or close to 10%

Tamper, let yo' geek freak fly, mon frere.

Agrees with Tamper. (just nod your heads everyone...)

TL .... be a dear and put that all in layman's terms for me would ya? That-a-boy, thanks!

Dems mahty beeg words, man. I ain't be understandin' it, but, like i always did wit mah prefessers, if ya can't do it, fake it impressively and baffle em' wit bull$#!+ !




Seriously, big stuff. Past my abilities.

Tamper Lad, are you sure you don't have any Coluan blood?

You took the words right out of my mouth sister!

I always knew there was some reason he's stuck with the same avatar for six years and counting.

We need more Tamper Lad on Legion World.

In English, it says that even something that happens once every 500 years has a 10% chance of damaging a nuclear power plant over its operating lifetime.

So you'd better be prepared for it. Imagine the implication for nuclear waste, which has a lifetime of 1 million years.

Murphy's law: whatever can go wrong will go wrong.

codicil to Murphy's law: whatever can go wrong will go wrong... at the worst possible time.

Which makes sense when dealing with man made events. Most people are at their worst during times of stress, which is usually the easy definition in most people's minds of "worst possible time". therefore, law of averages says that people will perform their worst when it counts most.

makes sense to me.

" "
pfffft!

no no, its okay... take your time. we'll wait. You'll get it.

But...I.....
How ....... ?
And then? .....


AWWWWW ferget it!!!!

Backatcher