N is the number of meltdowns we can expect during Y, the total reactor-years until we shut down all fission reactors. To estimate N, Y is multiplied by the sum of all the risk-factors inside the parenthesis. We would like that total risk to be very, very small; if we plan to use fission as a bridge out of carbon, thus makng Y very big, we would like the total risk to be something like k × 10-macy's —a zero and a decimal with a Thanksgiving Day Parade of zeros trailing after, and all of the floats decorated with brightly colored zeros, then, at the very end, a small car full of klowns.
E is the probability, per reactor-year, of a catastrophic engineering failure—the chance that a properly built, maintained and operated nuclear power plant was unfortunately designed by a team of lunatics, and the design checked by an independent team of interior decorators who failed to notice that a giant propeller beanie, while certainly a brilliant use of space and color, is not a proper containment dome. We will set E to zero. As we shall see, it makes no difference.
G is the act of God factor. Any unforeseen circumstance, such as a 9.0 earthquake and a tsunami when you were expecting pizza and beer. Thanks to Fukushima, we can estimate G: As of December 30th, 2004, total reactor-years was 11,695. Since then @440 reactors, and two new reactors coming on line added @3,090 reactor-years so, rounding up a bit, G≅3/15,000 or 0.0002, but as we shall see, it does not matter.
H is human error—not a bad hair day, but someone saying, "Hey, let's see what this baby can do!" We can derive it from Chernobyl: H≅0.00007, but as we shall see, it does not matter.
S is the sociopathy factor, the probability that somewhere, sometime, swinish self-interest will overrule sanity, or cut one corner too many. It represents the number of sociopaths, on average, involved in the design, construction, and operation of nuclear power plants, weighted by their authority—their ability to do harm. For instance, a sociopath interior decorator might equal 0, while a sociopath CEO could equal 1,000 or more.
It might seem that S must be pretty small, since we've had only a few teensy incidents in all of the 15,000 reactor-years of nuclear plant operation. The trouble is, S varies by culture, and culture varies over time. A lot. So the past may not be a reliable predictor of the future.
Especially important is the number of sociopaths in positions of authority. Since the inception of nuclear power, average CEO pay has skyrocketed. In 2010, the CEO of GE received nearly $10,000,000 in "compensation." Chumming the water with money like that is not how you attract people who love the work (observe that they must be "compensated"). It is how you attract sharks. GE's chief bean-counter (who is paid to cut corners) was "compensated" even more. $14,000,000 is a lot of corner-cutting.
We can infer from the "so-far-we've only had four catastrophes" safety record of nuclear power that when we began to build our first nuclear power plants, most people in the industry were responsible and careful. But the companies involved weren't chumming the waters for sharks in those days. The USA™ of 2011 is a very different place. The USA™ of 2011 is a kleptocracy. In a kleptocracy, the majority of people in power are sociopaths. In a kleptocracy, S could be huge. Frankly, I think it less dangerous to build a nuclear power plant on top of a giant pile of banana peels than to build one in Bedrock, Kansas, USA™, circa 2011.
In a kleptocracy, S swamps every other risk factor, all of the preceding calculations become meaningless mathisms, and the Drat Equation reduces to
As the US continues to descend into kleptocracy, S will approach 1.0.
I would like to suggest to GE's CFO that a great deal of time, effort and, most-of-all, money could be saved if, instead of trying to shave another corner off the next Mark I, GE simply hired the Chinese to build a pool of radioactive slag. In that way, the Chinese could choose the location, and it would save the President of the United States an embarrassing phone call:
"…Well, we're not sure, but we think…Beijing…"
It's a win-win.
If we could leave the dratted S out of the equation, maybe we could use nuclear power for a short time to shut down coal plants while we transition to a renewable grid. But we cannot do that. Not in this country. Because this country is a kleptocracy, and in a kleptocracy you cannot leave the S out of any equation.
Of course, in a kleptocracy, the people don't get to decide whether nuclear power plants get built, or by whom, nor how long or safely they might be operated, so all of this has been an exercise in pure mathematics: Unlike the Drake Equation, the Drat Equation has no practical application.
On the bright side, as S approaches unity, reactors will be melting down faster than new ones can be built, so the end of nuclear power is in sight.