The nuclear genie appears to the public this week as a monstrous beast capable of terrifying an entire hemisphere as it renders a goodly portion of Japan uninhabitable. Setting aside the most hysterical comments, one finds a large number of questions regarding the placement and design of the reactor. Commentators suggest a criminal negligence by those in charge of governmental oversight and by the private design and construction companies. The truth is I suspect substantially more complicated than it appears at first glance. A discussion of risk management seems in order to clarify the process for those interested in a rational consideration of the enabling sequence of events.
Decision making under uncertainty centers on controlling the costs of risk regardless if the decision involves reaching for the boiling pan of water or building a nuclear power plant. Assuming a rational decision-maker, the process would involve generating a decision tree assigning probabilities and costs to specific choices and then selecting the preferred alternative.
The process begins, not with a problem statement, but with the choice of parties involved in the decision. Ideally, the final arbiter might be a diverse group of involved stakeholders, but more often it involves a governing agency (led by a politically appointed administrator and supported by public tax dollars) negotiating with a private entity within a politically charged arena. This might well have been the case for the nuclear reactor. It can easily be seen that more than one risk assessment is underway by each involved party and they all influence the primary choice even if not represented on the decision tree.
In terms of actually settling on a site, the private entity generates a tree that looks like this:
Tsunami
Earthquake
No Tsunami
BUILD
Tsunami
No Earthquake
No Tsunami
No Build ———
Then based upon “science” a risk for the earthquakes of various magnitudes is generated and a cost estimate for the design of a suitable reactor is calculated. The design may also account for a tsunami depending upon the estimated risks but this could also depend upon the industry or governmental oversight requirements. As part of the design/engineering process there will be negotiations before a preferred design alternative is selected and every single part of the project might be discussed from the likely maximum earthquake to the expected life-time of the reactor. The agreed upon standards might reflect short term political realities much more than the longer term uncertainties of science.
The final result might decide that the reactor would be designed to last 50 years and that according to the agreed upon science the likelihood of an earthquake greater than 7.0 is estimated to be 1:1,000 or 0.001* and the likelihood of a damaging tsunami would be 1:100 or 0.001 over the course of those 50 years. Further estimates would show that a critical meltdown would cause damage equal to X dollars and a tsunami would add Y dollars. Thus the final tree would look like this:
Tsunami (0.001 x 0.01) x Cost A
Earthquake
Build No Tsunami (0.001) x Cost B
Tsunami (essentially 0%) x Cost C
No Earthquake
No Tsunami (99.99999) x Cost D
You can clearly see that given the relatively low probability of an earthquake or an earthquake AND a tsunami decision-maker can accept quite a large amount of damage before the cost becomes an issue (i.e. more than the cost for no earthquake AND no tsunami). The chance of both events occurring over the course of the 50 years is 0.00001. Thus even a $1 billion dollar clean-up isn’t too terrible (note they’d also likely calculate the rate of inflation out over 50 years to account for present day value of future clean-up and this has its own set of issues).
The decision is additionally complicated by the estimated profits from the generation of electricity over the next 50 years which has its own set of assumptions regarding demand, other costs, and regulatory requirements.
What may not be immediately obvious is that there could very well be 4 earthquakes with tsunamis in a five year period because averages and estimates are just that. The tricky problem is as someone once said not “knowing what you don’t know”, but rather “not knowing what you don’t know”. So did they build a reactor and failed (as a group) to think through the possibilities or did they consider those possibilities to be so remote that failing to design for them was an acceptable risk?
*This number is pulled from thin air for the purpose of example only.
