–By way of answer, let’s start with an anecdote:
There is an apocryphal story about Frederick Mosteller, a famous professor of statistics at Harvard University. Sometime in the 1950s, a student of Mosteller´s was unconvinced that a six-sided die had a precise 1/6 chance of landing on any of its six sides, so he collected a bunch of (cheap) dice and tossed them a few thousand times to test his professor´s theory… Evidently, according to said (bored) student the numbers five and six appeared more frequently than the numbers one through four. Professor Mosteller´s unsurprising response was that the student had not tossed the dice enough times. ‘Rest assumed’, the student was told, the law of large numbers would ‘kick in’ and everything would (eventually) converge to 1/6. Undeterred, the student continued rolling a few thousand more times, but the fives and sixes were still showing up way too frequently. Something fishy was afoot. It turns out that the observed frequencies were not quite 1/6 because the holes bored into dice – to represent the numbers themselves – shift the centers of gravity toward the smaller numbers, which are opposite the numbers five and six. Ergo, the two highest numbers were observed with greater frequency.https://cpes.org.uk/wp-content/uploads/2016/06/stefan_voss_paper.pdf
In other words, it takes a very great deal of work to undertake a randomized control experiment, if only because the “control” is so misleading in the real world. As so many have pointed out before, there is always something uncontrolled/uncontrollable that intervenes significantly between treatment and measurement.
–This means, minimally, that the reason why there haven’t been more nuclear accidents (given their complex and unpredictably interactive technologies) is not because “we haven’t waited long enough.” It’s far more likely other reasons are at work.
One such reason is that the plants have been managed beyond their technologies. They are managed more reliably than theory predicts precisely because of the next failure ahead–that is, precisely because there are no guarantees.