The Wall Street Journal had a great article over the weekend titled, "Near Misses are a Hit in Disaster Science." The article discussed how various industries study "near misses" - i.e. incidents which almost result in catastrophe, so as to gain a better understanding of the true probability of so-called low probability events.
While the article is very useful, it does not emphasize enough the most important value that an organization derives from studying near misses. I don't think the most valuable result is a better understanding of probability. I think the real value from near-miss examination and analysis comes from an understanding of the small problems, errors, and breakdowns that could result in a catastrophe. In a near miss, a redundancy in the system or an astute individual caught that small breakdown and prevented a catastrophic failure. However,a catastrophe was only narrowly averted in many instances. Examining the near miss carefully can help solve that problem or prevent that breakdown so that it doesn't occur again.
The key is that near-misses occur much more frequently than large-scale catastrophes. Thus, a true learning organization wants to surface and discuss near-misses, because you can learn and improve more frequently and more quickly, rather than waiting to conduct a lesson learned exercise after a terrible failure.