Originally Posted by wagathon
...Surely it must be intuitive that getting a flat at an inopportune time must present a far greater risk than a CF frame going post toastie under a rider, and that if you fall under the wheels of a bus or go over the side of a mountain, it doesn't matter what kind of frame your bike has...
You're right again, wag, but here, instead of talking carbon fiber specifically, we're talking about risk. In fact, risk has two parts - likelihood and severity. We'll call them "L" and "S." For general purposes L * S = Risk.
Let's look at severities first. Assuming your carbon fiber frame, fork, or handlebars fail while riding, I'd estimate that you have a 10% chance of no injury, a 40% chance of minor injury, a 40% chance of major injury, and a 10% chance of death. We could argue the percentages a bit, but they're probably ball park right.
Looking at likelihoods:
if you weigh A, your likelihood (over the service life of the carbon-fiber part) of a failure is B for the chart below:
A - B
150# or less - 0%
150-180# - 1%
180-220# - 2%
220-250# - 4%
250-300# - 25%
300-350# - 50%
350-up - 100%
Given these estimates, let's assume I weigh 275. The likelihood of failure (0.25) times the probability of a given severity (let's say death at 0.10) provide a risk (over the service life of the part) of 0.025 that I'll be killed if my carbon part fails.
I don't like those odds.
All of this fails to account for design of the part. If a part is designed with a large safety margin, then the likelihoods of failure change significantly (the severities, however, stay the same). The estimates provided above assume carbon fiber "racing" parts designed for light-weight racing riders. These wouldn't be accurate at all if we were looking at a heavy-duty, carbon-fiber cyclocross fork.
The bottom line is, provided you've selected the right part for your riding style and body weight, the risk declines significantly. If you're a serious Clydesdale and try to run high-buck carbon-fiber racing parts, you're playing roulette.