4 ms·

>If this is the 13th serious accident of a Tesla, it's unlikely that the probability is very low. I'm not sure you've followed the thread here...I don't think

by samman 13y ago

>If this is the 13th serious accident of a Tesla, it's unlikely that the probability is very low. I'm not sure you've followed the thread here...I don't think anyone's (accurately) saying that this is the 13th spontaneous battery accident. I'm pretty sure the other 12 are standard traffic accidents, of which this is the first to produce a battery fire. All in all, it seems a rather small sample size to make any kind of determination.

tedunangst 13y ago
Assuming that the normal rate of battery fires after collisions is one per million, the probability of observing such a fire after only 13 collisions is rather low. (Not impossible, just unlikely.) so perhaps the rate is not one per million. Doesn't mean it's one in thirteen, just not one in a million.
- 286c8cb04bda 13y ago
  If the chance of a catastrophic event happening is one-in-a-million, then it is equally likely to happen on the 13th and on the millionth coin toss. > Assuming that the normal rate of battery fires after collisions is one per million, the probability of observing such a fire after only 13 collisions is rather low. What you're arguing is that the probability of it happening on or before the 13th time is less than it happening on or before the millionth time -- Which is self-evidently true of _any_ probability, and is a much weaker argument. > perhaps the rate is not one per million This is much closer to the argument you should be making. I.e. "Given that a purported one-in-a-million event occurred after only the 13th test, what is the probability that their estimate of one-in-a-million is accurate?" (I don't know the math to answer that question, but I hope somebody that does will come along and chime in.)
  - chimeracoder 13y ago
    Time for some fun with binomial probabilities! Assuming I interpret the actual problem at hand correctly, this is how we formulate it statistically. We have an event that occurs with probability p = 1/1000000, given an accident (of which there were 13). The probability of having zero catastrophic events, given that we have observed 13 accidents, is (1-p)^13 = .99987 (For some real hair-raising fun, try this calculation with the success/failure rate of a typical condom.) Note that this is a purely frequentist interpretation and ignores any Bayesian inference (ie, we assigning a weight of 0 to our Bayesian prior, which is atypical). It's not a very robust way of modeling the situation, for a number of reasons.
    - tedunangst 13y ago
      I think the right test to apply is the Wilson test.
stonemetal 13y ago
http://what-if.xkcd.com/65/ http://what-if.xkcd.com/65/ Given this XKCD article, I would suggest the probability of a battery fire after an accident is around 1 in 26.
- ofthecaribbean 13y ago
  That estimate is a little bold: we can reject the hypothesis that the probability is smaller than 1/260 with p-value 0.05 (good confidence), but with your threshold of 1/26 the p-value becomes poor. Note that due to the lack of selection bias (battery fire was already among the top security concerns before the accident), we don't actually need a very stringent p-value, so we can be fairly confident that the probability is greater than 1/260. But my point was that even with probability 1/260, it's likely to be much higher than for gas cars, or you wouldn't have to dig up 20-year-old articles about "freak accidents".
  - DanBC 13y ago
    > But my point was that even with probability 1/260, it's likely to be much higher than for gas cars, or you wouldn't have to dig up 20-year-old articles about "freak accidents". Gas cars have electrical fires all the time. We don't read about it because it's not news. Admittedly, those cars tend to be poorly maintained, and not nearly new high end expensive vehicles.
    - jacquesm 13y ago
      Even new cars are not exempt. Electrical fires are often a total loss even if the car looks ok otherwise because of the way the wiring looms are embedded in the chassis.
philwelch 13y ago
If 1/13 car crashes resulted in the car bursting into flames, that car would be recalled.
- andrewtbham 13y ago
  What is the threshold for a recall?
abalone 13y ago
I'm not sure you've followed the thread. The previous poster claimed the sample size is sufficient: > Statistically, there have been fewer fatalities with Model S than the average for the number of miles driven Which of course it's not. But the general tone here of "move along nothing to see here" is transparently wishful thinking. Of course a battery fire after hitting some road debris after only a dozen accidents is something to be concerned about. Maybe we don't know just how much yet but no one should be dismissing it offhandedly.

by samman 13y ago

tedunangst 13y ago

Assuming that the normal rate of battery fires after collisions is one per million, the probability of observing such a fire after only 13 collisions is rather low. (Not impossible, just unlikely.) so perhaps the rate is not one per million. Doesn't mean it's one in thirteen, just not one in a million.

286c8cb04bda 13y ago
If the chance of a catastrophic event happening is one-in-a-million, then it is equally likely to happen on the 13th and on the millionth coin toss. > Assuming that the normal rate of battery fires after collisions is one per million, the probability of observing such a fire after only 13 collisions is rather low. What you're arguing is that the probability of it happening on or before the 13th time is less than it happening on or before the millionth time -- Which is self-evidently true of _any_ probability, and is a much weaker argument. > perhaps the rate is not one per million This is much closer to the argument you should be making. I.e. "Given that a purported one-in-a-million event occurred after only the 13th test, what is the probability that their estimate of one-in-a-million is accurate?" (I don't know the math to answer that question, but I hope somebody that does will come along and chime in.)
- chimeracoder 13y ago
  Time for some fun with binomial probabilities! Assuming I interpret the actual problem at hand correctly, this is how we formulate it statistically. We have an event that occurs with probability p = 1/1000000, given an accident (of which there were 13). The probability of having zero catastrophic events, given that we have observed 13 accidents, is (1-p)^13 = .99987 (For some real hair-raising fun, try this calculation with the success/failure rate of a typical condom.) Note that this is a purely frequentist interpretation and ignores any Bayesian inference (ie, we assigning a weight of 0 to our Bayesian prior, which is atypical). It's not a very robust way of modeling the situation, for a number of reasons.
  - tedunangst 13y ago
    I think the right test to apply is the Wilson test.

stonemetal 13y ago

http://what-if.xkcd.com/65/ http://what-if.xkcd.com/65/ Given this XKCD article, I would suggest the probability of a battery fire after an accident is around 1 in 26.

ofthecaribbean 13y ago
That estimate is a little bold: we can reject the hypothesis that the probability is smaller than 1/260 with p-value 0.05 (good confidence), but with your threshold of 1/26 the p-value becomes poor. Note that due to the lack of selection bias (battery fire was already among the top security concerns before the accident), we don't actually need a very stringent p-value, so we can be fairly confident that the probability is greater than 1/260. But my point was that even with probability 1/260, it's likely to be much higher than for gas cars, or you wouldn't have to dig up 20-year-old articles about "freak accidents".
- DanBC 13y ago
  > But my point was that even with probability 1/260, it's likely to be much higher than for gas cars, or you wouldn't have to dig up 20-year-old articles about "freak accidents". Gas cars have electrical fires all the time. We don't read about it because it's not news. Admittedly, those cars tend to be poorly maintained, and not nearly new high end expensive vehicles.
  - jacquesm 13y ago
    Even new cars are not exempt. Electrical fires are often a total loss even if the car looks ok otherwise because of the way the wiring looms are embedded in the chassis.

philwelch 13y ago

If 1/13 car crashes resulted in the car bursting into flames, that car would be recalled.

andrewtbham 13y ago
What is the threshold for a recall?

abalone 13y ago

I'm not sure you've followed the thread. The previous poster claimed the sample size is sufficient: > Statistically, there have been fewer fatalities with Model S than the average for the number of miles driven Which of course it's not. But the general tone here of "move along nothing to see here" is transparently wishful thinking. Of course a battery fire after hitting some road debris after only a dozen accidents is something to be concerned about. Maybe we don't know just how much yet but no one should be dismissing it offhandedly.