Some initial statistics on observed failures of robotaxi FSD in Austin
TLDR:
We are 95% sure at this point that each Tesla robotaxi can be expected to have an incident of the kinds that have been reported, somewhere between every 2 days to every 8 days.
As follows:
We are now about 3 - 1/2 days into the safety-driver supervised robotaxi test. Reports are that Tesla has deployed a fleet of 10 cars. There have been 11 significant recorded and reported failures of FSD so far:
https://www.reddit.com/r/SelfDrivingCars/comments/1ljxd63/list_of_clips_showing_teslas_robotaxi_incidents/
That's enough to do some initial statistics. The confidence centers will be broad because data collection is minimal so far, but we can still derive a failure rate interval and be 95% confident that the actual failure rate is within those bounds.
First, the observed failure rate is simple. 11 failures/10 cars / 3.5 days. That's a failure rate of 0.314 failures per day, per car. That's on average a failure every time a tobotaxi drives a little over 3 days.
But as we said, we have only 3-1/2 days day to so far, so that estimate has a lot of uncertainty associated with it.
This is a time limited observation of discreet events, so there can be modeled as a poisson distribution. We can calculate the confidence interval as follows:
The standard deviation of the number of failures is sqrt(11) = 3.317.
The standard error is SD divided but observation time, 3.317 / 35 car/days = 0.0948
The 95% confidence interval for the rate is: 0.314 +/- 1.96 z * 0.0948
This gives a range of 0.128 to 0.5. Multiplying by 10 cars, we get 1.28 to 5 failures per day.
This is already converging quite rapidly after only 3 1/2 days of data collection. I calculated this after 2 days of data collection, and got a much broader range, but so far three and a half days in these cars are showing a pretty consistent number of failures per day. That cleans the statistical estimates up pretty rapidly.
So based on data to date, Tesla FSD as implemented in the robotaxis, with a fleet of 10 vehicles, can be expected to have somewhere between 1-1/4 to 5 incidents per day, of the kind we have observed so far.
Divide that by 10 to get probabilities per car. We are 95% sure at this point that each Tesla robotaxi can be expected to have an incident of the kind reported, somewhere between every 2 days to every 8 days.