Bones was right about the transporter
Star Trek canon records at least 11 transporter accidents:
* Splitting Kirk into good and evil halves (TOS: The Enemy Within)
* Transport to the mirror universe (TOS: Mirror, Mirror) --- not counting later deliberate action
* Transport to another universe (TOS: The Tholian Web)
* Two deaths in Star Trek: The Motion Picture
* Weyoun 5 dies in DS9: Treachery, Faith, and the Great River
* Clone of Riker (TNG: Second Chances)
* Reverting four individuals to younger versions of themselves (TNG: Rascals)
* Travel through time (DS9, Past Tense)
* Merging multiple individuals (VOY, Tuvix)
* Damaging the holographic doctor's mobile emitter (VOY, Drone)
* Rendering two crew members incorporeal (TNG, The Next Phase)
To calculate a malfunction rate, we need some estimate of how many times the transporter was used in total during this period. There are 79 TOS episodes, 178 TNG episodes, 176 DS9 episodes, and 172 VOY expisodes. That gives 605 episodes. If we generously estimate 4 transports per episode that gives a failure rate of 0.4%, unacceptably high.
Transporters appear to be able to cross planetary distances easily (no waiting for proper orbital alignment.) An estimate of 25,000 miles per transport --- that is, assuming starships are usually in high orbit --- and 6 people at a time gives an accident rate of around 30 per billion passenger-miles. Modern cars and light trucks have a fatality risk of 7.3 per billion passenger-miles. (However, it should be noted that many of the transporter accidents were reversible or otherwise non-fatal.)
* Splitting Kirk into good and evil halves (TOS: The Enemy Within)
* Transport to the mirror universe (TOS: Mirror, Mirror) --- not counting later deliberate action
* Transport to another universe (TOS: The Tholian Web)
* Two deaths in Star Trek: The Motion Picture
* Weyoun 5 dies in DS9: Treachery, Faith, and the Great River
* Clone of Riker (TNG: Second Chances)
* Reverting four individuals to younger versions of themselves (TNG: Rascals)
* Travel through time (DS9, Past Tense)
* Merging multiple individuals (VOY, Tuvix)
* Damaging the holographic doctor's mobile emitter (VOY, Drone)
* Rendering two crew members incorporeal (TNG, The Next Phase)
To calculate a malfunction rate, we need some estimate of how many times the transporter was used in total during this period. There are 79 TOS episodes, 178 TNG episodes, 176 DS9 episodes, and 172 VOY expisodes. That gives 605 episodes. If we generously estimate 4 transports per episode that gives a failure rate of 0.4%, unacceptably high.
Transporters appear to be able to cross planetary distances easily (no waiting for proper orbital alignment.) An estimate of 25,000 miles per transport --- that is, assuming starships are usually in high orbit --- and 6 people at a time gives an accident rate of around 30 per billion passenger-miles. Modern cars and light trucks have a fatality risk of 7.3 per billion passenger-miles. (However, it should be noted that many of the transporter accidents were reversible or otherwise non-fatal.)