The most serious incident is probably the partial meltdown at Three Mile Island. While it wasn't as serious as Chernobyl or Fukushima, "without incident" seems at best a stretch.
I think parent was referencing the nuke ships in the US Navy fleet, which have been without any known incident. I have no idea, however, if their production is comparable. OTOH, it seems harder to keep a mobile plant operating safely versus a stationary one.
The US Navy has 300+ reactors and has been operating them for decades without incident.