I think most rail systems do this; it would be considered a reliability problem, not a punctuality problem.
You definitely have to be careful with the definition of these things, though. For instance, Irish Rail considers intercity rail to be on time if it's within 10 mins of schedule. Commuter is within five minutes of schedule. Given that, at peak times, some commuter services run once every ten minutes, and thus are ~always on time per this definition, it's wise to be a bit skeptical of the punctuality reporting.