In my European country if a train was running very late they could turn around the train some stops earlier, thereby not servicing the stations further down the track. Since the train would never arrive there it implied it also couldn't be late and thus it would not be counted in the statistics as such.

The rail company has a government-imposed punctuality target and their result is used in the calculation of how much money they get from the government the next year, i.e. the usual "once a KPI becomes a target..."