Ninety-minute-delay is the new qualifier for rail transportation ticket refund in Taiwan. In order to study the quality of service of railway operations, this paper investigates the probability and duration of delay by stochastic simulation technique for a train, a section, and a whole operation plan, as well as for a specific time period or a whole day. As a result, the total delay or reliability of a railway timetable can be tested in advance of its real world operations.