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This paper explores the internal mechanism of flight departure delay for the Delta Air Lines (IATA-Code: DL) from the viewpoint of statistical law. We roughly divide all of delay factors into two sorts: propagation factor (PF), and nonpropagation factors (NPF). From the statistical results, we find that the distribution of the flight departure delay caused by only NPF exhibits obvious power law (PL) feature, which can be explained by queuing model, while the original distribution of flight departure delay follows the shift power law (SPL). The mechanism of SPL distribution of flight departure delay is considered as the results of the aircraft queue for take-off due to the airports congestion and the propagation delay caused by late-arriving aircraft. Based on the above mechanism, we develop a specific measure for formulating flight planning from the perspective of mathematical statistics, which is easy to implement and reduces flight delays without increasing operational costs. We analyze the punctuality performance for 10 of the busiest and the highest delay ratio airports from 155 airports where DL took off and landed in the second half of 2017. Then, the scheduled turnaround time for all flights and the average scheduled turnaround time for all aircraft operated by DL has been counted. At last, the effectiveness and practicability of our method is verified by the flights operation data of the first half of 2018.