The development of the smart distribution system results in wide installation of distribution terminal units into the distribution system, especially the installation of three remote terminal units that make switches controllable, which greatly affects the reliability of the distribution system. Distribution system reliability analysis method under different types of distribution automation scheme is especially important to accurately reflect the effect of distribution automation. This paper proposes a new method of distribution system reliability analysis with multiple distribution terminal units, which can directly locate the switch that decide the interruption duration of loads, so we can use its switching time as the fault isolation time. The method can reflect effects of different types of terminal units on distribution system reliability. Besides, the method processes controllable three remote units using shortest path algorithm in graph theory. The RBTS BUS 2 test system is used to prove the validity of the proposed method. The proposed method is intuitively clear, has low computational complexity and can meet the requirements of real engineering.