Reliability evaluation is crucial in assessing the power supply capacity and guiding the planning and operation of the distribution system. Traditional analytical reliability evaluation usually assumes a constant failure rate for components, implying that the life distribution follows an exponential distribution. However, in reality, the failure rate of components varies over time due to external disturbances and aging. As a result, traditional analytical reliability evaluation methods are no longer applicable. To address this issue, this paper presents an analytical method for evaluating the reliability of the distribution system with time-varying failure rates. The method considers short-term and long-term time-varying failure rates using density evolution and non-homogeneous Poisson process techniques, respectively. Both steady-state and instantaneous indices are calculated to reflect the level of system reliability. Finally, the proposed method is applied to the IEEE RBTS Bus 6 test system, demonstrating its correctness and efficiency.