This paper proposes a new method to assess the reliability of closed-ring grids by combining the total loss of continuity approach and the classical Monte Carlo simulation. The proposed method is called the Modified Monte Carlo Simulation (MMCS). The MMCS method is tested by Roy Billinton Test System (RBTS) Bus-2 and Bus-4 in three different scenarios: radial, open-ring, and closed-ring. Besides, the method proposed is applied to a real 6-bus closed-ring distribution system. The sensitivity analysis based on fuzzy logic is applied to determine the uncertainties associated with the reliability input data. It is shown that the MMCS method is appropriate to assess the reliability of both open-ring and closed-ring systems, and the sensitivity analysis is crucial to draw the real picture of reliability assessment, and an essential tool for power utilities to determine the most risk parameters that significantly deteriorate system reliability.