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The assessment of customer power quality & reliability is an important issue for future Smart Grid research in general and the operation and planning of distribution system in particular. Based on the failure modes and effects analysis framework (FMEA), the paper presents a non-sequential Monte-Carlo method (FMEA-NSMC) for distribution system reliability assessment considering sustained interruptions, momentary interruptions and voltage sags which are the main power disturbances involved in the operating continuity of customer equipments or processes. The deterministic and stochastic data are relatively independent in the framework of FMEA-NSMC. A case study is used to show the effectiveness of the method where different indices chosen for the convergence test are checked. The convergence speed is faster when the coefficient of variation (CV) of the frequency index of sags is chosen for the convergence test than CV of the frequency index of sustained interruptions, and also than CV of the frequency index of momentary interruptions.