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In distribution system planning and operation, accurate assessment of reliability performance is essential for making informed decisions. Also, performance-based regulation, accompanied by quality regulation, increases the need to understand and quantify differences in reliability performance between networks. Distribution system reliability performance indices exhibit stochastic behavior due to the impact of severe weather. In this paper, a new reliability model is presented which incorporates the stochastic nature of the severe weather intensity and duration to model variations in failure rate and restoration time. The model considers the impact of high winds and lightning and can be expanded to account for more types of severe weather. Furthermore, the modeling approach considers when severe weather is likely to occur during the year by using a nonhomogeneous Poisson process (NHPP). The proposed model is validated and applied to a test system to estimate reliability indices. Results show that the stochasticity in weather has a great impact on the variance in the reliability indices.