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Results obtained from reliability assessment benefit many aspects of distribution planning and engineering and operations. A reliability assessment model quantifies reliability characteristics based on system topology and component reliability data. One difficult problem therein is the quantification of the model parameters, which are not accurate and are subject to uncertainties in most cases. In order to study a system with parameters over a possible range of variations due to uncertainty, the authors propose a novel interval mathematics based reliability evaluation method for large-scale distribution systems. Interval mathematics makes possible taking into consideration the uncertainty of each and every parameter and providing strict bounds of reliability indices, by executing the evaluation only once. The final interval will contain all possible solutions due to the variations in input parameters. The new algorithm, which can widen the degree of freedom of sensitivity analysis tip to unlimited, is a breakthrough of reliability sensitivity analysis. A software package DSIR2002 (interval analysis based Distribution System Reliability evaluation software) with proprietary copyright has been developed and successfully served in several utilities in China. The numerical results of IEEE RBTS test system and a 573-bus distribution system demonstrate that the proposed approach and DSIR2002 are efficient and feasible.