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This research work presents a linear contribution factor model (LCFM) between a component's contribution to reliability indices and the failure rate of the component in distribution systems. This linear model can be applied to risk analysis (based on Monte Carlo simulation) and sensitivity analysis. Traditional approaches for both analyses require many repetitions of reliability index assessment (RIA). If this linear model is applied to either risk analysis or sensitivity analysis, only one RIA is needed and the computation is tremendously simplified.