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Monte Carlo simulation is commonly employed for risk analysis, which evaluates the risk associated with rare events in distribution systems. The traditional approach of Monte Carlo simulation requires a distribution reliability assessment for each sample year. This may be very time-consuming, since hundreds of sample years are necessary to obtain a precise result. This paper presents a linear contribution factor model (LCFM) to simplify the Monte Carlo simulation. The linear model considers three major distribution reliability indices (SAIFI, SAIDI, and MAIFIE) and two failure modes (permanent fault and temporary fault). While the result from the proposed simplified approach is identical to the traditional approach, the simplified approach may reduce the running time by up to 98%.