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The modern microgrid is designed to withstand various disruptive events that have a high probability of occurrence but have a low impact on the system. This improves the reliability of the system but does not take into consideration the disruptive events that have a low probability of occurrence but have a large impact on the system, such as extreme weather or natural disasters. Redesigning a microgrid to withstand low probability high impact events is very costly and is not a feasible solution to existing microgrids. This paper proposes a method to improve the resilience of an existing microgrid to quickly recover from low probability high impact events. The method used for this purpose is a combination of Monte Carlo simulation and prioritization of load of the microgrid. The efficacy of the method is examined by modeling microgrids using a fragility model. Using the proposed novel resilience index, the resilience of the IEEE 5-Bus system and IEEE 14-Bus system and the effect of load shedding on the resilience of the microgrid are analyzed and presented. The effect on smaller and larger grids and their resilience is examined. A novel resilience index is used to quantify the improvement of resilience of the proposed method when compared to other methods available in the literature.