Due to the increased frequency of natural calamities, resilience in power distribution system has gained a lot of importance. It is crucial to ensure resilient operation after a natural disaster, as there are tremendous losses to the economy and society as a whole. In this paper, a novel way to improve the resiliency of the distribution system to extreme events is proposed using an advanced feeder restoration approach. In the proposed method, due to isolation of the distribution system from the main grid, the critical loads are majorly restored using distributed energy resources (DERs). To ensure resilient operation after a natural disaster, the proposed restoration framework aims at maximizing the availability of restored networks making restoration plan robust to post-restoration failures. This approach uses a graph-theoretic approach and formulates the restoration problem as a mixed-integer linear program (MILP), while satisfying the operational and connectivity constraints of a typical power distribution system. The framework is tested using IEEE 123-node feeder with 6 DERs supplying 12 critical loads. In order to replicate a realistic scenario, variability of DER generation and load demand is introduced. The simulation results validate the effectiveness of the proposed strategy in maximizing restoration availability, enabling maximum duration of load serving.