Since extreme disasters become more frequent with climate change, resilience indices of power systems having low probability but large impact events gains increasing attention in both academia and industry. Either in the component hardening strategy before disaster or the rush repair strategy during disaster, disaster prevention and mitigation of distribution systems will be greatly improved if critical components can be identified dynamically especially for disaster characteristics and operational condition. This paper proposes component importance indices and evaluation methods for disaster prevention and mitigation in distribution systems. First, the proportional hazard model is introduced to model failure rate where influencing factors, such as aging condition and external weather condition, are considered. The inverse sampling method is introduced to generate outage scenarios. Then the paper assumes the status of component i online and offline in each scenario to calculate corresponding resilience restoration decisions. The importance indices of i based on the resilience difference between the two restoration decisions are evaluated. Finally, the convergence criterion is established to ensure accuracy. The rationality and effectiveness of the proposed indices and method are verified in case studies. This work is supported by Science and Technology Project of the Headquarter of State Grid Corporation of China (No. PDB17201800056).