Progressively incentivized by the deregulation of electricity market and injection requirement of renewable energy generations into power grids, configurations of contemporary power systems are under fast evolving. As a consequence, the traditional power system reliability evaluation methods, which basically require sufficient statistical samples from relatively stable system configuration, are difficult, if not impossible, to validate effective when applied to evaluating a fast evolving system. On the basis of a given back propagation neural artificial network, this paper proposes a methodology of computing sensitivity of a certain index with respect to an involved factor. The proposed method, by establishing a concept of “neuron link” a priori, derives the analytical expression of sensitivity of an index with respect to a driving factor, and then derives the sensitivity of any index with respect to any driving factor with full consideration of all the neuron links. Through case studies based on field records and taking the index of total customer outage hours (TOH) for instance, it is validated that the method is able to correctly classify any driving factor into either the beneficial or the detrimental, and is also able to quantitatively rank the indices falling into an identical category as per their sensitivity contributions to the TOH. This work is supported by National Natural Science Foundation of China (No. 51507177) and Science and Technology of State Grid Corporation of China (No. JSFW0901KJ020202D1000220 160000).