Link capacity reductions, which occur often, degrade the service quality and performance of urban rail transit (URT) networks. To measure the reliability of a URT network when link capacity reductions occur in a given time period, the passengers’ generalized travel cost (GTC) is computed and passengers are divided into three categories. The GTC considers here the crowding in trains, seat availability, and perceived travel time. Passengers whose relative increase in GTC on a URT is below or above a preset threshold belong to category I or II, respectively, while passengers who cannot travel on the URT due to insufficient capacities on their paths belong to category III. Passenger trips in categories I are acceptable since their GTC increases only slightly with link capacity reductions. The fraction of acceptable trip (FAT) and total GTC increase ratio (TGCR) in a given time period are defined here as the network’s reliability and unreliability metrics, respectively. The ratio of affected passenger trip (RAPT) is proposed to identify each line’s most critical links. The reliability and unreliability metrics of Wuhan’s URT network during evening peak hours are computed when the capacities of the most critical link or multiple most critical links are reduced. The results show that the proposed RAPT indicator is effective in identifying the most critical links that greatly affect the reliability and performance of a URT network. For capacity reductions on a line’s most critical link, the proposed method can determine the capacity reduction ratio corresponding to network’s high FAT and low TGCR as well as the priorities of lines needing emergency measures to maintain high network reliability and performance. For capacity reductions on critical links of multiple lines, the proposed method can identify the number of reduction links and the capacity reduction ratio that the network can withstand while maintaining its reliability and performance above a specified level.