In a bulk power system， cascading failures initiated by branch open events often lead to blackout. So， it is definitely necessary to make an event reliability analysis in an emergency. A kind of line current fast calculating method in an emergency and the safety margin index of line current are described. These indices are used to identify the key lines affected by the tripping line and forecast system multiple failure events. Based on the above considerations， the reliability evaluation algorithm using state pruning by the margin of safety is proposed and the margin of safety indices are applied to screening the failure event with a small safety margin. It can effectively prune system failure state space and harmonize the conflict between speed and precision of the event reliability analysis. Application shows that the method proposed can not only effectively perform influencing and pruning analysis of event reliability， but also reflect the relation of variation of system indices with the safety margin of line current. The critical value of safety margin in relation to the risk of cascading failure can be obtained， providing decision-making reference for preventing the occurrence of blackout.