Conventional fault tree analysis (FTA) is a well recognized technique used for detecting potential faults and quantifying the failures in civil or architectural structures during and after construction based on objective probabilities of fault events or components. However, estimating exact probabilities of occurrence of fault events for the use in the conventional FTA is difficult when failure data are insufficient or fault events are imprecise such as human error. To overcome this problem, this paper presented a hybrid approach employing fuzzy sets and possibility theory to effectively assess the fault possibilities based on expert subjective assessments. In the approach, failure possibilities of vague events are characterized by fuzzy sets to translate expert subjective judgments while fuzzy fault rates are derived from fuzzy possibility scores by using a modified possibility transformation function. Bridge failures during balanced cantilever construction were analyzed by using the proposed model. The results demonstrate the capability of this approach.