Accurate assessment of system reliability with limited or insufficient statistical data is difficult. This paper presents a method which overcomes the drawbacks of traditional fault tree analysis (FTA) by using FTA based on possibilistic measures and fuzzy logic. This method is designed specifically for situations wherein reliability and safety assessment is imprecise by nature and necessary statistical data is scarce. Based on fundamentals of fuzzy logic, failure possibility is first defined and then fuzzy variables are characterized in the context of possibility theory. Next, subevents in FTA described with natural language are viewed as a collection of elastic constraints of fuzzy variables. Fuzzy rules are generated from linguistic quantification and meaning inference in fuzzy logic. Lastly, an example is used to illustrate the proposed analytical method and reasoning mechanism. Unlike previously reported fuzzy FTA or fuzzy logic-based FTA, this method is an integration of the possibilistic approach and the fuzzy logic-based reasoning approach which is of potential value for creating expert knowledge databases. It can also be applied to other aspects of reliability engineering, addressing ambiguous and subjective uncertainty problems qualitatively and quantitatively