Fault tree analysis is one of the key approaches used to analyze the reliability of critical systems. Fault trees are usually analyzed using mathematical approaches or Monte Carlo simulation (MCS). This paper presents a Fuzzy-Monte Carlo simulation (FMCS) approach in which the uncertain data is generated by the MCS approach. The FMCS approach is applied to the Weibull probability distribution which is widely been used in the analysis of reliability, availability, maintainability and safety (RAMS). Using the fuzzy arithmetic, times to failure (TTF) of the components are generated. These results are processed by a kind of fault tree (e.g. time-to-failure tree) to produce the TTF of the whole system. The FMCS can estimate the TTF of the system which contains components that fail gradually (e.g. degradation). A comparison between the FMCS and the traditional MCS approaches shows that the time order of the FMCS approach is equal to the multiplication of the time order of the traditional MCS by a fuzzy number's representing the array length.