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In conventional fault-tree analysis, the failure probabilities of components of a system are treated as exact values in estimating the failure probability of the top event. For many systems, it is often difficult to evaluate the failure probabilities of components from past occurrences because the environments of the systems change. Furthermore, it might be necessary to consider possible failure of components even if they have never failed before. We, therefore, propose to employ the possibility of failure, viz. a fuzzy set defined in probability space. The notion of the possibility of failure is more predictive than that of the probability of failure; the latter is a limiting case of the former. In the present approach based on a fuzzy fault-tree model, the maximum possibility of system failure is determined from the possibility of failure of each component within the system according to the extension principle. In calculating the possibility of system failure, some approximation is made for simplicity.