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Intuitionistic fuzzy set is a useful tool to express experts' uncertain knowledge and experience information. Most computer security systems have abnormal states and their failure behaviors are always characterized in uncertainty and inaccuracy. How to calculate fault interval of system components is an interesting and important issue in intuitionistic fuzzy fault-tree analysis (IFFTA). Intuitionistic fuzzy fault diagnosis models are proposed in this paper to analyze fuzzy system reliability and to find the most critical system component for the decision-making based on some basic definitions. The proposed method is applied for the failure analysis problem of computer security systems and comparative studies are conducted to show its flexibility and effectiveness with the other fault tree analysis models.