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Failure behavior is the state change process of product or part of a product which is relative to its environment, over time performance and can be detected from the outside. According to the different level of analysis, failure behavior analysis method can be divided into element failure behavior analysis method and system failure behavior analysis method. The formal reveals the variety failure mechanisms under the alone or coupled action of internal cause and external cause using coupling analysis method; the latter focuses on product failure performance law under the effect of variety failure mechanisms by means of failure propagation analysis or state analysis. This critical review from two aspects of element and system investigates and summarizes the current research status of failure behavior analysis method. The result shows that coupling analysis method has been mature at present, and there is plenty of supporting software for computer-aided analysis. Failure propagation analysis method consists of graph theory based method, Petri Net method and complex network method. But the above-mentioned methods are unilateral and isolated from each other. System failure behavior analysis method needs to synthetically use the current methods - coupling analysis, failure propagation analysis and state analysis method so that forms an analysis methodology which needs to clear the input and output of each method and improve the interface between application software. The comprehensive methodology that the failure behavior analysis follows will provide support to product reliability analysis and design improvement.