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The breakdown of traffic flow is directly related with the abnormal phenomena such as road traffic incidents. It results in the discontinuities of traffic and reduces the service level. The research of traffic flow breakdown is often narrowly confined to incident detection, and there are approximately 4 kinds of algorithms: pattern recognition algorithm, statistical inference algorithm, catastrophic theory and neural network algorithm. These methods have played important roles in their past applications, and each has shortcomings. This paper introduces a nonlinear and nonparametric statistical method to analyze traffic flow breakdown. Based on traffic flow theory and combined with mean-value change-point model, the hypothesis testing of the existence of change points and the local-comparison algorithm to search change-points are discussed. The method is calibrated with the data from the city of Southampton, UK. An example of the applications is also included to test the effectiveness of the method.