## 1 Introduction  
High-speed railways have been widely applied in various countries during the past several decades. Compared with normal-speed railways, the high-speed railways place high requirements on track systems. Under the actions of external factors such as cyclic temperature loadings and train impact loadings, various diseases easily emerge in the parts of the track systems during operation [1, 2]. To ensure safe operation, several monitoring systems have been constructed to monitor the service status of track systems in real time. Massive monitoring data were accumulated in this process [3, 4, 5]. Due to a range of reasons, including external environmental actions, poor installation, and hardware problems, data loss occurred during wireless transmission and led to lots of discontinuous monitoring data [6, 7, 8, 9]. Data loss decreases the quality of analysis results and adds challenges to the data processing and analysis. Researchers have proposed several methods to recover the data loss, including acknowledgments [10, 11], forward error correction [12], convolutional neural networks [13], compressive sensing [8, 9], etc. However, these methods are effective only under certain conditions. The in-depth analysis and full utilization on discontinuous data play essential roles in optimizing monitoring technology, evaluating the service status and prolonging the life of track systems [14, 15]. A statistical process control (SPC) framework was proposed to fulfil the efficient monitoring and management of structures. The framework was built based on the SPC notion [16, 17], in which changes in the output of a stochastic process consist of common-cause variation, special-cause variation, and inherent random variation. In the case of a track system, the common-cause variation is produced by usual environmental and operational conditions, such as normal weather and train loadings. The special-cause variation is attributed to special events, including extreme weather, unusual loads, structural damage, etc. The inherent random variation is related to the cumulative effects of many small, unavoidable causes [18]. Importantly, the detection of special events could deepen the understanding of decision-makers on the monitoring data, thereby initiating immediate management of infrastructure [19]. In the past several decades, SPC has been widely applied in the structural health monitoring (SHM) of civil engineering infrastructure [19; 20; 21; 22; 23; 24; 25]. [PERSON] et al. [20] applied an X-bar control chart of SPC in the vibration-based damage diagnosis of a concrete bridge column. [PERSON] et al. [21] utilized an autoregressive (AR) model to fit the acceleration time histories of a concrete bridge column and employed X-bar and S control charts to monitor the mean and variance of the AR model residual. [PERSON] et al. [22] validated the damage detection ability of the Shewhart control chart based on the predamage and postdamage data of a bridge. [PERSON] et al. [23] identified the damage of a concrete arch bridge with the construction of T\({}^{2}\) control charts. [PERSON] et al. [24; 25] developed a two-part SPC framework to excavate the continuous monitoring data of the Hurley Bridge, that is, separating common-cause variation by using statistical models at first and then detecting special-cause variation with the use of univariate and multivariate control charts. [PERSON] et al. [19] extended the two-part SPC framework and analyzed continuous delamination data of the Grace Church building. However, so far, little research has used the SPC framework to analyze the discontinuous monitoring data of high-speed railway track systems. Responses of track systems include static and dynamic responses determined by whether the trains pass by or not. Evaluation of the anomalies in track systems by dynamic responses is featured with high sensitivity but also high complexity. Moreover, the train impacting in a turnout leads to relatively large dynamic responses [26], which brings interference to data analysis.