## 1 Introduction  
Intrusion detection is a process of monitoring events within a computer system or network, where subsequent analysis of the monitored data is conducted to identify any signs of attempted intrusions. Intrusion refers to attempts to gain unauthorized access to a computer system or network, potentially threatening the availability, integrity, and confidentiality of a computer network system. The system used to perform intrusion detection is known as an intrusion detection system (IDS) [1]. Intrusion detection matches network traffic patterns with known attack patterns or identifies abnormal network traffic patterns [2]. Anomaly-based network intrusion detection systems are generally categorized into knowledge-based systems, computational approaches, and statistical approaches [3]. One statistical methodological approach used in intrusion detection is Statistical Process Control (SPC), which is widely applied across various sectors, including services and industries. SPC can also be applied to intrusion detection systems (IDS), and its conventional use is in monitoring changes within manufacturing and service processes. Recent research has investigated how SPC can detect unauthorized intrusions [4]. Statistical Process Control (SPC) has played a significant role in product quality control since [PERSON] [5] introduced the control chart techniques by applying statistical methods to monitor the industrial and manufacturing processes. One of the multivariate control charts to monitor the process mean is [PERSON]'s \(T^{2}\) control chart [6], which can be used to monitor individual or subgroup observations. In SPC concepts, an outlier can be defined as an observation that significantly deviates from other observations, which indicates that the observation is observed by a different process [7]. [PERSON]'s \(T^{2}\) chart is unsuitable for detecting the presence of multiple outliers [8] due to the masking and swamping effect [9], especially for highly outlier-contaminated data. The statistic of \(T^{2}\), which is based on the classical estimator, is easily affected and decreased by the presence of outliers [10; 11]. Moreover, the performance of control charts will decrease if the variables monitored increase [12]. Several methods have been proposed to overcome this problem and minimize the effects of outliers by changing the classical estimator with a robust one, especially for the covariance matrix estimator. The performance of the \(T^{2}\) control chart in detecting shifts in the mean could be enhanced by using a robust estimator [13]. Many robust methods have been adopted to develop a \(T^{2}\) control chart to minimize the effect of outliers. These methods such as Minimum Volume Ellipsoid (MVE) [14], Trimming Method [15; 16], Minimum Vector Variance [17; 18], Successive Difference Covariance Matrix (SDCM) [10; 19], Minimum Covariance Determinant (MCD) [15; 20], Reweighted minimum covariance determinant (RMCD) [21], and Fast Minimum Covariance Determinant (Fast-MCD), whose good performance on monitoring small to medium outlier contaminated data with 30% breakdown point [22]. The latest development of robust estimators is the Minimum Regularized Covariance Determinant (MRCD) method [23], which uses a data-driven algorithm and regularization to avoid over-fitting problems. The MRCD estimator can be used to detect outliers in high-dimensional data. Besides the robust estimator, the [PERSON]' \(T^{2}\) chart can also be developed using a non-parametric approach as a control limit, namely the bootstrap resampling method [24]. This research focuses on developing bootstrap-based robust \(T^{2}\) control charts with MRCD estimators for detecting intrusion. This method will be applied to the UNSW-NB15 dataset. The primary contributions of this research are as follows:  
* Development: A novel control chart methodology based on the MRCD estimator is introduced for the identification of anomalous observation. The efficacy of the proposed method is assessed under diverse simulation conditions.