A criterion for robust estimation of location and covariance matrix is considered, and its application in outlier labeling is discussed. This method, unlike the methods based on MVE and MCD, is applicable to large and high-dimension data sets. The method proposed here is also robust and has the same breakdown point as the MVE-and MCD-based methods. Furthermore, the computational complexity of the proposed method is significantly smaller than that of other methods.

Two types of control charts exist based on different quality characteristics: variable and attribute. These characteristics are commonly monitored using separate procedures. Only a few studies focused on the utilization of control charts to monitor a process with mixed characteristics. This study develops a new concept of the T 2 control chart based on a Principal Component Analysis (PCA) Mix, that is a PCA method that can jointly handle continuous and categorical data. The Kernel Density Estimation (KDE) method is used to estimate the control limit. Through simulation studies, the performance of the proposed chart is evaluated using the Average Run Length (ARL). T 2 control limits obtained from KDE produce a stable ARL 0 at~370 for α ¼ 0:00273: For the shifted process, the proposed chart demonstrates excellent performance for an appropriate number of principal components used. Applications of the simulated process and real cases show that the proposed chart is sensitive to monitoring the shifted process.

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Statistical Process Control (SPC) has been widely used in industry and services. The SPC can be applied not only to monitor manufacture processes but also can be applied to the Intrusion Detection System (IDS). In network monitoring and intrusion detection, SPC can be a powerful tool to ensure system security and stability in a network. Theoretically, Hotelling's T 2 chart can be used in intrusion detection. However, there are two reasons why the chart is not suitable to be used. First, the intrusion detection data involves large volumes of high-dimensional process data. Second, intrusion detection requires a fast computational process so an intrusion can be detected as soon as possible. To overcome the problems caused by large number of quality characteristics, Principal Component Analysis (PCA) can be used. The PCA can reduce not only the dimension leading a faster computational, but also can eliminate the multicollinearity (among characteristic variables) problem. This paper is focused on the usage of multivariate control chart T 2 based on PCA for IDS. KDD99 dataset is used to evaluate the performance of the proposed method. Furthermore, the performance of T 2 based PCA will be compared with conventional T 2 control chart. The empirical results of this research show that the multivariate control chart using Hotelling's T 2 based on PCA has excellent performance to detect anomaly in network. Compared to conventional T 2 control chart, the T 2 based on PCA has similar performance with 97 percent hit rate. It also requires shorter computation time.

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The need for a control chart that can visualize and recognize the symmetric or asymmetric pattern of the monitoring process with more than one type of quality characteristic is a necessity in the era of Industry 4.0. In the past, the control charts were only developed to monitor one kind of quality characteristic. Several control charts were created to deal with this problem. However, there are some problems and drawbacks to the conventional mixed charts. In this study, another approach is used to monitor mixed quality characteristics by applying the Kernel Principal Component Analyisis (KPCA) method. Using the Hotelling’s T2 statistic, the kernel PCA mix chart is proposed to simultaneously monitor the variable and attribute quality characteristics. Due to its ability to estimate the asymmetric pattern of the mixed process, the kernel density estimation (KDE) used in the proposed chart has successfully estimated the control limits that produce ARL0 at about 370 for α=0.00273. Through several experiments based on the proportion of the attribute characteristics and kernel functions, the proposed chart demonstrates better performance in detecting outlier and shift in the process. When it is applied to monitor the synthetic data, the proposed chart can detect the shift accurately. Additionally, the proposed chart outperforms the performance of the conventional mixed chart based on PCA mix by producing lower false alarm with more accurate detection of out of control processes.