Maximum multivariate cumulative sum (Max-MCUSUM) is one of the single control charts that plot single statistic as a representation of mean vector and covariance matrix. The Max-MCUSUM statistic has unknown specific distribution. The objective of this paper is to propose bootstrap-based Max-MCUSUM control chart for which reference value is predetermined in Phase I monitoring process. For various numbers of quality characteristics and correlation coefficients, the control limits estimated using bootstrap approach are presented in this paper. Furthermore, the average run lengths of bootstrap-based Max-MCUSUM control chart prove that the proposed control chart tends to be effective for monitoring the small shift in both mean and variance of a process. The illustrative examples are provided to demonstrate the applications of the proposed control chart for both simulation and real data.

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 T2 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 a 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 T2 based on PCA for IDS. The KDD99 dataset is used to evaluate the performance of the proposed method. Furthermore, the performance of T2 based PCA will be compared with conventional T2 control chart. The empirical results of this research show that the multivariate control chart using Hotelling’s T2 based on PCA has excellent performance to detect an anomaly in the network. Compared to conventional T2 control chart, the T2 based on PCA has similar performance with 97 percent hit rate. It also requires shorter computation time.

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 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). control limits obtained from KDE produce a stable ARL₀ at ~ 370 for 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.

The multivariate control charts are not only used to monitor the mean vector but also can be used to monitor the covariance matrix. The multivariate variability charts are used to guarantee the consistency of products in the subgroup. Many researchers have been studied the multivariate control chart for variability. Nevertheless, those conventional methods have several drawbacks because it is developed based on the determinant of the covariance matrix and not free of the measurement unit. To overcome such issues, this paper proposes the multivariate control chart for variability based on trace of the squared correlation matrix. Kernel Density Estimation is used to improve estimated control limit. The kernel density estimation method is used to calculate the control limit. Through simulation studies, the performance of the proposed chart is evaluated using the average run length (ARL). The control limits of the proposed chart are produced in control ARL at about 370 for α = 0.00273. Meanwhile, the proposed chart demonstrated better performance to detect the shift for the large value of quality characteristics and sample size. The proposed chart also produces a better performance than the conventional generalized variance chart when used to monitor the real case data.