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.

Understanding multivariate variability is a difficult task because there is no single measure that can be properly used. This article presents a new measure that features good properties. If this measure is simultaneously used with generalized variance, it will give a better understanding of multivariate variability. It can also efficiently be used for large data sets with high dimensions. Furthermore, when it is used for constructing a Shewhart-type chart to monitor multivariate variability, the resulting chart has a much better out-of-control ARL than the generalized variance chart. An example illustrates its advantage.

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.

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.