# An Improved Real-Time Contrasts Control Chart Using Novelty Detection and Variable Importance
## 1 Introduction  
Recently, developments in manufacturing have led to an increase in the amount of multivariate data collected from the manufacturing processes. Because of the importance of multivariate data, multivariate statistical process control (MSPC) is nowadays essential to enable the simultaneous monitoring of multivariate variables [1; 2]. The multivariate exponentially weighted moving average (MEWMA) control chart [3], multivariate cumulative sum (MCUSUM) control chart [4], and \(T^{2}\) control chart [5] are examples of representative multivariate process controls. Typical multivariate process control charts assume a normal distribution of data, estimate the parameters in the normal state, and use them as a statistic for control charts. However, in actual manufacturing processes, hardly any data satisfy the normal distribution. If the normal distribution is assumed, the performance is degraded. To overcome these problems, several approaches have been proposed to classify the state of multivariate process control charts as normal or abnormal by using machine-learning techniques. Although the performance is better than that of a conventional multivariate process control chart, once the model learned in phase I is generated, the decision boundary does not change, and the performance may deteriorate. To improve this problem, there have been some studies to generate artificial contrasts [6; 7; 8] and a method called real-time contrasts (RTC) has been proposed [9]. RTC learns a new classifier as the sliding window progresses. This method calculates the statistics based on sequential classifications. Because it learns a new classifier in real time, it offers the advantageof better reflecting the characteristics of the observations in Phase II in the control chart. RTC uses random forests as the classifier to calculate the statistics. This classifier offers the advantage of being able to check variables that are considered the cause of abnormal observations in real time. However, a problem associated with RTC is that the monitoring statistics of the original RTC have discrete value because these monitoring statistics are computed based on the binary classification probabilities of several decision trees [10]. To overcome these limitations, distance-based RTC has been proposed. This method uses a support vector machine (SVM) and kernel linear discriminant analysis (KLDA) as a classifier to calculate the statistics [11]. Attempts have been made to improve the performance of the classifier by applying weighted voting to random forests to improve the performance of RTC while using random forests to maintain the advantage of being able to identify anomalous cause variables in real time [10]. Most previous attempts to improve RTC performance have used other classifiers instead of random forests. However, these studies could not identify the abnormal cause variable in real time. Some studies have attempted to use random forests to improve the detection ability of the control chart by improving the performance of the classifier. RTC creates contrasts using a sliding window. However, when both normal and abnormal data exist together in the sliding window, the sensitivity to detect abnormalities is decreased. In addition, in an abnormal state, when some normal observations are input to the sliding window, they can act as noise and degrade the RTC performance. Also, although the process is out of control, when normal and abnormal data are mixed and normal data is intermittently observed in the sliding window, the out-of-control state cannot be detected quickly. Therefore, in this study, we suggest a means of improving the performance of the RTC control chart. We improved the classification performance of the RTC control chart by enhancing it with a variable importance chart using random forests, novelty detection using SVM, and MEWMA. The proposed method consists of two phases. In Phase I, novelty detection is performed using the reference data.