Estimating change point in multivariate processes via simultaneous mean vector and covariance matrix

Abstract

In many industrial processes, several quality characteristics are inevitably related. In this situation, the mean vector and covariance matrix must be simultaneously monitored and controlled to determine whether a multivariate process is in control. With the increase in the number of variables, the performance of control charts is significantly reduced, and the time delay between the actual time of change in the process and the warning time of the control chart increases, which is one of the main challenges when using multivariable control charts. Between the real-time and the change time (called the change-point - CP), especially during the simultaneous monitoring and controlling of the parameters, the mean vector, and the covariance matrix cause problems such as delay or stoppage of the production lines or services, as well as inconsistent production of products or services. To improve this, a new way of estimating the CP will help statistical process control (SPC) professionals identify the cause(s) of out-of-control (OC) conditions, thus providing better feedback for process improvement. This study presented a new method based on an artificial neural network (ANN), which first examined the OC conditions for a multivariate process using the multivariate exponentially weighted moving average (MEWMA) and multivariate exponentially weighted mean square (MEWMS) control charts. Then, the ANN-fitting method was used to diagnose the cause(s) of OC conditions using the machine learning (ML)-classifier and estimating the length of delay time. Finally, the change point (CP) was estimated by integrating all these methods. The performance of the new approach was validated by comparing it with the results from another study. It also validated the proposed method developed by evaluating the accuracy and precision of this research. As a conclusion, the MEWMS chart was the best for detecting the OC condition while the support vector machines (SVM) gaussian model best to diagnoses the cause(s) o f the OC condition. The model provided has estimated the change point on one sample with difference over 10,000 tested cases (simulated) with a probability of 99%, which is an accurate and reliable model for a practical approach.