Estimation of the point of change in the multivariate normal process covariance matrix using neural networks
Volume 6, Issue 1, Spring 2016, Pages 21-34
Amirhossain Amiri, mohammadreza Maleki, Mohammadhossain Kalani
Abstract In most cases, the alert received from a control chart does not indicate the actual time of the process change due to the delay between the actual change time and the time of receiving the alert from the control chart. As a result, it is necessary to examine the real time of change, which is referred to as the "point of change". By reviewing the literature on identifying real-time process changes, it can be concluded that most research in this field focuses on univariate processes and little research is devoted to multivariate processes. In addition, most research in the field of estimating change time in multivariate processes has focused on changes in the mean process vector, and only one research has been done on the covariance matrix. In this paper, a model based on artificial neural network is proposed to estimate the point of change in the covariance matrix of multivariate normal processes. The method presented in phase 2 is control diagrams and the type of change that occurred in the variance of qualitative characteristics is assumed to be the type of step changes. The performance of the proposed method in estimating the change point is evaluated based on two criteria of experimental distribution of estimates as well as the mean and standard deviation of the change point estimator for different step shifts in the variance of process variables in a simulation study. Finally, in order to further explain the proposed method, a numerical example is provided. The results show the proper performance of the proposed method in estimating the change point in the covariance matrix of multivariate normal processes.