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In some applications, the quality of a process or product is characterized by correlated multivariate linear and generalized linear model (GLM) regression profiles. Monitoring these profiles separately leads to misleading results because the correlation structure among the multivariate linear and GLM profiles is neglected. In this paper, we specifically concentrate on Phase II and propose some procedures for monitoring multivariate linear and GLM regression profiles. Simulation studies are used to compare the performance of the proposed methods under different magnitudes of shifts in the regression parameters in terms of the average run length criterion. The results of simulation studies show the superior performance of the proposed methods compared to monitoring multivariate linear and GLM profiles separately. In addition, the performance of the proposed monitoring schemes is illustrated by a numerical example. Finally, the application of the proposed methods is shown by a real-world case.

Change point estimation is a useful concept that helps quality engineers to effectively search for assignable causes and improve quality of the process or product. In this paper, the maximum likelihood approach is developed to estimate change point in the mean of multivariate linear profiles in Phase II. After the change point, parameters are estimated through filtering and smoothing approaches in dynamic linear model. The proposed change point estimator can be applied without any prior knowledge about the change type against existing estimators which assume change type is known in advance. Besides, sporadic change point can be identified as well. Simulation results show the effectiveness of the proposed estimators to estimate step, drift and monotonic, as well as sporadic changes in small to large shifts. In addition, effect of different values of the Multivariate Exponentially Weighted Moving Average (MEWMA) control chart smoothing coefficient on the performance of the proposed estimator is investigated presenting that the smoothing estimator has more uniform performance. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a control chart is proposed to detect changes in the covariance matrix of a multivariate normal process, when sample size is one. The proposed chart statistic is constructed based on the exponentially weighted form of sample covariance matrix given by individual observation over time. Distance between the values of variance and covariance components in this multivariate exponentially weighted moving sample covariance matrix and, the in-control corresponding elements of process variance-covariance matrix provides a basis for process variability monitoring. The statistical performance of the proposed method is evaluated through the use of a Monte Carlo simulation. The results show the superiority of the proposed control chart performance especially in the case of incremental changes in covariance matrix.