Simultaneous monitoring of correlated multivariate linear and GLM regression profiles in Phase II

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.