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.