Phase II monitoring of multivariate multiple linear regression profiles

In certain cases, the quality of a process or a product can be effectively characterized by two or more multiple linear regression profiles in which response variables are correlated. This structure can be modeled as multivariate multiple linear regression profiles. When linear profiles are monitored separately, then correlation between response variables is ignored and misleading results could be expected. To overcome this problem, the use of methods that consider the multivariate structure between response variables is inevitable. In this paper, we propose four methods to monitor this structure in Phase II. The performance of the methods is compared through simulation studies in terms of the average run length criterion. Furthermore, a method based on likelihood ratio approach is developed to determine the location of shifts and a numerical simulation is used to evaluate the performance of the proposed method. Finally, the use of the methods is illustrated by a numerical example.