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.

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In some statistical process control applications, there are some correlated quality characteristics which can be modeled as linear functions of some explanatory variables. We refer to this structure as multivariate multiple linear regression profiles. When the correlation structure between quality characteristics is ignored and profiles are monitored separately then misleading results could be expected. Hence, developing methods to account for this multivariate structure is required. In this paper, we specifically focus on phase I monitoring of multivariate multiple linear regression profiles and develop four methods for this purpose. The performance of the developed methods is compared through simulation studies in terms of probability of a signal. In addition, a diagnostic scheme to find the out-of-control samples is developed. Finally, the application of the proposed methods is illustrated using a calibration application at the National Aeronautics and Space Administration (NASA) Langley Research Center.

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