Statistical Monitoring of Multivariate Multiple Linear Regression Profiles in Phase I with Calibration Application

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. Copyright (C) 2009 John Wiley & Sons, Ltd.