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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, quality of a process or product is characterized by a relationship between two or more variables which is referred to as profile. In many practical situations, a profile can be modeled as a polynomial regression. In this article, three methods are developed for monitoring polynomial profiles in Phase I. Their performance is evaluated using power criterion. Furthermore, a method based on likelihood ratio test is developed to identify the location of shifts. Numerical simulation is used to evaluate the performance of the developed method.