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Abstract
In this paper, we consider the problem of monitoring a linear functional relationship between a response variable and one or more explanatory variables (a linear profile). The design and application of a generalized likelihood ratio (GLR) control chart are discussed. The likelihood ratio test of the GLR chart is generalized over the regression coefficients, the variance of the error term, and the possible change point. The performance of the GLR chart is compared with various existing control charts. We show that the overall performance of the GLR chart is much better than other options in detecting a wide range of shift sizes. The existing control charts designed for certain shifts that may be of particular interest have several chart parameters that need to be specified by the user, which makes the design of such control charts more difficult. The GLR chart is very simple to design, as it is invariant to the choice of design matrix and the values of in-control parameters. Therefore, there is only one design parameter (the control limit) that needs to be specified. Another advantage of the GLR chart is its built-in diagnostic aids that provide estimates of both the change point and the values of linear profile parameters.
Additional information
Notes on contributors
Liaosa Xu
Mr. Xu is a PhD Candidate in the Department of Statistics. His email address is [email protected].
Sai Wang
Dr. Wang is a Sr. Statistician at Capital One Financial Corp. His email address is [email protected].
Yiming Peng
Mr. Peng is a PhD Candidate in the Department of Statistics. His email address is [email protected].
J. P. Morgan
Dr. Morgan is Professor in the Department of Statistics. His email address is [email protected].
Marion R. Reynolds
Dr. Reynolds is Professor in the Department of Statistics and the Department of Forest Resources and Environmental Conservation. He is a Member of ASQ. His email address is [email protected].
William H. Woodall
Dr. Woodall is Professor in the Department of Statistics. He is a Fellow of ASQ. His email address is [email protected].