In many applications the quality of a process or product is best characterized and summarized by a functional relationship between a response variable and one or more explanatory variables. Profile monitoring is used to understand and to check the stability of this relationship over time. At each sampling stage one observes a collection of data points that can be represented by a curve (or profile). In some calibration applications, the profile can be represented adequately by a simple linear regression model, while in other applications more complicated models are needed. The purposes of this paper are to review recent research on the use of control charts to monitor process and product quality profiles and to encourage further research in this area.
Calibration; functional data analysis; linear regression; multivariate quality control; nonlinear regression; statistical process control; wavelets