Control Charts for Monitoring Linear Profiles with Within-Profile Correlation Using Gaussian Process Models

Profile monitoring is the utilization of control charts for checking the stability of the quality of a product over time when the product quality is characterized by a function at each time point. Most existing control charts for monitoring profiles are based on the assumption that the observations within each profile are independent of each other, which is often invalid in practice. Successive measurements within profiles often exhibit spatial or serial correlation. This paper focuses on Phase II linear profile monitoring when within‐profile data are correlated. A Gaussian process model is used to describe the within‐profile correlation (WPC). Two Shewhart‐type multivariate control charts are proposed to monitor the linear trend term and the WPC separately in Phase II. Our proposed approaches are compared with alternative methods through numerical simulations in which different in‐control WPCs are considered. Simulation studies show that the proposed control charts are sensitive to changes in the linear trend term when the correlation is strong and effective in detecting large shifts in the WPC. Finally, an example is given to illustrate the implementation of our proposed control charts.