Online monitoring of nonlinear profiles using a Gaussian process model with heteroscedasticity

There is extensive research in the monitoring of a process whose characteristics are represented as profiles. However, most current techniques require all observations from each profile to determine the process state. We study the use of a Shewhart chart based on a Gaussian process model with heteroscedasticity for the online monitoring of profiles, while these are being developed, where the central line is the predictive mean and the control limits are based on the prediction band. The advantage is that we do not have to wait until a profile ends to make process corrections. Our results indicate that our method is effective.