Statistical Methods for Non-Linear Profile Monitoring

We have seen an increased interest and extensive research in the monitoring of a process over time whose characteristics are represented mathematically in functional forms such as profiles. Most of the current techniques require all of the data for each profile to determine the state of the process. Thus, quality engineers from industrial processes such as agricultural, aquacultural, and chemical cannot make process corrections to the current profile that are essential for correcting their processes at an early stage. In addition, the focus of most of the current techniques is on the statistical significance of the parameters or features of the model instead of the practical significance, which often relates to the actual quality characteristic. The goal of this research is to provide alternatives to address these two main concerns. First, we study the use of a Shewhart type control chart to monitor within profiles, where the central line is the predictive mean profile and the control limits are formed based on the prediction band. Second, we study a statistic based on a non-linear mixed model recognizing that the model leads to correlations among the estimated parameters.