Nonlinear Profile Monitoring Using Spline Functions

In this study, two new integrated control charts, named T2-MAE chart and MS-MAE chart, are introduced for monitoring the quality of a process when the mathematical form of nonlinear profile model for quality measure is complicated and unable to be specified. The T2-MAE chart is composed of two memoryless-type control charts and the MS-MAE chart is composed of one memory-type and one memoryless-type control charts. The normality assumption of error terms in the nonlinear profile model for both proposed control charts are extended to a generalized model. An intensive simulation study is conducted to evaluate the performance of the T2-MAE and MS-MAE charts. Simulation results show that the MS-MAE chart outperforms the T2-MAE chart with less false alarms during the Phase I monitoring. Moreover, the MS-MAE chart is sensitive to different shifts on the model parameters and profile shape during the Phase II monitoring. An example about the vertical density profile is used for illustration.