Nonlinear Profile Monitoring Using Spline Functions

• Main Authors: Hua Xin, Wan-Ju Hsieh, Yuhlong Lio, Tzong-Ru Tsai
• Format: Article
• Language: English
• Published: MDPI AG 2020-09-01
• Series: Mathematics
• Subjects: cubic B-spline approximation; Hotelling <i>T</i>² chart; maximum likelihood estimate; multivariate exponentially weighted moving average; statistical process control
• Online Access: https://www.mdpi.com/2227-7390/8/9/1588

In this study, two new integrated control charts, named <inline-formula><math display="inline"><semantics><msup><mi>T</mi><mn>2</mn></msup></semantics></math></inline-formula>-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 <inline-formula><math display="inline"><semantics><msup><mi>T</mi><mn>2</mn></msup></semantics></math></inline-formula>-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 <inline-formula><math display="inline"><semantics><msup><mi>T</mi><mn>2</mn></msup></semantics></math></inline-formula>-MAE and MS-MAE charts. Simulation results show that the MS-MAE chart outperforms the <inline-formula><math display="inline"><semantics><msup><mi>T</mi><mn>2</mn></msup></semantics></math></inline-formula>-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.