Nonlinear profile monitoring using spline functions

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Title:	Nonlinear profile monitoring using spline functions
Authors:	Xi, H;Hsieh, W-J;Lio, YL;Tsai, Tzong-Ru
Keywords:	cubic B-spline approximation;Hotelling T2 chart;maximum likelihood estimate;multivariate exponentially weighted moving average;statistical process control
Date:	2020-09-15
Issue Date:	2021-03-05 12:13:59 (UTC+8)
Abstract:	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.
Relation:	Mathematics 8(9), 1588
DOI:	10.3390/math8091588
Appears in Collections:	[Graduate Institute & Department of Statistics] Journal Article

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