论文信息 - Monitoring the Slopes of Linear Profiles

Monitoring the Slopes of Linear Profiles

ABSTRACT Motivated by a vertical density profile problem, in this article we focus on monitoring the slopes of linear profiles. A Shewhart-type control chart for monitoring slopes of linear profiles is proposed. Both Phase I and Phase II applications are discussed. The performance of the proposed chart in Phase I applications is demonstrated using both real-life data in an illustrative example and simulated data in a probability of signal study. For Phase II applications, it is shown that the average run length (ARL) of the proposed control chart depends only on the shifts of slopes, whereas the ARL of the multivariate T 2 chart depends on both the shifts of slopes and the correlation between the estimated slope and the intercept. When such a correlation is low, the proposed control chart has a better ARL performance than the T 2 chart.

Dennis K. J. Lin | Junjia Zhu | Junjia Zhu | D. Lin

[1] S. P. Wright,et al. Comparing Curves Using Additive Models , 2002 .

[2] Jammalamadaka. Introduction to Linear Regression Analysis (3rd ed.) , 2003 .

[3] Douglas C. Montgomery,et al. Using Control Charts to Monitor Process and Product Quality Profiles , 2004 .

[4] J. Brian Gray,et al. Introduction to Linear Regression Analysis , 2002, Technometrics.

[5] J. Neter,et al. Applied Linear Statistical Models (3rd ed.). , 1992 .

[6] Fred Spiring,et al. Introduction to Statistical Quality Control , 2007, Technometrics.

[7] V. Barnett,et al. Applied Linear Statistical Models , 1975 .

[8] Roger M. Sauter,et al. Introduction to Statistical Quality Control (2nd ed.) , 1992 .

[9] B. J. Murphy. Selecting Out of Control Variables with the T2 Multivariate Quality Control Procedure , 1987 .

[10] William H. Woodall,et al. Phase I Analysis of Linear Profiles With Calibration Applications , 2004, Technometrics.

[11] Mahmoud A. Mahmoud,et al. On the Monitoring of Linear Profiles , 2003 .

[12] Lan Kang,et al. On-Line Monitoring When the Process Yields a Linear Profile , 2000 .