Monitoring Nonlinear Profiles with Random Effects by Nonparametric Regression

Abstract

The monitoring of process/product profiles is presently a growing and promising area of research in statistical process control. This study is aimed at developing monitoring schemes for nonlinear profiles with random effects. We utilize the technique of principal components analysis to analyze the covariance structure of the profiles and propose monitoring schemes based on principal component (PC) scores. The number of the PC scores used in constructing control charts is crucial to the detecting power. In the Phase I analysis of historical data, due to the dependency of the PC-scores, we adopt the usual Hotelling T ² chart to check the stability. For Phase II monitoring, we study individual PC-score control charts, a combined chart scheme that combines all the PC-score charts, and a T ² chart. Although an individual PC-score chart may be perfect for monitoring a particular mode of variation, a chart that can detect general shifts, such as the T ² chart and the combined chart scheme, is more feasible in practice. The performances of the schemes under study are evaluated in terms of the average run length.

Keywords:

• Average run length
• Control charts
• Nonlinear profile monitoring
• Principal components analysis
• Profile-to-profile variation
• Spline smoothing

Mathematics Subject Classification:

• 62P30
• 62H25
• 62G08

Acknowledgments

The authors would like to express their gratitude to the Editor, an Associate Editor, and two referees for the careful review and constructive suggestions. This work was supported in part by the National Research Council of Taiwan, Grant No. NSC93-2118-M009-007 and NSC95-2118-M-009-006-MY2.