在許多生產製造的過程，品質特性是由反應變數和一個或多個解釋變數間的關係來界定，而若品質特性是以一個函數或是一個曲線的型態來呈現，則稱之為輪廓。本研究主要是著重在第二階段的製程輪廓監控，我們先使用懲罰樣條迴歸模型來描述反應變數和解釋變數之間的複雜關係，並利用線性混合模型的配適來估計懲罰樣條迴歸模型中的參數。接著我們再利用建立同時信賴區帶的概念提出一個新的Shewhart管制圖，並利用這個管制圖來監控輪廓製程。我們經由統計模擬來評估所提出的管制圖的偵測效率，同時也透過一個例子來說明這種管制圖在實際上如何使用。

Chen, G., Cheng, S. W. and Xie, H. (2001). “Monitoring Process Mean and Variabili-
ty With One EWMA Chart,” Journal of Quality Technology, 33, 223-233.
Croarkin, C. and Varner, R. (1982). “Measurement Assurance for Dimensional Mea-
Surements on Integrated-Crircuit Photomasks,” NBS Technical Note 1164, U.S.
Department of Commerce.
Crowder, S. V. (1987a). “A simple Method for Studying Run-Length Distributions of
Exponentially Weighted Moving Average Charts,” Technometrics, 29, 401-407.
Crowder, S. V.(1989).“Design of Exponentially Weighted Moving Average Schemes,”
Journal of Quality Technonlgy, 21, 155-162.
Ding, Y., Zeng, L. and Zhou, S. (2006). “Phase I Analysis for Monitoring Nonlinear Profiles in Manufacturing Process,” Journal of Quality Technonlgy, 38, 199-216.
Fan, J., and Gijbels, I. (1996). Local Polynomial Modeling and Its Applications, London：Chapman & Hall.
Fan, J. and Huang, L-S. (2001). “Goodness-of-Fit Tests for Parametric Regression Models,” Journal of the American Statistical Association, 96, 640-652.
Fan, J., Zhang, C. and Zhang, J. (2001). “Generalized Likelihood Ratio Statistics and Wilks Phenomenon,” The Annals of Statistics, 29, 153-193.
Gupta, S., Montgomery, D. C. and Woodall, W. H. (2006). “Performance Evaluation of Two Methods for Online Monitoring of Linear Calibration Profiles,” Internatio-
nal Journal of Production Research, 44, 1927-1942.
Hall, P. and Marron, J. S. (1990). “On Variance Estimation in Nonparametric Regres-
sion,” Biometrika, 77, 415-419.

Hayes, K. and Haslett, J. (1999). Simplifying general least squares. American Statisti-
cian, 53, 376-81.
Jin, J. and Shi, J. (1999). “Feature-Preserving Data Compression of Stamping Tonn-
age Information Using Wavelet,” Technometrics, 41, 327-339.
Kang, L., and Albin, S. L. (2000). “On-Line Monitoring When the Process Yields a Li- near Profile,” Journal of Quality Technonlgy, 32, 418-426.
Kim, K., Mahmoud, M. A. and Woodall, W. H. (2003). ”On the Monitoring of Line-
ar Profiles,” Journal of Quality Technonlgy, 35, 317-328.
Lada, E. K., Lu, J.-C. and Wilson, J. R. (2002). “A Wavelet-Based Procedure for Pr-
ocess Fault Detection,” IEEE Transactions on Semiconductor Manufacturing, 15,
79-90.
Lucas, J. M. and Saccucci, M. S. (1990). “Exponentially Weighted Moving Average Control Scheme Properties and Enhancements,” Technometrics, 32, 1-29.
Mahmoud, M. A., Parker, P. A., Woodall, W. H., and Hawkins. D. M. (2007). “A Ch-
ange Point Method for Linear Profile Data,” Quality and Reliability Engineering
International, 23, 247-268.
McCulloch, C. E. and Searle, S. R. (2001). Generalized Linear and Mixed Models. New York：Wiley.
Mestek, O., Pavlik, J. and Suchanek, M. (1994). “Multivariate Control Charts：Cont-
rol Charts for Calibration Curves,” Journal of Analytical Chemistry, 350, 344-351.
Page, E. S. (1954). “Continuous Inspection Schemes,” Biometrics, 41, 100-115.
Quesenberry, C. P. (1995). “On Properties of Q Charts for Variables,” Journal of Qual-
ity Technology, 27, 184-203.
Roberts, S. W. (1959). “Control Chart Tests Based on Geometric Moving Averages,”
Technometrics, 42, 97-102.
Robinson, G. K. (1991). The BLUP is a good thing：The Estimation of Random Effec-
ts. Statistical Science 6, 15-51.
Ruppert, D., Wand, M. P. and R. J. Carroll, (2003). Semiparametric Regression, Cam-
bridge University Press.
Walker, E. and Wright, S. P. (2002). “Comparing Curves Using Additive Models,”
Journal of Quality Technonlgy, 34, 118-129.
Williams, J. D., Woodall, W. H. and Birch, J. B. (2007). “Statistical Monitoring of No-
nlinear Product and Process Quality Profiles,” Quality and Reliability Engineering
International, 23, 925-941.
Williams, J. D., Birch, J. B., Woodall, W. H., and Ferry, N. M. (2007). “Statistical Mo-
nitoring of Heteroscedastic Dose-Response Profiles From High-Throught Screeni-
ng,”Journal of Agricultural, Biological, and Environmental Statistics, 12, 216-235.
Woodall, W. H., Spitzner, D. J., Montgomery, D.C., and Gupta, S. (2004). “Using Co-
ntrol Charts to Monitor Process and Product Quality Profiles,” Journal of Quality Technonlgy, 36, 309-320.
Zou, C., Zhang, Y., and Wang, Z. (2006). “Control Chart Based on Change-Point Mo- del for Monitoring Linear Profiles,” IIE Transactions, 38, 1093-1103.
Zou, C., Tsung, F., and Wang, Z. (2008). “Monitoring Profiles Based on Nonparamet- ric Regression Methods,” Technometrics, 50, 512-526.