在許多實際的製程裡，產品或製程的品質特性是由一反應變數和一個或多個解釋變數的函數關係來界定，這種反應變數和解釋變數之間的關係稱為輪廓，而其資料形式被稱為輪廓的數據。在第二階段製程監控的實際應用中，製程參數往往是未知的，但可以用管制狀態下的歷史資料來估計，而Self-starting是一個可以結合歷史資料與新資料資訊來估計參數的方法，且同時可以進行線上監控。在大部分研究輪廓監控的文獻上，都是假設每組樣本有n對觀測值，然而在實際應用上，常因生產成本或生產速度等其他因素，導致每組樣本只有一對觀測值。在本文中，我們提出一個在第二階段裡針對單一觀測值之輪廓資料的監控方法。我們提出將Self-starting技術應用在兩個管制圖上，並比較兩者的監控能力。同時，我們討論在製程失控警訊發生後，如何準確估計製程改變點以及診斷造成可歸屬變因的參數，這些檢查將幫助使用者準確快速地採取改正動作。最後，我們以一個實例來闡述我們所提出的方法是如何操作及使用。

[1] Box, G. E. P. (1954). Some Theorems on Quadratic Forms Applied in the Study of
Analysis of Variance Problems: Effect on Inequality of Variance in One-Way Cla-
ssification. Annals of Mathematical Statistics 25, pp. 290-302.
[2] Hawkins, D. M. (1987). Self-Starting CUSUM Charts for Location and Scale.
The Statistician 36, pp. 299-315.
[3] Hawkins, D. M. (1991). Diagnostics for Use with Regression Recursive Residuals.
Technometrics 33, pp. 221-234.
[4] Hawkins, D. M. and Olwell, D. H. (1998). Cumulative Sum Charts and Charting
for Quality Improvement. Springer-Verlag, New York, NY.
[5] Hawkins, D. M., Qiu, P., and Kang, C. W. (2003). The Changepoint Model for Sta-
tistical Process Control. Journal of Quality Technology 35, pp. 355-366.
[6] Hawkins, D. M. and Zamba, K. D. (2005a). A Change-Point Model for a shift in
Variance. Journal of Quality Technology 37, pp. 21-31.
[7] Hawkins, D. M. and Zamba, K. D. (2005b). Statistical Process Control for Shifts
in Mean or Variance Using a Change-Point Formulation. Technometrics 47, pp.
164-173.
[8] Huwang, Longcheen, Yeh, Wang, Yi-Hua Tina and Chen, Z. Jason (2008). On the
Exponentially Weighted Moving Variance. Technical report. Statistics Institute,
NTHU.
[9] Jensen, W. A., Birch, J. B., and Woodall, W. H. (2007). High Breakdown Estima-
tion Methods for Phase I Multivariate Control Charts, To appear in Quality and
Reliability Engineering International.
[10] Kang, L. and Albin, S. L. (2000). On-Line Monitoring When Process Yields Li-
near Profiles. Journal of Quality Technology 32, pp. 418-426.
[11] Kim, K., Mahmoud, M.A., and Woodall, W. H. (2003). On the Monitoring of Li-
near Profiles. Journal of Quality Technology 35, pp. 317-328.
[12] Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data. 2nd ed.,
John Wiley & Sons, New York, NY.
[13] MacGregor, J. F. and Harris, T. J. (1993). The Exponentially Weighted Moving
Variance. Journal of Quality Technology 25, pp. 106–118.
[14] Mestek, O., Pavlik, J., and Sucjanek, M. (1994). Multivariate Control Charts:
Control Charts for Calibration Curves. Fresenius’ Journal of Analytical Chemistry
350, pp. 344-351.
[15] Reynolds, M. R. JR. and Stoumbos, Z. G. (2001). Monitoring the Process Mean
and Variance Using Individual Observations and Variable Sampling Intervals.
Journal of Quality Technology 33, pp. 181-204.
[16] Mahmoud, M. A., and Woodall, W. H. (2004). Phase I Analysis of Linear Profiles
with Calibration Applications. Technometrics 46, pp. 380-391.
[17] Roberts, S. W. (1959). Control Chart Tests Based on Geometric Moving Average-
s. Technometrics 1, pp. 239-250.
[18] Walker, E., and Wright, S. (2002). Comparing Curves Using Additive Models.
Journal of Quality Technology 34, pp. 118-129.
[19] Williams, J. D. (2005). Contributions to Profile Monitoring and Multivariate Sta-
tistical Process Control. Unpublished doctoral dissertation, Department of Statisti-
cs, Virginia Polytechnic Institute & State University.
[20] Williams, J. D., Woodall, W. H., and Ferry, N. M. (2006). Statistical Monitoring
of Heteroscedastic Dose-Response Profiles from High-Throughput Screening.
Submitted to Journal of Agricultural, Biological, and Environmental Statistics.
[21] Zou, C., Zhou, C., Wang, Z. and Tsung, F. (2007). A Self-Starting Control Chart
for Linear Profiles. Journal of Quality Technology 39, pp. 364-375.
[22] Zou, C., Tsung, F. and Wang, Z. (2007). Monitoring General Linear Profiles Usi-
ng Multivariate Exponentially Weighted Moving Average Schemes.
Technometrics 49, pp. 395-408.