資料前處理為決定虛擬量測精度的關鍵因素之一，其主要目的為確保資料品質，以避免異常資料影響虛擬量測預測之精度。為達到資料之完整性與正確性，必須透過一評估基準偵測正常與異常資料之特性，以便將異常資料排除，進而提昇預測精確性。

本研究提出一資料品質評估指標 (Data Quality Index, DQI) 架構，以便能精確地偵測出異常資料。本研究依據製程參數之物理特性與量測參數之穩定性，針對量測資料及製程資料分別建構其資料品質評估指標，並定義合理之偵測門檻值。一般而言，量測資料為單一且獨立之變數，所以其資料品質評估指標能以個別值管制圖建構之，而其門檻值則可視其製程穩定情況來訂定管制上下限。因製程資料為多變量型態且變數與變數之間存在自我相關性，所以必須採多變量殘差管制方法建構之，即以自我迴歸整合移動平均之時間序列模型將數據模型化，再利用 Hotelling T2 管制方法將其殘差整合成一個綜合性的資料品質指標；而判斷異常之基準則以其是否符合 T2 本身的分配，來訂定其門檻值。為避免因時間漂移而發生過多的誤警，可利用雙階段虛擬量測架構的自動調整機制，來即時更新資料品質評估指標模型，如此即可降低誤警率。最終，藉由與其他學者所提出之兩種方法來進行實驗與比較，並考量應用於虛擬量測之實作上的需求來進行相關修正，以驗證本架構之可行性與效能。

Data preprocess is one of the critical factors in determining the conjecture accuracy of virtual metrology (VM). Abnormal data will influence VM’s conjecture accuracy. To assure the completeness and accuracy of data, an evaluation scheme must be established to distinguish abnormal data from normal ones. By detecting and deleting abnormal data, VM’s conjecture accuracy can be effectively enhanced.

This work proposes an data quality evaluation scheme to check each data set’s data quality index (DQI) for precisely detecting abnormal data. The DQI of production data and the DQI of metrology data are constructed according to the physical properties of production data and the stable characters of metrology data, respectively. In general, metrology data are independent uni-variates, so we can use X chart to construct DQI for monitoring the performance of metrology data. Thus, the threshold of metrology DQI can be determined by setting the regular SPC upper and lower control limits. Since parameters of production data are not only multiple but autocorrelated, multiple residual control chart is adopted in this study to monitor its performance. This study employs ARIMA method to model the time series data first, then utilizes Hotelling T2 control method to convert those multiple residuals to a synthetic data quality index (DQI). The threshold of production DQI is defined by using the confidence region of the F distribution. Re-training is essential for keeping the DQI models fresh. The DQI-model re-training timing should be synchronized with the VM-model re-training timing specified in the dual-phase VM scheme. Finally, considering VM’s real-time requirements, experimental results show that the proposed DQI scheme is more efficient and feasible than the two existing methods.

[1] 2003 International Technology Roadmap for Semiconductors (ITRS), December 2003. http://public.itrs.net/.
[2] Y.-C. Chang and F.-T. Cheng, “Application Development of Virtual Metrology in Semiconductor Industry,” in Pro. of the 31st Annual Conference of the IEEE Industrial Electronics (IECON 2005), Raleigh, North Carolina, USA, pp. 124-129, November 2005.
[3] P.-H. Chen, S. Wu, J.-S. Lin, F. Ko, H. Lo, J. Wang, C.-H. Yu, and M.-S. Liang, “Virtual Metrology: a Solution for Wafer to Wafer Advanced Process Control,” in Proc. 2005 IEEE International Symposium on Semiconductor Manufacturing, San Jose, CA ,USA, pp.155-157, Sept. 2005.
[4] Y.-C. Su, M.-H. Hung, F.-T. Cheng, and Y.-T. Chen, “A Processing Quality Prognostics Scheme for Plasma Sputtering in TFT-LCD Manufacturing,” IEEE Transactions on Semiconductor Manufacturing, vol. 19, no. 2, pp. 183-194, May 2006.
[5] Y.-C. Su, F.-T. Cheng, M.-H. Hung, and H.-C. Huang, “Intelligent Prognostics System Design and Implementation,” IEEE Transactions on Semiconductor Manufacturing, vol. 19, no. 2, pp. 195-207, May 2006.
[6] Y.-J. Chang, Y. Kang, C.-L. Hsu, C.-T. Chang, and T. Y. Chan, “Virtual Metrology Technique for Semiconductor Manufacturing,” in Proc. 2006 International Joint Conference on Neural Networks (IJCNN’06), pp. 5289-5293, July 2006.
[7] M.-H. Hung, T.-H. Lin, F.-T. Cheng, and R.-C. Lin, “A Novel Virtual Metrology Scheme for Predicting CVD Thickness in Semiconductor Manufacturing,” to appear in IEEE/ASME Transactions on Mechatronics, vol. 12, no. 3, June 2007.
[8] Y.-T. Huang, F.-T. Cheng, and Y.-T. Chen, “Importance of data quality in virtual metrology,” in Proc. of the 32nd Annual Conference of the IEEE Industrial Electronics Society (IECON 2006), Paris, France, pp.3727-3732, Nov. 2006.
[9] 梁志翔 「虛擬量測自變數之篩選法則」，國立成功大學製造工程研究所碩士論文，2006。
[10] Y.-C. Su, M.-H. Hung, F.-T. Cheng, and Y.-T. Chen, “A Processing Quality Prognostics Scheme for Plasma Sputtering in TFT-LCD Manufacturing,” IEEE Transactions on Semiconductor Manufacturing , vol. 19, issue 2, pp. 183-194, 2006.
[11] T.-H. Lin, M.-H. Hung, R.-C. Lin, and F.-T. Cheng, “A Virtual Metrology Scheme for Predicting CVD Thickness in Semiconductor Manufacturing,” in Proc. Of IEEE International Conference on Robotics and Automation, 2006.
[12] F.-T. Cheng, H.-C. Huang, and C.-A. Kao, “Developing a Dual-Phase Virtual Metrology Scheme,” to appear in IEEE Transactions on Semiconductor Manufacturing.
[13] G. Spitzlsperger, C. Schmidt, G. Ernst, H. Strasser, and M. Speil, “Fault Detection for a Via Etch Process Using Adaptive Multivariate Methods,” IEEE Transactions on Semiconductor Manufacturing, vol. 18, no. 4, pp. 528-533, Nov. 2005.
[14] C. J. Spanos, H. F. Guo, A. Miller, and J. Levine-Parrill, “Real-Time Statistical Process Control Using Tool Data,” IEEE Transactions on Semiconductor Manufacturing, vol. 5, no. 4, pp. 308-318, Nov. 1992.
[15] 陳炳宏 「半導體電漿製程的錯誤診斷與預測─時間序列的光譜多變數模型與分析」，國立東華大學電機工程研究所碩士論文，2005。
[16] 王慧君 「馬氏─田口系統之特性探討及其於信用評分之應用」，國立交通大學工業工程與管理所博士論文，2004。
[17] R. Azencott, “System monitoring method,” United States Patent, Jul. 2003.
[18] 徐雅甄 「EWMA管制圖對自相關性製程的常態假設穩健性之研究」，國立交通大學統計學研究所碩士論文，2003。
[19] E. G. Schilling and P. R. Nelson, “The Effect of Nonnormality on the Control Limits of Charts,” Journal of Quality Technology , vol. 8 , no. 4, pp. 183-188, 1976.
[20] 鄭春生 「品質管理」，三民書局，台北，1995。
[21] D. C. Montgomery, “Introduction to Statistical Quality Control,” Willy, New York, 2001.
[22] 王亞倫 「診斷多變量管制圖之研究」，國立中央大學工業管理研究所碩士論文，2000。
[23] 楊曉靜 「多變量之多重比較─應用於品質管制圖」，國立台北大學統計學研究所碩士論文，1999。
[24] 許雅棠 「多變量與加權總平均之多重比較─應用於多變量品質管制」，國立台北大學統計學研究所碩士論文，2000。
[25] S. A. Yourstone and D. C. Montgomery, “Time-series approach to discrete real-time process quality control,” Quality and Reliability Engineering International, 5, 309-317, 1989.
[26] G. E. P. Box and G. M. Jenkins, “Time Series Analysis, Forecasting and Control,” Holden Day, San Francisco, CA, 1976.
[27] 楊奕農 「時間序列分析：經濟與財務上之應用」，雙葉書廊，2005。
[28] 陳耀茂 「時間序列分析的SPSS使用手冊」，鼎茂圖書，2004。
[29] 張智星 「MATLAB程式設計」，清蔚科技，2004。