因應高效、節能與輕薄的電子產品需求，晶圓代工廠無不極力開發更小奈米製程，然而此種製程需要以電子束檢測不良之晶片。本研究個案公司為知名的設備開發商，在因應訂單少量客製化之特性下，於組裝檢測機台時，在高壓模組灌膠製程並無充足的資料進行缺陷原因分析。在考量其試產資料特性後，本論文提出一個新虛擬樣本產生法，其藉由將輸入數值屬性視為名目屬性，學習輸入值與輸出值之模糊關係，並基於此模糊關係產生虛擬樣本而增加訓練樣本數量。在實驗部分，本研究從個案公司取得52筆真實試產資料進行不同訓練樣本數的交互驗證，並以倒傳遞類神經網路以及支撐向量迴歸進行預測模式的建構。方法比較部分，本論文採用Bootstrap aggregating (Bagging) 以及Synthetic Minority Over-sampling Technique (SMOTE)兩種虛擬樣本產生法，進行樣本增量後的預測準確度比較。實驗結果發現，除本研究所提出的方法外，Bagging與SMOTE並無法有效改善倒傳遞類神經網路以及支撐向量迴歸對於個案資料的預測準確度。透過本論文之方法，期待能持續協助個案公司之製程工程師發展出高產出良率的製造參數。

In response to the demand for high-efficiency, energy-saving, and light electronic products, foundries are all striving to develop smaller nano-fabrication processes. However, such processes require E-beam inspection of defective chips. In this case, the company is a well-known equipment developer. Under the characteristics of a small amount of customization in response to orders, when assembling the inspection machine, there is not enough information in the high-voltage module potting process for defect analysis. After considering the characteristics of its trial-run data, this paper proposes a new virtual sample generation method, which learns the fuzzy relationship between input values and output values by treating input numerical attributes as nominal attributes, and generates virtual samples based on this fuzzy relationship. Increase the number of training samples. In the experimental part, we obtained 52 real trial production data from the case company to conduct interactive verification of different training sample numbers, and used the back-propagation neural network and support vector regression to construct the prediction model. In the method comparison, this thesis uses Bootstrap aggregating (Bagging) and Synthetic Minority Over-sampling Technique (SMOTE) two virtual sample generation methods to compare the prediction accuracy after sample increment. The experimental results show that, in addition to the methods proposed in this research, Bagging and SMOTE cannot effectively improve the prediction accuracy of the back-propagation neural network and support vector regression for case data. Through the method of this paper, we look forward to continuously assisting the engineer of the case company to develop high-yield parameters.

中文文獻
1. 郭家宏.(2019,0612).TechOrange,台積電兩奈米技術落腳竹科,摩爾定律在台灣延續不死!.取自https://buzzorange.com/techorange/2019/06/12/tsmc-3nm-and-2nm/
2. 張秉鳳.(2012,0224).工商時報.電子束檢測設備出頭天.取自　　https://tw.news.yahoo.com/%E9%9B%BB%E5%AD%90%E6%9D%9F%E6%AA%A2%E6%B8%AC%E8%A8%AD%E5%82%99%E5%87%BA%E9%A0%AD%E5%A4%A9-213000176.html
3. Liu, M.(2016,0725). 科技新報.解析英特爾、台積電、三星14/16奈米的魔幻數字,三者製程真的差很大?取自http://technews.tw/2016/07/25/intel-tsmc-samsung-node/
4. 陳惠昭 (2013) 。使用整體趨勢擴展技術提升多模式整合法之預測準確率。國立成功大學工業管理科學研究所碩士論文。
5. 黃文定 (2013) 。使用基於屬性趨勢相似度生成之虛擬樣本建構液晶面板廠之高維度資料製造模式。國立成功大學工業管理科學研究所博士論文。
6. 陳建頲(2012) 。整合以模糊分群擷取之事前知識的資訊擴散方法學習小樣本資料。國立成功大學工業管理科學研究所碩士論文。
7. 陳誌瑋(2013) 。藉由盒鬚圖產生之虛擬樣本提升拔靴集成法的分類正確率。國立成功大學工業管理科學研究所碩士論文。

英文文獻
1. Breiman, L., Friedman, J. H., Olshen, R. A., & Stone, C. J. (1984). Classification and Regression Trees. Wadsworth and Brooks.
2. Cortes, C., & Vapnik, V. (1995). Support-Vector Networks. Machine Learning, 20(3), 273-297.
3. Dobra, A., & Gehrke, J. E. (2002). SECRET: A Scalable Linear Regression Tree Algorithm. Proceedings Eighth ACM SIGKDD International Conferenceon Knowledge Discovery and Data Mining, 481-487.
4. Efron, B., & Tibshirani, R. J. (1993). An Introduction to the Bootstrap: New York: Chapmen & Hall.
5. Guo, G. D., & Dyer, C. R. (2005). Learning from examples in the small sample case: Face expression recognition. IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics, 35(3), 477-488.
6. Hong, T. P., Tseng, L. H., & Chien, B. C. (2010). Mining from incomplete quantitative data by fuzzy rough sets. Expert Systems with Applications, 37(3), 2644-2653.
7. Huang, C. F. (1997). Principle of information. Fuzzy Sets and Systems, 91(1), 69-90.
8. Huang, C. F., &Moraga, C. (2004). A diffusion-neural-network for learning from small samples. International Journal of Approximate Reasoning, 35(2), 137-161.
9. Huang, C. J., Wang, H. F., Chiu, H. J., Lan, T. H., Hu, T. M., & Loh, E. W. (2009). Prediction of the Period of Psychotic Episode in Individual Schizophrenics by Simulation-Data Construction Approach. Journal of Medical Systems, 34(5), 799-808.
10. Ivănescu, V. C., Bertrand, J. W. M., Fransoo, J. C., & Kleijnen, J. P. C. (2006). Bootstrapping to solve the limited data problem in production control: an application in batch process industries. Journal of the Operational Research Society, 57(1), 2-9.
11. Jang, J. S. R. (1993). ANFIS: adaptive-network-based fuzzy inference system. IEEE Transactions on Systems, Man and Cybernetics, 23(3), 665-685.
12. Jennrich, R. I., & Schluchter, M. D. (1986). Unbalanced repeated-measures models with structured covariance matrices. Biometrics, 42(4), 805-820.
13. Karalic, A. (1992). Employing linear regression in regression tree leaves. Paper presented at the Proceedings of the 10th European Conference on Artificial Intelligence, Vienna, Austria.
14. Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38(4), 963-974.
15. Lanouette, R., Thibault, J., & Valade, J. L. (1999). Process modeling with neural networks using small experimental datasets. Computers & Chemical Engineering, 23(9), 1167-1176.
16. Lapedus, M.(2018,0118).SemiconductorEngineering,E-Beam Inspection Makes Inroads.Retrieved from https://semiengineering.com/e-beam-inspection-makes-inroads/
17. Li, D. C., Chang, F. M. M., & Chen, K. C. (2010a). Building reliability growth model using sequential experiments and the Bayesian theorem for small datasets. Expert Systems with Applications, 37(4), 3434-3443.
18. Li, D. C., Chen, C. C., Chang, C. J., & Chen, W. C. (2012a). Employing Box-and-Whisker plots for learning more knowledge in TFT-LCD pilot runs. International Journal of Production Research, 50(6), 1539-1553.
19. Li, D. C., Chen, C. C., Chen, W. C., & Chang, C. J. (2012b). Employing dependent virtual samples to obtain more manufacturing information in pilot runs. International Journal of Production Research, 50(23), 6886-6903.
20. Li, D. C., Chen, C. C., Chang, C. J., & Lin, W. K. (2012c). A Tree-based-Trend-Diffusion prediction procedure for small sample sets in the early stages of manufacturing systems. Expert Systems with Applications, 39(1), 1575-1581.
21. Li, D. C., Chen, L. S., & Lin, Y. S. (2003). Using Functional Virtual Population as assistance to learn scheduling knowledge in dynamic manufacturing environments. International Journal of Production Research, 41(17), 4011-4024.
22. Li, D. C., Fang, Y. H., Lai, Y. Y., & Hu, S. C. (2009a). Utilization of virtual samples to facilitate cancer identification for DNA microarray data in the early stages of an investigation. Information Sciences, 179(16), 2740-2753.
23. Li, D. C., Hsu, H. C., Tsai, T. I., Lu, T. J., & Hu, S. C. (2007a). A new method to help diagnose cancers for small sample size. Expert Systems with Applications, 33(2), 420-424.
24. Li, D. C., & Lin, Y. S. (2006). Using virtual sample generation to build up management knowledge in the early manufacturing stages. European Journal of Operational Research, 175(1), 413-434.
25. Li, D. C., Liu, C. W., Fang, Y. H., & Chen, C. C. (2010b). A yield forecast model for pilot products using support vector regression and manufacturing experience-the case of large-size polariser. International Journal of Production Research, 48(18), 5481-5496.
26. Li, D. C., Shi, Q. S., & Li, M. D.(2018). Using an attribute conversion approach for sample generation to learn small data with highly uncertain features. International Journal of Production Research, 56(14), 4954-4967.
27. Li, D. C., Tsai, T. I., & Shi, S. (2009b). A prediction of the dielectric constant of multi-layer ceramic capacitors using the mega-trend-diffusion technique in powder pilot runs: case study. International Journal of Production Research, 47(1), 51-69.
28. Li, D. C., Wu, C. S., & Chang, F. M. M. (2005). Using data-fuzzification technology in small data set learning to improve FMS scheduling accuracy. International Journal of Advanced Manufacturing Technology, 27(3-4), 321-328.
29. Li, D. C., Wu, C. S., Tsai, T. I., & Chang, F. M. M. (2006). Using mega-fuzzification and data trend estimation in small data set learning for early FMS scheduling knowledge. Computers & Operations Research, 33(6), 1857-1869.
30. Li, D. C., Wu, C. S., Tsai, T. I., & Lina, Y. S. (2007b). Using mega-trend-diffusion and artificial samples in small data set learning for early flexible manufacturing system scheduling knowledge. Computers & Operations Research, 34(4), 966-982.
31. Loh, W. Y. (2002). Regression trees with unbiased variable selection and interaction detection. Statistica Sinica, 12(2), 361-386.
32. Ma, E., Chou, K., Ebert, M., Liu, X., Ren, W., Hu, X.,…, Patterson, O. D. (2019,0326).SPIE.DIGITAL LIBRARY. Multiple beam inspection (MBI) for 7nm node and beyond : technologies and applications. Retrieved from https://www.spiedigitallibrary.org/conference-proceedings-of-spie/10959/109591R/Multiple-beam-inspection-MBI-for-7nm-node-and-beyond/10.1117/12.2515272.full
33. Niyogi, P., Girosi, F., & Poggio, T. (1998). Incorporating prior information in machine learning by creating virtual examples. Proceedings of the IEEE, 86(11), 2196-2209.
34. Oberai, A., Yuan, J. S. (2017,1020).Researchgate.Smart E-Beam for Defect Identification & Analysis int the Nanoscale Technology Nodes: Technical Perspectives. Retrieved from
https://www.researchgate.net/publication/320561955_Smart_E-Beam_for_Defect_Identification_Analysis_in_the_Nanoscale_Technology_Nodes_Technical_Perspectives
35. Oniśko, A., Druzdzel, M. J., & Wasyluk, H. (2001). Learning Bayesian network parameters from small data sets: application of Noisy-OR gates. International Journal of Approximate Reasoning, 27(2), 165-182.
36. Quinlan, J. R. (1992). Learning with Continuous Classes. Paper presented at the Proceedings Australian Joint Conference on Artificial Intelligence, World Scientific, Singapore.
37. Rumelhart, D. E., Hintont, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. Nature, 323(6088), 533-536.
38. Sugeno, M.,& Kang, G. T. (1988).Structure identification of fuzzy model, Fuzzy Sets and Systems, 28,15–33.
39. Thomas, M., Kanstein, A., & Goser, K. (1997). Rare fault detection by possibilistic reasoning. Paper presented at the In Proceedings of Fuzzy Days, Reusch, Bernd, Berlin.
40. Tukey, J. W. (1977). Exploratory data analysis: Reading (MA): Addison-Wesley.
41. Wang, H. F., & Huang, C. J. (2009). Data construction method for the analysis of the spatial distribution of disastrous earthquakes in Taiwan. International Transactions in Operational Research, 16(2), 189-212.
42. Wang, Y., &Witten, I. (1997). Inducing Model Trees for Continuous Classes. Paper presented at the Proceedings of the Poster Papers of the European Conference on Machine Learning, Prague, Czech Republic.
43. Wang, Y. F. (2003). On-demand forecasting of stock prices using a real-time predictor. IEEE Transactions on Knowledge and Data Engineering, 15(4), 1033-1037.
44. Willemain, T. R., Bress, R. A., & Halleck, L. S. (2003). Enhanced simulation inference using bootstraps of historical inputs. IIE Transactions, 35(9), 851-862.
45. Wolpert, D. H. (1992). Stacked Generalization. Neural Networks, 5(2), 241-259.
46. Witten, I. H., Frank, E. (2005). Data Mining：Practical Machine Learning Tools and Techniques (2nd ed.). San Francisco：Morgan Kaufmann.