隨著半導體摩爾定律不斷推進，積體電路不斷得微縮，製程的複雜度日益提高，只要製程有一環節出錯，都將造成時間和金錢成本的巨大浪費，甚至導致公司整體競爭力下降。再者，隨著製程精進，設備投資愈大，產品良率的提高才能創造獲利空間。然而，製程的進步導致資料量龐大而復雜，因此難以從如此龐大的歷史資料中快速搜尋影響良率的根本原因。有鑑於此，Cheng et al. [1] 提出了Key-variable Search Algorithm（KSA）來解決此問題。KSA透過分析歷史資料：機台路徑資料、製程資料、站點間量測資料、缺陷資料和最終檢測資料，為用戶提供了一種快速有效的方法來確定良率損失的根本原因。
然而，在半導體工業中，產品品質通常可分為兩種類型：1）良率，其定義為晶圓中起作用的晶片數與晶圓的總晶片數之比。 2）缺陷晶片的累積數量。缺陷晶片的累積數量通常在統計學中定義為計數型資料，而不是在第1類型中提到的連續型的良率資料。
此外，具有正偏態分佈的計數型資料並不適合使用線性回歸模型進行分析，這意味著，當需要分析計數型資料（例：缺陷晶片的累積數量）時，KSA無法準確搜尋出關鍵設備或關鍵參數。為了彌補這一不足，本研究提出了計數型資料搜尋演算法。在計數型資料搜尋模組中提出了三個階段的搜尋流程，分別為關鍵參數的搜尋、關鍵交互作用參數的搜尋和關鍵路徑的搜尋，並可用於在高維度（p >> n）的情況下進行有效的計數型資料搜索，這可以提高KSA在線性回歸搜尋限制中的表現。

As the evolution of Moore’s Law in semiconductor industry, the dimension of integrated circuit shrinks which increases the complexity of the manufacturing process gradually. Once one of the process failed, it will not only cost great loss in time and money but even lower the overall competitiveness of the company. What’s more, as the process progressed, the higher investment in device to have higher yield is the key to generate more profit. However, the process progression leads to large and complicated production-related data, it causes trouble to quickly identify the root causes which affects the yield in such huge historical data. In view of resolving the problem, Cheng et al. [1] proposed the Key-variable Search Algorithm（KSA）. KSA scheme offers a quick and efficient way for users to identify the root causes which caused yield loss via analyzing the historical data including production routes, process data, inline data, defects, and final inspection results.
Nevertheless, in the semiconductor industry, product quality performance is often divided into two types: 1) The common yield, which defines as the ratio of the number of functioning dies to the total number of dies in the wafer; 2) The number of defect dies. The cumulative number of defective dies is usually defined statistically as count data, rather than continuous yield data mentioned previously.
Moreover, the count data with a positively-skewed distribution may not fit well in the linear regression model, which means when encountering the analysis data of count data (such as the cumulative number of defective dies), KSA cannot accurately search for the key devices/parameters. In order to compensate for the insufficiency, this study proposed the Count-Data Search Algorithm (CDSA). CDSA proposed 3 search phases flow: key-variable search, interaction-effect search, and golden-path search for the effective count data search under the circumstances of p >> n, which can improve the performance of KSA under linear regression search restriction.

[1] F.-T. Cheng, Y.-S. Hsieh, J.-W. Zheng, S.-M. Chen, R.-X. Xiao and C.-Y. Lin, “A scheme of high-dimensional key-variable search algorithms for yield improvement,” IEEE Robotics and Automation Letters, vol. 2, no. 1, pp. 179-186, January 2017.
[2] L. C. Briand, V. R. Basili, and W. M. Thomas, “A pattern recognition approach for software engineering data analysis,” IEEE Transactions on Software Engineering, vol. 18, no. ll, pp. 931-942, Nov. 1992.
[3] S. J. Hong, W. Y. Lim, T. Cheong, and G. S. May, “Fault detection and classification in plasma etch equipment for semiconductor manufacturing e-Diagnostics,” IEEE Transactions on Semiconductor Manufacturing, vol. 25, issue 1, pp.83-93, Feb 2012.
[4] T. Tsuda, S. Inoue, A. Kayahara, S.-I. Imai, T. Tanaka, N. Sato, and S. Yasuda, “Advanced semiconductor manufacturing using big data,” IEEE Transactions on Semiconductor Manufacturing, vol. 28, no. 3, pp. 229-235, Aug. 2015.
[5] W. H. Woodall, and D. C. Montgomery “Research issues and ideas in statistical process control,” Journal of Quality Technology, vol. 31, no. 4, pp. 376-386, 1993.
[6] S. Cunningham, C. Spanos, and K. Voros, “Semiconductor yield improvement: results and best practices,” IEEE Transactions on Semiconductor Manufacturing , vol. 8, no. 2, pp. 103-109, May 1995.
[7] F. Bergeret and C. L. Gall, “Yield improvement using statistical analysis of process dates,” IEEE Transactions on Semiconductor Manufacturing, vol. 16, no. 3, pp. 535-542, Aug. 2003
[8] F.-L. Chen and S.-F. Liu, “A neural-network approach to recognize defect spatial pattern in semiconductor fabrication,” IEEE Transactions on Semiconductor Manufacturing, vol. 13, no. 3, pp. 366-373, Aug. 2000
[9] U. Hessinger, W. K. Chan, and B. T. Schafman, “Data mining for significance in yield-defect correlation analysis,” IEEE Transactions on Semiconductor Manufacturing, vol. 27, no. 3, pp. 347-356, 2014.
[10] K.-B. Lee, S. Cheon, and C.-O. Kim, “A convolutional neural network for fault classification and diagnosis in semiconductor manufacturing processes,” IEEE Transactions on Semiconductor Manufacturing., vol. 30, no. 2, pp. 135-142, May. 2017.
[11] F.-T. Cheng, C.-Y. Lin, C.-F, Chen, R.-X. Xiao, J.-W. Zheng, and Y.-S. Hsieh, “Blind-stage search algorithm for the key-variable search scheme,” IEEE Robotics and Automation Letters, vol. 2, no. 4, pp. 1840-1847, Oct. 2017.
[12] C.-Y. Lin, Y.-M. Hsieh, F.-T. Cheng, Y.-R. Yang, and M. Adnan, “Interaction-effect search algorithm for the KSA scheme,” IEEE Robotics and Automation Letters, vol. 3, no. 4, pp. 2778-2785, Oct. 2018.
[13] S.M. Sze, “Semiconductor devices: physics and technology,” John wiley & sons, 2018
[14] J. Mullahy, “Specification and testing of some modified count data models,” Journal of econometrics, vol. 33, no. 3, pp. 341-365, Dec. 1986.
[15] G. C. White, R. E. Bennetts, “Analysis of frequency count data using the negative binomial distribution,” Ecology, vol. 77, no. 8, pp. 2549-2557, Dec. 1996.
[16] W. Gardner, E. P. Mulvey, and & E. C. Shaw, “Regression analyses of counts and rates: Poisson, overdispersed Poisson, and negative binomial models,” Psychological bulletin, vol. 118, no. 3, pp. 392-404, 1995.
[17] G. King, “Statistical models for political science event counts: Bias in conventional procedures and evidence for the exponential Poisson regression model,” American Journal of Political Science, vol. 32, no. 3, pp. 838-863, Aug. 1988.
[18] V. Temlyakov, “Greedy algorithms in convex optimization on Banach spaces,” Constructive Approximation, vol. 41, no. 2, pp. 269-296, 2015.
[19] C.-K. Ing. “Model selection for high-dimensional linear regression with dependent observations,” ArXiv abs/1906.07395, 2019.
[20] Park MY, Hastie T., “L1-regularization path algorithm for generalized linear models,” Journal of the Royal Statistical Society B, 69, 659–677, August 2007.
[21] N. Hao, and H. Zhang, “Interaction screening for ultrahigh-dimensional data,” Journal of the American Statistical Association, vol. 109, no. 507, pp. 1285–1301, Feb. 2014.
[22] N.-H. Chan, C.-K. Ing, Y. Li, and C.-Y. Yau, “Threshold estimation via group orthogonal greedy algorithm,” Journal of Business & Economic Statistics, vol. 35, no. 2, pp. 334-345, Mar. 2017.
[23] L. Meier, S. V. D. Geer, and P. Buhlmann, “The group lasso for logistic regression,” Journal of the Royal Statistical Society, vol. 70, no. 1, pp. 54-71, Mar. 2008.
[24] J. M. Marstrand, “The dimension of Cartesian product sets,” In Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 50, No. 2, pp. 198-202, Apr. 1954.