現今消費性電子產品之規格型號多樣且生命週期短，多委外由電子製造代工廠透過大量人力進行整機組裝的工作，尚無一彈性自動化解決方案可完全取代。若一個半成品在歷經人力組裝成整機之後，未通過測試且發現缺陷來自於板端階段時，則必需拆解、維修並重回板端階段測試，無疑造成浪費。
　　本研究提出一個包含三階段的方法，以馬可夫鏈表達一個半成品在板端測試階段之有限狀態轉移機率為始，再透過機器學習之類神經網路演算法進行訓練和學習半成品測試結果為失敗之特徵，讓生產管理人員能夠在半成品進入組裝線之前，便能預測是否能通過後續測試工站的測試，降低前述問題發生機率和提早進行相應的措施。
　　本研究透過一間製造智慧型行動電話的工廠，運用已儲存於現場管制系統(SFC)的資料，實證可成功辦識出93%以上的半成品可能在接續的製程無法通過測試。除了不需額外投資相關物聯網感應器至人力組裝產線外，更提供一個成功應用隨機過程理論和機器學習於電子產品組裝線之實證案例。

Today's consumer electronics have a variety of specifications and models; moreover, the life-cycle of such products is getting shorter as well. Most of the electronics are produced by outsourced manufacturing foundries under a large amount of manpower to assemble the end items. For most cases, no flexible automation solutions can be completely exploited. If a semi-manufactured product undergoes manpower assembly into a complete product but fails the test due to the defect from the board-level stage, it must be dismantled, repaired, and returned to the board-level test, which is undoubtedly time- and cost-consuming.
This study proposes a three-stage approach that uses the Markov chain property to represent the limited state transition probability of a semi-finished product in the board-level test phase, and then learns the failure features of test data by training through neural network algorithms. The machine learning approach can help production managers to predict whether they can pass the test of the station tests before the semi-finished product enters the assembly line, which reduces the probability of the aforementioned problems and even take appropriate actions earlier.
The practical data that has been already stored in the SFC system to process at a smartphone manufacturing foundry were tested by using our approach. The experimental result shows that more than 93% of the semi-finished products may fail to pass the test in the subsequent process. Based on our approach, an empirical and successful application of such machine learning techniques to electronic product assembly lines was demonstrated. In particular, there is no need of the additional investments in related IOT sensors to the human assembly line.

中文文獻
[1] 吳嘉芳(譯)(2017)。Deep Learning 用Python進行深度學習的基礎理論實作(原作者：斎藤康毅)。臺北市：碁峰資訊。
[2] 施威麟(2015)。運用倒傳遞類神經網路預測錫銀凸塊電鍍參數。國立清華大學工業工程與工程管理學系碩士在職專班論文。
[3] 陳俊元(2002)。筆記型電腦廠系統組裝線診斷與改善。國立清華大學工業工程與工程管理學系碩士論文。
[4] 張殿文(2008)。虎與狐：郭台銘的全球競爭策略。臺北市：遠見天下文化。
[5] 潘照賢、葉瑞徽(譯)(2011)。作業研究 第九版(原作者：Frederick S. Hillier & Gerald J. Lieberman)。臺北市：麥格羅希爾。

英文文獻
[6] Alex Braylan, Risto Miikkulainen (2015). A Neural Network Approach to Model Learning for Stochastic Discrete Environments. Proceedings of the 2015 General Intelligence in Game-Playing Agents Workshop.
[7] Clark, A.J., A.J. White, P.G. Leany, A.J. Wycherley (1995). A Quality Modeling System for Predicting the Yield of Assembly and Test Processes in the Printed Circuit Assembly Industry. Journal of Electronics Manufacturing, 5(2), 75-87.
[8] Darui Zhang, Bin Xu, Jasmine Wood (2016). Predict Failures in Production Lines. IEEE International Conference on Big Data. doi:10.1109/BigData.2016.7840832
[9] Felipe Helo (2000). Decision Support System to Predict the Manufacturing Yield of Printed Circuit Board Assembly Lines. Master thesis to the Faulty of the Virginia Polytechnic Institute and State University.

[10] George C. Hadjinicola (2002). A Markov chain model of serial production systems with rework. A thesis to the department of Public and Business Administration, School of Economics and Management.
[11] Hiroshi Saito, Ken Takiyama, Masato Okada (2015). Estimation of State Transition Probabilities: A Neural Network Model. Journal of the Physical Society of Japan, 84(12). doi:10.7566/JPSJ.84.124801
[12] Hitest Rajput, Lalit Kumar Singh (2013). An approach to find the transition probabilities in Markov chain for early prediction of software reliability. International Journal of Latest Research in Science and Technology, 2(6), 111-115.
[13] Iuliana Teodorescu(2009). Maximum Likelihood Estimation for Markov Chains. A thesis to the department of Statistics, University of New Mexico, Albuquerque.
[14] Jongpil Lee, Jiyoung Park, Keunhyoung Luke Kim and Juhan Nam (2018). SampleCNN: End-to-End Deep Convolutional Neural Networks Using Very Small Filters for Music Classification. Applied Sciences. doi:10.3390/app8010150
[15] Joseph, L.A., J.T. Watt, and N. Wigglesworth (1990). Modeling and Analysis of a New Product Development in Electronics Sub-Assembly Manufacturing. Proceedings of the 1990 Winter Simulation Conference.
[16] Kei-Yuan Yu, Dennis L. Bricker (1990). Analysis of a Markov Chain Model of a Multistage Manufacturing System with Inspection, Rejection, and Rework. IIE Transactions, 25(1), 109-112. doi:10.1080/07408179308964271
[17] Luciana C. D. Campos, Marley M. B. R., Vellasco, Juan G. L. Lazo (2011). A Stochastic Model based on Neural Networks. The 2011 Internatinal Joint Conference on Neural Networks. doi:10.1109/IJCNN.2011.6033399
[18] Orsejo (1998). Test Strategies for PCB Manufacturing. Future Circuits International.
[19] Ossama Abdel-Hamid, Abdel-rahman Mohamed, Hui Jiang, Li Deng, Gerald Penn, and Dong Yu (2014). Convolutional Neural Networks for Speech Recognition. IEEE/ACM Transactions on Audio, Speech, And Language Processing, 22(10). 1533-1545. doi:10.1109/TASLP.2014.2339736
[20] Stanley B. Gershwin, Saeideh Fallah-Fini (2007). A General Model and Analysis of a Discrete Two-Machine Production Line. A thesis to the Massachusetts Institute of Technology.
[21] Tie Liu (2010). Application of Markov Chains to Analyze and Predict the Time Series. Modern Applied Science, 4(5). doi:10.5539/mas.v4n5p162
[22] Xi Xiao, Zhenlong Wang, Qing Li, Shutao Xia, Yong Jiang (2015). Back-propagation neural network on Markov chains from system call sequences: a new approach for detecting Android malware with system call sequences. IET Information Security, 11(1), 8-15. doi:10.1049/iet-ifs.2015.0211
[23] Zhiguang Wang, Tim Oates (2015). Encoding Time Series as Images for Visual Inspection and Classification Using Tiled Convolutional Neural Networks. Workshops at the Twenty-Ninth AAAI Conference on Artificial Intelligence.