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研究生： 游韋翔
Wei-Hsiang YU
論文名稱： Unreplicated Designs for Random Noise Exploration
指導教授： 張明中
Ming-Chung Chang
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 統計研究所
Graduate Institute of Statistics
論文出版年： 2020
畢業學年度： 108
語文別： 英文
論文頁數： 34
中文關鍵詞： 純誤差 、高斯過程 、質量改善 、色散效應
外文關鍵詞： Pure error, Gaussian process, Quality improvement, Dispersion effects
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    • 在工業系統當中，了解系統變異非常重要。雖然不同的處理組合提供了反應曲面波動的訊息，但當系統較為複雜時，不同的處理組合將難以萃取真實系統變異的資訊。一種常見的解決方式為執行重複實驗點，然而重複實驗點卻無法提供反應曲面波動的訊息，而且經常被視為增加成本的一種做法。在本篇論文我們推導出一個期望損失準則，並藉由此準則來建立沒有重複實驗點卻包含系統變異資訊的實驗設計，同時這些設計點也提供反應曲面波動的資訊。

    Grasping the variation of system plays a crucial role in industrial systems. Different treatment combinations provide the information about the fluctuation of response surfaces. However, they are unable to extract the exact information of pure errors if the model is complex. Conducting replicates is one solution. On the other hand, replication does not provide information about response surfaces and is usually treated as a waste. In this thesis, we derive an expected loss criterion and aim at constructing unreplicated designs containing as much information of pure error as possible. These points are capable of exploring the response surface as well.

    Contents Abstract i List of Tables ii List of Figures iii 1 Introduction 1 2 Literature Review 3 2.1 Gaussian Process . . . . . . . . . . . . . . . . . 3 2.2 Expected Improvement Optimization . . . . . . . . 4 3 Methodology 6 3.1 Loss Function . .. . . . . . . . . . . . . . . . . 6 3.2 Algorithm . . . . . . . . . . . . . . . . . . . . 7 4 Simulation Study 9 5 Real Example 19 6 Conclusion 21 References 22

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