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研究生:游韋翔
研究生(外文):Wei-Hsiang YU
論文名稱(外文):Unreplicated Designs for Random Noise Exploration
指導教授:張明中張明中引用關係
指導教授(外文):Ming-Chung Chang
學位類別:碩士
校院名稱:國立中央大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
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 errorGaussian processQuality improvementDispersion 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
References
[1] Box, G. E. P. and Meyer, R. D. (1986). Dispersion effects from fractional factorial designs.
Technometrics, 28, 19-27.
[2] Wang, P.C. (1989). Tests for dispersion effects from orthogonal arrays. Comput. Statist. Data Anal,
8, 109-117.
[3] Bergman, B. and Hynen, A. (1997). Dispersion effects from unreplicated designs in the 2^k-p series. Technometrics, 39, 191-198.
[4] Liao, C. T. (2000). Identication of dispersion effects from unreplicated 2^n-k fractional factorial
designs. Comput. Statist. Data Anal, 33, 291-289.
[5] Brenneman, W. A. and Nair, V. N. (2001). Methods for identifying dispersion effects in unreplicated factorial experiments: A critical analysis and proposed strategies. Technometrics, 43,
388-405.
[6] McGrath, R. N. and Lin, D. K. J. (2001a). Testing multiple dispersion effects in unreplicated
fractional factorial designs. Technometrics, 43, 406-414.
[7] Tsai, S. F., Liao, C. T., and Chai, F. S. (2012). D-optimal partially replicated two-level factorial
designs. Statist. Sinica, 22, 419-432.
[8] Tsai, S. F., Liao, C. T., and Chai, F. S. (2015). Identication of dispersion effects from partially
replicated two-level factorial designs. J. Quality Tech, 47, 43-53.
[9] Schonlau, M., Welch, W. J., and Jones, D. R. (1998). Effcient global versus local search in
constrained optimization of computer models. Lecture Notes-Monograph Series, 11-25.
[10] Jones, D. R., Schonlau, M., and Welch, W. J. (1998). Effcient global optimization of expensive black-box functions. J. Global Optim, 13, 455-492.
[11] Ranjan, P., Bingham, D., and Michailidis, G. (2008). Sequential experiment design for contour
estimation from complex computer codes. Technometrics, 50(4), 527{541.
[12] Surjanovic, S. and Bingham, D. (2013). Virtual Library of Simulation Experiments: Test Functions and Datasets. Retrieved July 6, 2020, from http://www.sfu.ca/ ssurjano.
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