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研究生:邱國程
研究生(外文):Kuo-cheng Chiu
論文名稱:利用最適樣本自我回歸T2管制圖監控碎形布朗運動製程
論文名稱(外文):Monitoring Fractional Brownian Motion Processes by the Autoregresive T2 Chart with Adaptive Sample Sizes
指導教授:周碩彥周碩彥引用關係
指導教授(外文):Shou-yan Chou
學位類別:碩士
校院名稱:國立臺灣科技大學
系所名稱:工業管理系
學門:商業及管理學門
學類:其他商業及管理學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:英文
論文頁數:35
中文關鍵詞:長期自我相關過程赫斯特冪數赫斯特定律碎形布朗運動最適樣本自我回歸T2管制圖
外文關鍵詞:long-term autocorrelated processHurst exponentHurst lawfractional Brownian motionautoregressive T2 Chart with adaptive sample siz
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在本論文中,我們使用碎形布朗運動去建造長期的自我相關模型並且開發出管制圖去監控它。這個研究結合了最適當樣本自我回歸T2管制圖與碎形布朗運動,並且根據碎形布朗運動的特性去轉換觀察值,進一步設計出監控它的指導方針。再將本篇論文所提出的管制圖與自我回歸T2管制圖及累積和管制圖進行比較,發覺不僅可以改善自我回歸T2管制圖在偵測小或中偏移表現不佳的缺點,其效能甚至更優於累積和管制圖。最後在實例部份,我們展示出使用最適樣本自我回歸T2管制圖去監控碎形布朗運動的成果。
In this thesis fractional Brownian motion (fBm) is used for modeling long-term autocorrelated processes and control charts in the context of quality control are subsequently developed for monitoring such processes. The autoregressive T2 chart with adaptive sample sizes, enhancing the performance of the autoregressive T2 chart, is utilized. And a guideline is developed for monitoring fBm processes by transforming the observations according to their properties. The performance of the autoregressive T2 chart with adaptive sample sizes is compared with those of the autoregressive T2 chart and the residual-based CUSUM chart. Finally, examples are used to illustrate the use of autoregressive T2 chart with adaptive sample sizes for monitoring the fBm process.
中文摘要................................................................................................................I
Abstract.................................................................................................................II
Acknowledgements.............................................................................................III
Contents...............................................................................................................IV
Figure List............................................................................................................VI
Table List.............................................................................................................VII
Chapter 1 Introduction..........................................................................................1
1.1 Background and Motivation......................................................................1
1.2 Objective.....................................................................................................2
1.3 Organization of Thesis..............................................................................3
Chapter 2 Literature Review...............................................................................4
2.1 The Hurst Law............................................................................................4
2.2 The Brownian motion and the fractional Brownian motion....................6
2.2.1 The Brownian motion................................................................................6
2.2.2 The Fractional Brownian Motion..............................................................8
2.3 Quality Control Charts.............................................................................11
2.3.1 The Residual-Based CUSUM Chart for autocorrelated processes..11
2.3.2 The autoregressive T2 chart for autocorrelated processes...............12
2.3.3 The Hotelling’s T2 chart with adaptive sample sizes..........................13
2.4 Non-central chi-square distribution.......................................................14
Chapter 3 Research method...........................................................................16
3.1 Introduction..............................................................................................16
3.2 Assumptions and Notations..................................................................16
3.3 Improved Guideline for monitoring fBm Processes............................18
3.4 Performance Comparison.....................................................................22
Chapter 4 Illustrative Example.........................................................................27
Chapter 5 Conclusion and Future Work.........................................................31
5.1 Conclusion..............................................................................................31
5.2 Future Work............................................................................................32
References........................................................................................................33
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