利用最適樣本自我回歸T2管制圖監控碎形布朗運動製程｜國立臺灣科技大學博碩士論文系統

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研究生：	邱國程 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 Monitoring Fractional Brownian Motion Processes by the Autoregresive T2 Chart with Adaptive Sample Sizes
指導教授：	周碩彥 Shuo-Yan Chou
口試委員:	喻奉天 Vincent F. Yu 林義貴 Yi-kuei Lin
學位類別：	碩士 Master
系所名稱：	管理學院 - 工業管理系 Department of Industrial Management
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 process, Hurst exponent, Hurst law, fractional Brownian motion, autoregressive T2 Chart with adaptive sample siz
相關次數：	點閱：141 下載：1
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上一筆

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
1.1Background and Motivation......................................................................1
1.2Objective.....................................................................................................2
1.3Organization of Thesis..............................................................................3
Chapter 2 Literature Review...............................................................................4
2.1The Hurst Law............................................................................................4
2.2The Brownian motion and the fractional Brownian motion....................6
2.2.1 The Brownian motion................................................................................6
2.2.2 The Fractional Brownian Motion..............................................................8
2.3Quality 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
2.4Non-central chi-square distribution.......................................................14
Chapter 3 Research method...........................................................................16
3.1Introduction..............................................................................................16
3.2Assumptions and Notations..................................................................16
3.3Improved Guideline for monitoring fBm Processes............................18
3.4Performance Comparison.....................................................................22
Chapter 4 Illustrative Example.........................................................................27
Chapter 5 Conclusion and Future Work.........................................................31
5.1Conclusion..............................................................................................31
5.2Future Work............................................................................................32
References........................................................................................................33

                                

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