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研究生:李姿儀
研究生(外文):Tzu-Yi Lee
論文名稱:運用雙曲線正切函數監控非線性剖面製程
論文名稱(外文):Using Hyperbolic Tangent Function in Nonlinear Profile Monitoring
指導教授:范書愷范書愷引用關係
指導教授(外文):Shu-Kai Fan
口試委員:劉建浩黃乾怡蔡篤名
口試委員(外文):Jian-Hao LiouChing-Ying HuangDu-Ming Tsai
口試日期:2012-06-12
學位類別:碩士
校院名稱:國立臺北科技大學
系所名稱:工業工程與管理系碩士班
學門:工程學門
學類:工業工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:84
中文關鍵詞:統計製程管制非線性剖面雙曲線正切函數Hotelling’s T2Smoothing Spline(平滑樣條)事先制定的測度(metrics)製程異常下平均連串長度(ARLout)
外文關鍵詞:Nonlinear ProfileHyperbolic Tangent FunctionSmoothing splineHotelling’s T2Average Run Length(ARLout)
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在品管應用上,一般而言,製程或產品之品質特性都是針對單一變數進行研究。然而對某些製程而言,品質特性是由反應變數和一個或多個解釋變數間之關係來界定,因此一個品質特性乃以一個函數、一條曲線或是一個曲面之資料型式來呈現,稱之為profile (剖面)。
在本研究提出一個新方法運用在如何有效地監控製程剖面。在此研究中,我們採用參數和非參數方法監控鋁合金於真空爐熱處理過程的溫度曲線。分別以雙曲線正切函數(Hyperbolic tangent)和Smoothing Spline (平滑樣條)來對曲線做配適,模型中參數採用Hotelling’s 統計量和事先制定的測度(metrics)及其管制界線對曲線做監控。在第一階段模擬結果顯示雙曲線正切函數在配適階段表現較平滑樣條佳,在第二階段模擬結果亦顯示雙曲線正切函數在偵測製程異常時的平均連串長度(ARLout)明顯優於平滑樣條。


For most of the SPC applications, the quality of a process or product is measured by one or multiple quality characteristics. Quality characteristics depend on the relationship between the response variable and one and/or explanatory variables. Therefore, a quality characteristic is represented by a function or a curve, which is called for a ‘profile’.
In this thesis, a new method of using the hyperbolic tangent function proposed is for monitoring the profile process. Thus, we adopt the parametric and nonparametric approaches to monitor the vacuum heat treatment process temperature curve. The hyperbolic tangent function is compared to the smoothing spline approach when modeling the nonlinear profiles. The vector of parameter estimates is monitored by Hotelling’s for the parametric approach and metrics method for the nonparametric. The results of the simulation study show that hyperbolic tangent function appears to perform very well for the vacuum heat treatment profiles by Hotelling’s . In Phase I, the proposed hyperbolic tangent approach can correctly identify the outlying profiles but the smoothing spline approach cannot. In phase II, the propose approach provides better out-of-control average run length (ARL) performance than the smoothing spline approach.


摘要 i
ABSTRACT ii
誌謝 iv
CONTENTS v
TABLE CONTENT vii
FIGURE CONTENT vii
Chapter1
Introduction 1
1.1 RESEARCH BACKGROUND 1
1.2 MOTIVATION 2
1.3 RESEARCH GOAL 3
1.4 ORGANIZATION OF THE THESIS 4
Chapter 2 5
Literature Review 5
2.1 STATISTICAL PROCESS CONTROL 5
2.2 STATISTICAL PROCESS CONTROL OF PROFILE 10
2.2.1 Linear Profile 11
2.2.2 Nonlinear Profile 16
2.3 HYPERBOLIC TANGENT FUNCTION 20
2.4 SMOOTHING SPLINE 22
2.5 HOTELLING T2 STATISTICS 23
2.6 NONPARAMETRIC APPROACH 27
2.7 AKAIK INFORMATION CRITERION (AIC) 29
2.7.1 Kullback-Leibler Information 29
2.7.2 Akaike Information Criterion 31
2.7.3 The Least Squares Case 34
2.7.4 Second Order Information Criterion (AICc) 35
2.7.5 Small Sample Correction for Schwarz Information Criterion (SICc) 36
Chapter 3 38
Hyperbolic Tangent Function 38
3.1 ALUMINUM ALLOYS VACUUM HEAT TREATMENT PROCESS 38
3.2 MODELING USING THE HYPERBOLIC TANGENT 40
3.3 MODELING USING THE SMOOTHING SPLINE 55
Chapter 4 65
Experimental Results on Phase II Profile Monitoring 65
4.1 PHASE II MONITORING FOR THE HYPERBOLIC TANGENT FUNCTION 65
4.2 PHASE II MONITORING FOR THE SMOOTHING SPLINE 69
Chapter 5 74
Conclusion and Future Research 74
5.1 CONCLUSION 74
5.2 FUTURE RESEARCH 74
REFERENCE 76
APPENDIX 80


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