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研究生:蔡朝泉
研究生(外文):Chao-Chuan Tsai
論文名稱:結合工程知識於T-Square管制圖之建構
論文名稱(外文):Accommodating Engineering Knowledge in T-Square Chart Construction for Equipment FDC
指導教授:陳正剛陳正剛引用關係
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:工業工程學研究所
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:2004
畢業學年度:92
語文別:英文
論文頁數:38
中文關鍵詞:多變量錯誤偵測與分類
外文關鍵詞:Multivariate FDCquadratic distance
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中文摘要

Hotelling’s T 2 管制圖是一個被廣泛使用的多變量管制圖。這要特別歸因於它類似Shewhart管制圖且易於操作。雖然T 2管制圖很受歡迎且功能強大,但在實際的半導體製程應用上高誤警率是一個非常大的問題。高誤警率通常可以歸因於兩個主要的原因:1、不同於單變量管制圖,在T 2管制圖裡我們無法針對每個變數去調整它的偵測靈敏度, 2、那些散佈於不同維修保養週期、不同處方或不同反應室的觀測樣本不易取得。但是如果我們可由過去的經驗去得到預先的知識,進而推測出不同變數對於製程的重要性資訊及散佈於不同維修保養週期、不同處方或不同反應室的樣本觀測值的分佈情形,然後藉由融入這預先的知識於我們的T 2管制圖的建構,如此發生誤警的次數就能有效的降低。在這篇研究當中,我們將提出方法去建構一個結合工程知識的T 2管制圖,我們將他命名為Knowledge-Based T2 管制圖。Knowledge-Based T 2 管制圖也被應用在半導體設備狀態的即時監控。在文章最後,實際的例子顯示出有了knowledge-based T 2 管制圖,無意義的警報可以明顯的被減少。
Abstract

The most popular multivariate control chart is the one based on Hotelling’s T 2 statistic. This is partially due to the fact that it is the multivariate analogue of the univariate Shewhart charting statistic and is easy to operate. Though the T 2 control chart is popular and powerful, a high false alarm rate, often seen in practice, has hindered the implementation and effective use of multivariate T 2 control charts. The high false alarm rate is usually due to two main reasons: 1. unlike univariate charts, one can’t adjust the detection sensitivities for individual variables, and 2. representative, sufficient sample observations across different PM (Preventive Maintenance) cycles, recipes and/or process chambers are difficult to collect. If the prior knowledge obtained from engineering experience can provide information on the variable criticality and how the data normally behave across different PM cycles, recipes and/or process chambers, then by accommodating the prior knowledge into T 2 control chart building the number of false alarms should be reduced effectively. In this research, we will propose methodologies to build a robust T 2 control chart, named knowledge-based T 2 control chart, by including the engineering knowledge in the chart building. The knowledge-based T2 control chart is also applied to semiconductor equipment monitoring. The result shows that the number of meaningless alarms can be reduced significantly.
Contents

Abstract i
中文摘要 ii
Contents iii
Contents of Figures iv
Contents of Tables vi
Chapter 1 Introduction 1
Chapter 2 Development of Knowledge-Based T 2 Control Limit 5
2.1 Control Limit and Engineering Limit 5
2.2 Constructing Knowledge-Based T 2 Control Limit 10
2.3 Constraints for Adjusting AK and RK 15
2.4 Problem Formulation 18
2.5 Algorithms for Constructing Knowledge-Based T 2 Control Limit 19
2.6 Special Case 25
Chapter 3 Evaluation of Knowledge-Based T 2 Control Limit 28
Chapter 4 Concluding Remarks 34
Reference 35
Appendix A 36
Appendix B 37
Reference

Harville, D. A., Matrix Algebra from A Statistician’s Perspective, New York: Springer, 1997.
Johnson, R. A.; and Wichern D. W., Applied Multivariate Statistical Analysis, 5th edition, Prentice Hall, 2002.
Jackson, J. E., “Multivariate Quality Control”, Communications in Statistics – Theory and Methods, Vol. 14, pp.2657-2688, 1985.
Montgomery, D. C., Introduction to Statistical Quality Control, 3th edition, New York: Wiley, 1996.
Mason, R. L.; Tracy, N. D.; and Young, J. C., “Decomposition of T2 for Multivariate Control Chart Interpretation”, Journal of Quality Technology, Vol. 27, pp. 99-108, 1995.
Mason, R. L.; Tracy, N. D.; and Young, J. C., “A Practical Approach for Interpreting Multivariate T2 Control Chart Signals”, Journal of Quality Technology, Vol. 29, pp. 396-406, 1997.
Ortega J. M., Matrix Theory-A Second Course, New York: Plenum Press, 1987.
Strang, G., Linear Algebra and its Applications, 3th edition, Harcourt, 2002.
Tracy, N. D.; Young, J. C.; and Mason, R. L., “Multivariate Control Charts for Individual Observations”, Journal of Quality Technology, Vol. 24, pp. 88-95, 1992.
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