Accommodating Engineering Knowledge in T-Square Chart Construction for Equipment FDC

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 3