針對非常態機台參數之多變數管制及其於電漿蝕刻機台之應用

在多變數統計製程管制方法中最常被應用的是T2管制圖(T2 control chart)，然而在實務上的使用卻仍然存在釵h問題，大大的降低了T2管制圖的效用，尤其是在機台的錯誤偵測與鑑別(equipment fault detection and classification)的應用上；最重要的問題是大多數的機台參數都違反了管制圖背後的常態分配(Normal distribution)的假設，而這些參數之間的關係又都是互相纏繞、互相相關的，所以使得傳統的單變數的製程管制圖已不再適合使用，因此本研究針對非常態(Non-normal)的機台參數提出一個有系統之多變數製程管制的方法。我們提出兩種方法來補救常態假設違反的問題：一種是常態轉換的方法(Normal Transformation Method)，一種是變異數調整的方法(Variance Adjustment Method)。在論文中，首先會在不考慮變數關係的情況下介紹這兩個方法，接著在介紹如何把變數之間的關係考慮進這兩個方法之中，然後對於所有方法作依個比較以及分析。針對所提出的方法，實際應用於半導體製造之電漿蝕刻的機台參數的錯誤偵測及鑑別，並得之驗證。

關鍵字

多變數製程管制；非常態參數

並列摘要

T2 control charts have been implemented in many multivariate statistical process control (MSPC) solutions. However, there are still problems hindering the implementation and the effective use of T2 control charts for equipment fault detection and classification (FDC). An important problem is that most equipment variables violate the normality assumption behind the T2 statistic. Even worse is that those non-normal variables are also correlated with one another and cause infeasibility of traditional T2 control charts. The objective of this paper is to propose a systematic multivariate FDC methodology for non-normal equipment variables. We propose two types of methodologies, namely, normal transformation method and variance adjustment method, to remedy for the normal violation in constructing the multivariate control charts. We first introduce the methodologies without considering correlation among variables, and then present methodologies with consideration of the multivariate structure. And we will show the method of fault classification of each T2 control chart constructing methodology. Then, the comparison of all methodologies will be given. The proposed methodologies are applied to detection and classification faults for a particular tool function of a plasma etcher in semiconductor fabrication.

並列關鍵字

Multivariate SPC ； Non-normal variables

參考文獻

[1] L.H Chiang, E.L Russell, R.D. Braatz , Fault Detection and Diagnosis in Industrial Syatems , Springer, 2001

[2] Richard A. Johnson; Dean W. Wichern , “Applied Multivariate Statistical Analysis” , Fifth Edition, 2002

[5] N.L Johnson , “Systems of Frequency Curves Generated by Methods of Translation”, Biometrika, Vol. 36, No. 1/2, p.149~176, Jun. 1949

[7] Youn-Min Chou, Alan M. Polansky, Robert L. Mason , “Transformation Non-Normal Data to Normality in Statistical Process Control”, Journal of Quality Technology, Vol. 30, No 2, April 1998

[8] D. F. Andrews, R.Gnanadesikan, J. L. Warner, “Transformations of Multivariate Data”, Biometrics, Vol.27, No.4 (825-840), 1971

國際替代計量

針對非常態機台參數之多變數管制及其於電漿蝕刻機台之應用

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