應用因素分析與VIKOR方法構建多變量管制程序

Using Factor Analysis and VIKOR Method Constructing the Multivariate Control Procedure

陳志堅(Chih-Chien Chen) ； 唐麗英(Lee-Ing Tong) ； 王春和(Chung-Ho Wang)

《品質學報》 14卷1期 (2007/03) Pp. 57-67

摘要

Hotelling T^2管制圖是工業界應用最廣的多變量管制圖，然而當監控變數有數十個甚至上百個時，T^2指標之共變異數矩陣(covariance matrix)過於龐大，常會導致計算速度變慢或系統當機，此外，當變數間相關性之結構太複雜時，也會造成Hotelling T^2管制圖的檢測能力會變差。本研究之主要目的即是針對上述Hotelling T^2管制圖的問題點，透過因素分析(factor analysis)先將變數分成數個子群，以簡化變數結構，然後計算各子群之T^2指標，再應用多準則決策中之VIKOR(VlseKriterijumska Optimizacija I Kompromisno Resenje in Serbian，means Multicriteria Optimization and Compromise Solution)程序，構建一個新的多變量製程監控指標，以有效解決製程上需監控太多變數的問題。本研究最後分別以一個模擬案例及一個半導體實際案例來說明本研究所提出之多變量管制程序確實比Hotelling T^2多變量管制圖有效。

關鍵字

Hotelling T^2管制圖 ； 因素分析 ； VIKOR程序 ； 多變量製程

並列摘要

Hotelling T^2 control chart is a popular multivariate control chart in industry. However, it is hard to detect the out of control situation of process in utilizing the Hotelling T^2 control chart when the relationships among process parameters are complex. Besides, the very larger number of variables in Hotelling T^2 control chart will result in T^2 index difficult to be computed. This study firstly clusters the variables into several groups by factor analysis, then compute the T^2 index for each group. Finally apply the VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje in Serbian, means Multicriteria Optimization and Compromise Solution) method to create a new procedure for monitoring multivariate processes. Two cases study demonstrate the proposed method is more effective than Hotelling T^2 control chart.

並列關鍵字

Hotelling T^2 control chart ； factor analysis ； VIKOR method ； multivariate processes

參考文獻

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