具有自我相關之二維管制圖正確選用之探討

An investigation on the selection of two-way control chart with autocorrelation data

黃朝興(Chao-xing Hang)

指導教授 ： 江行全

元智大學/工程學院/工業工程與管理學系/碩士(2002年)

摘要

當數據之間存在著兩個品質特性的相關性，與各個品質特性本身的自我相關性，使用不正確的多變量管制圖將導致管制圖的錯誤訊號明顯的增加，也就是說，兩個品質特性之間的相關性與本身自我相關性將會干擾到管制圖偵測製程發生異常變動的能力，使其發生錯誤判斷之機率隨之提高，若依然採用不正確的管制圖來對具有自我相關性之數據進行管制並不恰當。
過去研究學者針對多變量自我相關問題，提出多種多變量管制圖，但因多變量管制圖種類繁多缺乏有效的整合，並且每一種多變量管制圖均有其缺點，因而造成線上工程師不易於選擇。
本文的研究重點針對多變量管制圖的選取做一深入研究，究竟在何種情況下應採用何種管制圖。文中針對資料具有多變量自我相關時，模擬兩個品質特性，且品質特性本身存在AR（1）與MA（1）模型的製程資料，針對不同平均數偏移量、相關係數、自我迴歸參數與移動平均參數，藉由不同方式組合，分別比較五種多變量管制圖的平均連串長度（Average Run Length，簡稱ARL），最後依照本研究提出的流程圖選取適當的多變量管制圖，做為未來研究學者的參考依據，另一方面也可以提供業界採用多變量管制圖的建議。

關鍵字

化學氣象沈積

並列摘要

It would result in increasing error signal on control chart using incorrect multivariate control chart, if it the correlation between two quality characteristics and the autocorrelation in each quality characteristic were existed. In addition, the correlation between two quality characteristics and the autocorrelation in each quality characteristic would influence the capability of the detection process on control chart. It is not appropriate to control the data having autocorrelation.
The purpose in this research is to design a procedure to select a suitable control chart under specific situation. In this research, the Average Run Length (ARL) is used as an criterion for comparing five multivariate control charts according to difference combination of average of shifts、correlation coefficient、autoregressive coefficient and moving average coefficient, and selecte a suitable multivariate control chart. Finally, the result yield a useful guidline when analyze data using multivariate control charts.

並列關鍵字

Chemical Vapor Deposition

參考文獻

2. Alwan, L. C., (1992), “Effects of Autocorrelation on Control Chart Performance,” Communications in Statistics-Theory and Methods, Vol. 21, No. 4, pp. 1025-1049.

4. Crosier, R. B., (1988), “Multivariate Generalizations of Cumulative Sum Quality Control Schemes,” Technometrics, Vol. 30, No. 3, pp. 291-303.

5. Guan, J. A., (1996), “A Study on Multivariate Process Control,” M.S. Thesis, Department of Statistics, National Chiao Tung University, Taiwan, ROC.

6. Harris, T. J., and W. H. Ross, (1991), “Statistical Process Control Procedures for Correlated Observations,” The Canadian Journal of Chemical Engineering, Vol. 69, No. 1, pp. 48-57.

7. Holmes, D. S., and A. E. Mergen, (1993), “Improving the Performance of