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研究生:黃華邦
研究生(外文):Hua Ben
論文名稱:結合連串規則於HotellingT2管制圖之設計
論文名稱(外文):Design of Hotelling''s T2 Control Chart with Runs Rules
指導教授:童超塵童超塵引用關係
指導教授(外文):Chau Chen Torng
學位類別:碩士
校院名稱:國立雲林科技大學
系所名稱:工業工程與管理研究所碩士班
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:2005
畢業學年度:93
語文別:中文
論文頁數:73
中文關鍵詞:ARL連串規則馬可夫鏈T2管制圖
外文關鍵詞:ARLRuns RulesMarkov ChainT2 Control Chart
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Hotelling於1947年提出T2 管制圖用於監控多變量製程(Multivariate Process),現今工業製程日趨複雜所考量的變數也日益增加,T2管制圖由於其簡便性而被廣泛地運用於監控多個相關變數。然而,當製程發生中型或小型偏移時,T2管制圖往往無法即時地發出警訊。為增加T2 管制圖之敏感度,本研究先利用馬可夫鏈推導得當ARL0分別為200、500、740、1000的情況下,適合於T2 管制圖之連串規則(Runs Rules)以供實務者選用參考,再以出現頻率檢測連串規則的貢獻性,並挑選出現頻率較高的連串規則組合使用,進一步放寬管制界線(Control Limit, CL)以控制型一誤差。為驗證此串連規則之可行性,研究中將結合串連法則之T2 管制圖、基本T2 管制圖和MEWMA管制圖,以平均串連長度(Average Run Length, ARL)進行管制圖監控表現的績效比較。研究結果則顯示,當製程發生小型偏移時,結合連串規則之T2 管制圖會有與MEWMA相當的績效表現,中、大型偏移時,則比MEWMA為佳。
Hotelling developed T2 control chart for monitoring multivariate process in 1947. Due to more complicated of industrial process nowadays, Hotelling’s T2 control chart is widely used on controlling several related characteristics because of its simplicity. However, T2 control chart cannot signal immediately when small or moderate process shift occurs. For increasing sensitivity of T2 control chart, firstly Markov chain is used to obtain runs rules appropriate for T2 control chart under ARL0 is 200, 500, 370 and 1000. Secondly, test the contribution of each rules by appearance frequency and combined rules which with high frequency. Furthermore, loosen the control limit to control the serious type I error of rules. For verifying the contribution and practicability, comparison based on ARL performance between the basic T2 control chart, T2 control chart which incorporates runs rules and MEWMA is practiced in this research. The research result indicates that T2 control chart combined runs rules can perform as better as MEWMA when small process shift occur, and even better when moderate or large process shift occur.
中文摘要 I
英文摘要 II
致謝 III
目錄 IV
圖目錄 IV
表目錄 VIIV
第一章 緒論 1
1.1 研究背景 1
1.2 研究動機 2
1.3 研究目的 2
1.4 研究假設 3
1.5 研究架構 3
第二章 文獻探討 4
2.1 連串規則 6
2.1.1 舒華特管制圖連串規則 6
2.1.2 舒華特管制圖連串規則之相關研究 7
2.1.3 多變量T2管制圖連串規則 8
2.2 多變量管制圖 13
2.2.1 Hotelling’s T2管制圖 13
2.2.2 MEWMA管制圖 19
第三章 研究方法 21
3.1 轉換T2統計量 21
3.2 推導連串規則 25
第四章 研究結果分析 28
4.1 直接組合連串規則 29
4.2 以連串規則出現頻率進行篩選 39
4.3 控制連串規則型一誤差 41
4.4 與MEWMA管制圖比較結果 46
第五章 結論與建議 50
5.1 直接組合連串規則 50
5.2 以連串規則出現頻率進行篩選 50
5.3 控制連串規則型一誤差 51
5.4 與其他管制圖的比較結果 51
5-5 後續研究發展 52
參考文獻 53
附錄一 連串規則推導過程 56
附錄二 連串規則組合之ARL表現 61
參考文獻

英文部分
1.Alt, F. B. (1985). “Multivariate Quality Control,” in Encyclopedia of Statistical Sciences, Vol. 6, edited by N. L. Johnson and S. Kotz, Wiley, New York, NY
2.Aparisi, F., Champ, C. W., and Garcia-Diaz, J. C. (2004). “A Performance Analysis of Hotelling’s χ2 Control Chart with Supplementary Runs Rules,” Quality Engineering, Vol. 16, No. 3, pp. 358-368.
3.Aparisi, F., and Haro, C. L. (2002). “A Comparison of T2 Control Charts with Variable Sampling Schhemes as opposed to MEWMA Chart,” International Journal of Production Research, Vol. 41, No. 10, pp. 2169-2182.
4.Champ, C. W., and Woodall, W. H. (1987). “Exact Results for Shewhart Control Charts with Supplementary Runs Rules,” Technometrics, Vol. 29, No. 4, pp. 393-399.
5.Grant, E. L., and Leavenworth, R. S. (1988). Statistical Quality Control, 6th ed., Mcgraw-Hill, New York, NY.
6.Huang, H. B., Chen, L. C., and Torng, C. C. (2004). “Analysis and Control Tools Assist for T2 Control Chart,” 10th National Quality Conference of the Chinese Society for Quality.
7.Khoo, M. B. C. (2003). “Design of Runs Rules Schemes,” Quality Engineering, Vol. 16, No. 1, pp. 27-43.
8.Khoo, M. B. C., and Quah, S. H. (2003). “Incorporating Runs Rules into Hotelling’s χ2 Control Charts,” Quality Engineering, Vol. 15, No. 4, pp. 671-675.
9.Lowry, C. A., and Montgomery, D. C. (1995). “A Review of Multivariate Control Charts,” IIE Transactions, Vol. 26, pp. 800-810
10.Lowry, C. A., Woodall, W. H., Champ, C. W., and Rigdon, S. E. (1992). “A Multivariate Exponentially Weighted Moving Average Control Charts,” Technometrics, Vol. 34, No. 1, pp. 46-53.
11.Mason, R. L., Chou, Y. M., Sullivan, J. H., Stoumbos, Z. G. and Tracy, N. D. (2003). “Systematic patterns in T2 control,” Journal of Quality Technology, Vol. 35, No. 1, pp. 47-58
12.Mason, R. L., Tracy, N. D., and Young, J. C. (1997). “A Practical Approach for Interpreting Multivariate T2 Control Chart Signals,” Journal of Quality Technology, Vol. 29, No. 4, pp.396-406.
13.Montgomery, D. C., (2000). Introduction to Statistical Quality Control, 4th ed., John Wiley & Sons, New York, NY.
14.Nelson, L. S. (1984). “The Shewhart Control Chart—Test for Special Causes, ” Journal of Quality Technology, Vol. 16, pp.237-239
15.Prabhu, S. S., and Runger, G. C. (1997). “Designing a Multivariate EWMA Control Chart,” Journal of Quality Technology, Vol. 29, No. 1, pp. 8-15.
16.Tracy, N. D., Young, J. C., and Mason, R. L. (1992). “Multivariate Control Charts for Individual Observations,” Journal of Quality Technology, Vol. 24, No. 2, pp. 88-95.
17.Western Electric (1956). Statistical Quality Control Handbook, Western Electric Corporation, Indianapolis, IN.

中文部分:
18.古東源(1990),管制圖上使用連串規則監測不穩定製程之研究,國科會專題研究計畫報告。
19.吳岳忠(1996),有叢聚現象的晶圓製程管制之研究,國立雲林科技大學工業工程與管理研究所,碩士論文。
20.陳志松(2002),應用多變量T2統計量於具漸層式紋路瑕疵之自動化檢測探討-以SBL之水紋瑕疵為例,朝陽科技大學工業工程與管理研究所,碩士論文。
21.葉卓華(2003),應用管制圖於存貨管理之研究,國立雲林科技大學工業工程與管理研究所,碩士論文。
22.游明新(2003),多變量管制圖之比較與探討,國立雲林科技大學工業工程與管理研究所,碩士論文。
23.廖慶榮(2002),作業研究,三民書局,台北。
24.鄭春生(2000),品質管理,育友圖書有限公司,台北。
25.戴久永(1998),品質管理,三民書局,台北。
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