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研究生:洪裕堂
研究生(外文):Yuk Tarng HONG
論文名稱:累積和管制圖之研究
論文名稱(外文):Cumulative sum Chart
指導教授:徐世輝徐世輝引用關係
學位類別:碩士
校院名稱:國立中正大學
系所名稱:數理統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:1999
畢業學年度:87
語文別:中文
論文頁數:79
中文關鍵詞:累積和管制圖
外文關鍵詞:Cumulative sum ChartCusum
相關次數:
  • 被引用被引用:1
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Cumulative sum chart是由E. S Page (1954) 及G. A. Barnard (1959) 在on-line process control中所發展出來的。主要的理論依據是由Sequential likelihood ratio test ( See A. Wald , Sequential Analysis) 所衍生出來的。
Cusum chart主要是針對製程移動小量時,能快速偵測製程偏移所創制的。一般的推導都是由Sequential likelihood ratio test所得出。之後的人也有對Cusum做過一些improve的工作。主要的有Lucas (1973) 的" A Modified V-Mask Control Scheme", Locus and Crosier (1982) 的" Fast Initial Response for Cusum Quality-Control Scheme", Lucas(1982)的 " Combined Shewhart-CUSUM Quality Control Schemes ",及F. F. Gan (1991) 由EWMA Optimal Design中得出的 "An Optimal Design of Cusum Quality Control charts" … etc。
傳統的 Cusum Scheme 是假設Data 為Normal 分佈,可是不一定每筆資料都一定 follow normal 假設。所以後來就陸續有人討論在不同分佈假設下,Cusum Scheme 的應用情形,主要的 paper 有J. M. Lucas(1985)的" Counted data CUSUM'S", F. F. Gan(1992),(1994) 對 Binomial Cusum與 Exponential Cusum 的討論,…等等,此會在後面論述。
衡量一個Cusum Chart Scheme的設計優劣,通常是以ARL ( Average Run Lenght )為衡量的基準,此會在後節加以討論。另外須注意的是,Control chart的設計是讓製程監控人員易於操作,且能明白圖形本身的意義。所以能有一個簡易的操作過程,及明確清楚的圖形表現,也是很重要的。本論文皆有詳細的論述。

1. 引言
2. Cusum Chart 的基本性質
3. Cumulative Sum Chart的設計方法
3-1. 傳統的Cusum設計
3-2. Tabular Cusum
3-3. The Standard Cusum
4. 一般推薦的Cusum Scheme參數設計
5. About ARL的計算
6. 一些改善Cusum Chart在Large Shifts時偵測不敏感的方法
6-1. Combined Shewhart-CUSUM Quality Control Charts
6-2. A Modified "V" Mask Control Scheme
7. The Fast Initial Response or Headstart Feature
8. 單邊的Cusums
9. A Cusum for Monitoring Process variability
10. The V-Mask Procedure
11. Cusum Depend on Other Distribution
11-1. Possion Cusum
11-2. Exponential Cusum
11-3. Binomial counts Cusum
12. An Optimal Design of CUSUM Quality Control Charts
13. Distribution-free Cusum Test
14. 其它一些在使用CUSUM Chart時須注意的地方
15. 結論
16. Reference

1. Adams, B. M., C. Lowery, and W. H. Woodall(1992). " The Use(and Misuse) Of False Alarm Probabilities in Control Chart Design, " in Frontiers in Statistical Quality Control 4, Edited by H. J. Lenz, G. B. Wetherill, and P.-Th Wilrich, Physica-Verlag, Heidelberg.
2. BARNARD G. A. (1959) " Control Chart and Stochastic Processes " , Journal of the Royal Statistical Society Vol. XXI , No. 2, pp. 239~271.
3. BISSELL A. F. " The Performance of Control Charts and Cusum under Linear Trend " (1984), Appl. Ststist. , 33, No. 2, pp.145~151.
4. Brook D. and Evans D. A. (1972) " An Approach to the Probability Distribution of CUSUM Run Length " , Biometria 29, pp.539~549.
5. Bowker P. O. (1991)."Detecting a Shift in the Fraction Nonconforming Using Run-Length Control Chart with 100% Inspection," Journal of Quality Technology, Vol, 23.
6. CAROLYN H. WHITE and J. BERT KENTS (1996). "ARLs and Higher-Order Run-Length Moments for the Poisson CUSUM " , JQT , pp.363~369.
7. CHARLES P. QUESENBERRY (1991). " SPC Q Chart for Start-Up Processes and Short or Long Runs " , JQT , pp.213~224.
8. David Siegmund (1985). " Sequential Analysis", Springer-Verlag , New York.
9. Dan Bradu (1984) " Response surface model diagnosis in two-way tables ", Commun. Statistic theory & method, 13(24), pp.3059~3106
10. F. F. GAN and K. P. CHOI (1994)." Computing Average Run Lengths for Exponential CUSUM Schemes " , JQT , pp.134~143.
11. F. F. GAN (1994). " Design of Optimal Exponential CUSUM Control Charts " , JQT , pp.109~124.
12. F. F. GAN (1993)." The Run Length Distribution of a Cumulative Sum Control Chart " , JQT , pp.205~207.
13. F. F. Gan (1993). "An Optimal Design of CUSUM Control Charts for Binomial Counts," Journal of Applied Statistic, Vol, 20.
14. F. F. GAN (1991). " An Optimal Design of CUSUM Quality Control Charts " , JQT , pp.279~286.
15. GEOREG E. P. BOX, DAVID E. COLEMAN and ROBERT V. BAXLEY, JR. (1997)" A Comparison of Statistical Process Control and Engineering Process Control" , JQT , pp.128~147.
16. GOLDSMITH P. L. and WHITFIELD H. (1961). " Average Run Lengths in Cumulative Chart Quality Control Schemes " , Technometrics , February , Vol. 3 , No.1 , pp.11~20.
17. Hawkins, D. M. (1993). " Robustification of Cumulative Sum Charts By Winsorization " , JQT , pp.248~261.
18. Hawkins, D. M. (1993a). "Cumulative Sum Control Charting: An Underutilized SPC Tool," Quality Engineering, Vol.25
19. Hawkins, D. M.(1992). "A Fast, Accurate Approximation of Average Lengths of CUSUM Control Charts," Journal of Quality Technology, Vol. 24
20. Hawkins, D. M. (1981). " A CUSUM for a Scale Parameter," Journal of Quality Technology, Vol. 13
21. Hawkins, D. M. (1992). " Evaluation of the Average Rum Length of Cumulative Sum Charts for an Arbitrary Data Distribution ", Communications in Statistics : Simulation and Computation 21, pp.1001~1020
22. Hawkins, D. M. (1981) "A Cusum for a Scale Parameter " , JQT 13 ,pp. 228~231.
23. HOWARD M. TAYLOR (1968) ." The Economic Design of Cumulative Sum Control Charts " , Technometrics ,Vol.10 NO.3 ,August, pp.479~488.
24. James M. Lucas and Ronald B. Crosier (1982). " Fast Initial Response for CUSUM Quality-Control Schemes : Give Your CUSUM A Head Start " , Technometrics VOL 24 . August , pp.199~205.
25. James M. Lucas (1985). " Counted Data CUSUM's " , Technometrics, May, Vol. 27 , No. 2 , pp.129~144.
26. James M. Lucas (1982). " Combined Shewhart-CUSUM Quality Control Schemes " , JQT , pp.51~59.
27. James M. Lucas (1973). " A Modified "V" Mask Control Scheme " , Tech -nometrics , November , Vol. 15, NO. 4 , pp.833~847.
28. JOE H. SULLIVAN and WILLIAM H. WOODALL (1996). " A Control Chart for Preliminary Analysis of Individual Observations ", JQT , pp.265 ~278.
29. JOE H. SULLIVAN and WILLIAM H. WOODALL "A Comparison of Multivariate Control Chart for Individual Observations " , JQT , (1996) , pp.398~408.
30. JOHNSON N. L. (1961) ." A Simple Theoretical Approach to Cumulative Sum Control Charts ", JASA, pp. 835~840
31. Kemp K. W. (1961). " The Average Run Length of the Cumulative Sum Chart when a V-Mask is used", Journal of the Royal Statistical Society B23, pp. 149~153.
32. Lowry, C. A., C, W, Champ, and W. H. Woodall(1995) " The Performance of Control Charts for Monitoring Process Variation," Communication in Statistics-Computation and Simulation, Vol. 21.
33. Montgomery D. C. (1997) " Introduction to Statistical Quality Control ", Third Edition , John Wiley & Sons, Inc.
34. Page E. S. (1954) "Continuous Inspection Schemes " Biometrika , 41, pp.100~114.
35. Page E. S. (1955) "Control Charts with Warning Lines " , Bometrika , 42, pp.243~257.
36. Page E. S. (1961) " Cumulative Sum Charts " , Technometrics ,February 1961, Vol. 3 , No. 1 , pp.1~9.
37. Ronald B. Crosier (1986) " A New Two-Sided Cumulative Sum Quality Control Scheme " , Technometrics August 1986, Vol. 28, No. 3, pp.187~194.
38. Ronald B. Crosier (1998) " Multivariate Generalizations of Cumulative Sum Quality-Control Schemes " , Technometrics , Vol 30, No.3, pp.291~303
39. Stephen V. Crowder (1989) " Design of Exponentially Weighted Moving Average Schemes " , Journal of Quality Technology Vol. 21, No. 3 , pp.153~162
40. VARDEMAN S. and RAY D. (1985) " Average Run Lengths for CUSUM Schemes When Observations Are Exponentially Distributed ", Technometrics 27, pp. 145~150.
41. Vance, L. C. (1986). "Average Run Lengths of Cumulative Sum Control Charts for Controlling Normal Means," Journal of Quality Technology, Vol. 18.
42. Woodall W. H., and B. M. Adams(1993). "The Statistical Design of CUSUM Charts," Quality Engineering, Vol. 5.
43. Woodall W. H. (1983) " The Distribution of the Run Length of One-sided CUSUM Procedures for Continuous Random Variables " , Technometrics 25, pp. 295~301.
44. ZACHARY G. STOUMBOS and MARION R. REYNOLDS, JR. (1997), " Control Charts Applying a Sequential Test at Fixed Sampling Intervals ", JQT , pp.21~40
45. Technical REPORT , ISO/TR 7871 , First Edition ,1997-02-15

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