臺灣博碩士論文加值系統

由於p管制圖是假設二項分配滿足逼近常態分配之前提下所建立，當製程不合格率p0很低時，會因二項分配無法滿足常態性假設之條件，而造成p管制圖錯誤警告增加。且因不合格率小，管制圖上易出現許多為零的點，而管制下限亦容易產生等於零之情形，無法作為判斷製程是否有顯著改善之依據。因此，p管制圖並不適合用來監控低不合格率製程，後續才發展出CCC管制圖用來取代p管制圖監控高產出製程。為了進一步地提升CCC管制圖偵測製程不合格率偏移之效率，比CCC管制圖多考慮r組樣本統計量之CCC-r管制圖因而產生。
然而CCC-r管制圖，當製程不合格率開始偏離目標值p0之初，其平均連串長度呈現遞增現象，亦即無法快速地發出警訊。故本研究之最大貢獻在於推導出CCC-r管制圖之管制界限調整係數通式kr，並證明經由調整係數kr修正後之CCC-rmodified管制圖，確實能夠改進CCC-r管制圖無法即時偵測製程偏移之能力，有效地提升CCC-r管制圖偵測製程偏移之靈敏度，提供一個更有效率的管制方法來監控低不合格率之高產出製程。

The p chart approximated by normal distribution is widely used to monitor the fraction nonconforming. However, the low process fraction nonconforming due to process improvement and small sample size usually make the assumptions invalid and generate too many false alarms. Since the fraction nonconforming is low, the lower control limit of a p chart is usually negative and no process improvement can be detected. For above mentioned reasons, the p chart is inadequate for monitoring and control of product attributes in the processes of very high yields.
The cumulative count control (CCC) chart based on cumulative count of items produced until r nonconforming items are detected has been proposed for the processes with low fraction nonconforming. In this research, an adjustment coefficient kr was developed to avoid the undesireable feature that the out-of-control ARL will increase as process deteriorates. With the adjusted control limits, we can assure that the in-control ARL is maximized.

目 錄
中文摘要 i
英文摘要 ii
致謝 iii
目錄 iv
表目錄 vi
圖目錄 vii
一、緒論 1
1.1 研究背景與動機 1
1.2 研究目的 3
1.3 研究架構 3
二、文獻探討 5
2.1 計數值管制圖 5
2.2 監控高產出製程之管制圖 8
2.2.1 CCC管制圖 8
2.2.2 CQC管制圖 11
2.2.3 CPC管制圖 12
三、研究方法 13
3.1 CCC-r管制圖之建立 13
3.1.1 管制圖之樣本統計量 13
3.1.2 管制界限之建立 14
3.1.3 管制圖之判斷方式 16
3.1.4 管制圖之範例說明 17
3.2 CCC-r管制圖之評估指標 20
四、修正CCC-r管制圖 24
4.1 CCC-2管制圖之調整係數k2 24
4.2 CCC-3管制圖之調整係數k3 28
4.3 CCC-4管制圖之調整係數k4 31
4.4 CCC-5管制圖之調整係數k5 34
4.5 CCC-r管制圖之調整係數kr 38
五、結論 47
參考文獻 48
表目錄
表1. 標準差水準及良率轉換表 1
表2. 當po=0.0004,n=200時，抽50組樣
之檢驗結果 17
表3. CCC管制圖之前置表格 18
圖目錄
圖1. 研究架構圖 4
圖2. p=0.5,n=50之二項分配圖 5
圖3. p=0.1,n=160之卜瓦松分配圖 6
圖4. p=0.05,n=50之二項分配圖 6
圖5. p=0.01,n=160之卜瓦松分配圖 7
圖6. CCC管制圖之ARL示意圖 9
圖7. CCCmodified管制圖之ARL示意圖 9
圖8. CCC-1管制圖之管制變數 13
圖9. CCC-r管制圖之管制變數 14
圖10. CCC管制圖 19
圖11. p管制圖 20
圖12. CCC管制圖之ARL(p0=0.0005 ) 21
圖13. CCCmodified管制圖之ARL(p0=0.0005 ) 22
圖14. CCC-2管制圖之ARL 23
圖15. CCC-3管制圖之ARL 23
圖16. CCC-4管制圖之ARL 23
圖17. CCC-5管制圖之ARL 23
圖18. CCC-2管制圖修正前後之ARL比較圖 28
圖19. CCC-3管制圖修正前後之ARL比較圖 31
圖20. CCC-4管制圖修正前後之ARL比較圖 34
圖21. CCC-5管制圖修正前後之ARL比較圖 37

參考文獻
1. Bourke, P. D. ,“Detecting a shift in fraction
nonconforming using run-length control charts with 100%
inspection,”Journal of Quality Technology, 23, 3, 225-238
(1991)
2. Calvin, T. W. ,“Quality control techniques for“Zero
Defects”,” IEEE Transactions on Components , Hybrids ,
And Manufacturing Technology, CHMT-6, 323-328 (1983)
3. Chan, L. Y. , M. Xie, and T. N. Goh,“Cumulative quantity
control charts for monitoring production processes,”
International Journal of Production Research, 38, 2, 397
-408 (2000)
4. Chan, L. Y. , K. J. Lin Dennis, and T. N. Goh,“Cumulative
probability control charts for geometric and exponential
process characteristics,”International Journal of
Production Research, 40, 1, 133-150 (2002)
5. Goh, T. N. ,“A control chart for very high yield
processes,”Quality Assurance, 13, 1, 18-22 (1987)
6. Johnson, N. L. and Kotz , S. Distributions in Statistics ,
Vol1：Discrete Distributions. New York (1969)
7. Ohta, H. , E. Kusukawa, and A. Rahim,“A CCC-r chart for
high-yield pro- cesses,”Quality And Reliability
Engineering International, 17, 439-446 (2001)
8. Sun, J. and G. Zhang,“Control charts based on the number
of consecutive conforming items between two successive
nonconforming items for the near zero-nonconformity
processes,”Total Quality Management & Business
Excellence, 11, 2, 235-250 (2000)
9. Tsai , T. R. An adjusted normal approximation method ,
Technical Report No.4, Department of Statistics, Tamkang
University. (2001)
10. Xie, M. and T. N. Goh,“Some procedures for decision
making in controlling high yield processes,”Quality And
Reliability Engineering International, 8, 355-360 (1992)
11. Xie, M. and T. N. Goh,“The use of probability limits for
process control based on geometric distribution,”
International Journal of Quality & Reliability Management,
14, 1, 64-73 (1995)
12. Xie, M. and T. N. Goh,“Statistical control of a six sigma
process,”Quality Engineering, 15, 4, 587-592 (2003)
13. Xie, M., T. N. Goh, and V. Kuralmani,“On optimal setting
of control limits for geometric chart,”International
Journal of Reliability,Quality and Safety Engineering, 7,
1, 17-25 (2000)
14. Xie, M., X. S. Lu, T. N. Goh, and L. Y. Chan,“A quality
monitoring and decision-making scheme for automated
production processes,”International Journal of Quality &
Reliability Management, 16, 2, 148-157 (1999)
15. 林建志，「改良的平方根轉換在計數值管制圖上之應用」，淡江
大學統計學研究所碩士論文，台北，2002。
16. 鄭春生，「品質管理」，三民書局，台北，1996。