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題名 統計品管中製程能力指標決策程序之研究
Some Decision Procedures For The Capability Index In Quality Control Process
作者 李仁棻
Lee, Ren Fen
貢獻者 黃登源
Huang, Deng-Yuan
李仁棻
Lee, Ren Fen
關鍵詞 製程能力指標、非中心性卡方分配、檢定、部份集合選擇
Process Capability Index、Noncentral Chi Square Distribution
日期 1993
上傳時間 10-May-2016 18:56:28 (UTC+8)
摘要 製程能力指標（process capability index）常被用來評量製程能力的高低。它結合規格及製程變異於一指標，便利使用者易於了解指標的意義。
     若吾人主張一製程能力大於某一定值，當同時控制型I及型II過誤，這時，臨界值（critical value）及樣本大小n即可決定。若同時存在有數個大於某一定值的製造過程，吾人欲挑選具有最大製程能力的製程，這時，我們提出一個客觀的準則來加以選擇。
     本篇論文的特色是以解析法來決定臨界值及樣本大小n，並於挑選最大的製程能力時能提出一個客觀的挑選準則。
     研究中發現：雖然逼近常用的統計上查表值時有些誤差，但誤差不大。故本文討論的過程中所用的方法及結論，適用於線上作業。
參考文獻 References
     1. Boyles, R. A. (1991). The Taguchi Capability Index. Journal of Quality Technology,23,17-26.
     2. Chan, L. K., Cheng, S. W., and Spiring, F. A. (1988). A New Measure of
     Process Capability: Cpm ` Journal of Quality Teclmology ,20,162-175.
     3. Chou, Y. M. and Owen, D. B. (1989). On The Distributions of The Estimated
     Process Capability Indices. Conuuun. Statist. - Theory Meth. )8,4549-4560.
     4. Franklin, L. A. and ,Vassennan, G. S. (1992). Bootstrap Lower Corrfidence
     Limits for Capability Indices. Journal of Quality Teclmology ,24,196-209.
     5. Fun, Y. P. and Li, C. C. (1991). Some Discussion and Proposition on Process
     Capability Index. Journal of The Chinese Institute of Industrial Engineers
     ,8,83-89.
     6. Gupta, S.S., and Huang, D.Y. (1981). Multiple Statistical Decision Theory.
     Lecture Notes in Statistics (6), Springer-Verlag, New York.
     7. Gupta, S.S., and Panchapakesan, S. (1979). Multiple Decision Procedures:
     Theory and Methodology of Selecting and Ranking Populatioons. John Wiley
     & Sons, New York.
     8. Haynam, G. E. , Govindarajulu, Z., Leone, F. C., and Siefert, P. (1982, 1983).
     Tables of The Cumulative Noncentral Chi-square Distribution. Parts 1, 2, 3,
     4, 5, and 6. iVIath. Operationsforsch. Statist. Sel`. Statistics 13 and 14.
     9. Johnson, N.L., and Kotz, S. (1970). Continuous Univariate Distributions-2.
     Houghton Mifflin company, Boston.
     10. Johnson, T. (1992). The Relationship of Cpm to Square Error Loss. Journal
     of Quality Technology ,24,211-215.
     11. Kane, V. E. (1986). Process Capability Indices. Journal of Quality Technology
     ,18,41-52.
     12. Kirmani, S. N. U. A., Kocherlakota, K., and Kocherlakota, S. (1991). Estirnation
     of iT and The Process Capability Index Based on Subsamples. Corrunun.
     Statist. - Theory :Meth. ,20,275-291.
     13. Ko cherlakot a, S. (1992). Process Capability Index: Recent developrnents .Sankhyal
     :The Indian Journal of Statistics,54, Series B ,352-369.
     14. Kotz, S. and Jolmson, N. 1. (1993). Process Capability Indices. Chapman &
     Hall.
     15. Kuchler, R. H. and Hurley, P. (1992). Confidence Bounds for Capability Indices.
     Journal of Quality Technology ,24,188-195.
     16. Montgomery, D.e. (1991). Introduction to Statistical Quality Control. 2nd ed.
     John Wiley & Sons, New York.
     17. Peam) W. L.) Kotz) S., and Johnson, N. L. (1992). Distributional and Inferential
     Propertices of Process Capability Indices. Journal of Quality Technology
     ,24,215-231.
     18. Rohatgi, V. K. (1984). Statistical Inference. John Wiley & Sons, New York.
     19. Spiring, F. A. (1991). Assessing Process Capability in The Presence of Sys~
     tematic Assignable Cause. Journal of Quality Technology ,23,125-134.
     20. Tseng, S.T. and Wu, T.Y. (1991). Selecting The Best Manufacturing Process.
     Journal of Quality Technology ,23,53-62.
     21. Wu, T.Y. (1990). A Study of MLR Rule on Sampling Plan. Ph.D. Thesis. Dept
     of Industrial rvlanagement, National Taiwan Institute of Tec1mology, R.O.C.
描述 博士
國立政治大學
統計學系
資料來源 http://thesis.lib.nccu.edu.tw/record/#G91NCCV9542012
資料類型 thesis
dc.contributor.advisor 黃登源zh_TW
dc.contributor.advisor Huang, Deng-Yuanen_US
dc.contributor.author (Authors) 李仁棻zh_TW
dc.contributor.author (Authors) Lee, Ren Fenen_US
dc.creator (作者) 李仁棻zh_TW
dc.creator (作者) Lee, Ren Fenen_US
dc.date (日期) 1993en_US
dc.date.accessioned 10-May-2016 18:56:28 (UTC+8)-
dc.date.available 10-May-2016 18:56:28 (UTC+8)-
dc.date.issued (上傳時間) 10-May-2016 18:56:28 (UTC+8)-
dc.identifier (Other Identifiers) G91NCCV9542012en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/96306-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description.abstract (摘要) 製程能力指標（process capability index）常被用來評量製程能力的高低。它結合規格及製程變異於一指標，便利使用者易於了解指標的意義。
     若吾人主張一製程能力大於某一定值，當同時控制型I及型II過誤，這時，臨界值（critical value）及樣本大小n即可決定。若同時存在有數個大於某一定值的製造過程，吾人欲挑選具有最大製程能力的製程，這時，我們提出一個客觀的準則來加以選擇。
     本篇論文的特色是以解析法來決定臨界值及樣本大小n，並於挑選最大的製程能力時能提出一個客觀的挑選準則。
     研究中發現：雖然逼近常用的統計上查表值時有些誤差，但誤差不大。故本文討論的過程中所用的方法及結論，適用於線上作業。		zh_TW
dc.description.tableofcontents 1Introduction..........1
     1.1Motivation..........1
     1.2Review..........2
     2Process Capability Index..........4
     2.1Introduction..........4
     2.2Definitions And Notations..........5
     2.3The Relations Of Process Capability Indices Cp,Cpk,Cpm,Cpmk..........7
     2.4Some Properties Of Process Capability Indices..........8
     2.5The Comparisons Among Process Capability Indices Cp,Cpk,Cpm..........9
     2.6Estimation..........12
     3Some Testing Procedures For The Capability Index In Quality Control Process..........14
     3.1Abstract..........14
     3.2Introducion..........15
     3.3Some Approximating Results Of Noncentral Chi Square Distribution..........17
     3.4Determining The Critical Value And Sample Size..........19
     3.5Example..........26
     4Selecing The Largest Capability index From Several Quality Control Processes..........27
     4.1Abstract..........27
     4.2Introduction..........28
     4.3Some Approximation Results Of Noncentral Chi Square Distribution And Normal Distribution..........30
     4.4Selectining The Process With The Largest Cpm..........31
     4.5The Expected Subset Size..........39
     4.6Example..........41
     4.7Simulation..........44
     5Conclusion..........45
     References..........46
     Table
     1.Sample Size And Critical Value For Testing Cp (Kane method)or Testing Cpm(Huang and Lee method),when u=T, a=B=0.1,RQL=1..........25
     2. Sample Size And Critical Value For Testing Cp (Kane method)or Testing Cpm(Huang and Lee method),when u=T, a=B=0.05,RQL=1..........25
     3.20 Samples Of 5 Observations Each..........41
     4.The Sample Mean, Variance, Cpm,T2, V In The Example 2..........42
     5.The c Value Associated With p* In The Example 2..........43
     6. The c Value Associated With p*, The Probability Of The Best Process Being Selected And The Expected Subset Size In The Simulation..........44
     Figure
     1.Meaning Of Process Capability Index..........5
     2.Three Processes With Cpk=1..........9		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G91NCCV9542012en_US
dc.subject (關鍵詞) 製程能力指標、非中心性卡方分配、檢定、部份集合選擇zh_TW
dc.subject (關鍵詞) Process Capability Index、Noncentral Chi Square Distributionen_US
dc.title (題名) 統計品管中製程能力指標決策程序之研究zh_TW
dc.title (題名) Some Decision Procedures For The Capability Index In Quality Control Processen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) References
     1. Boyles, R. A. (1991). The Taguchi Capability Index. Journal of Quality Technology,23,17-26.
     2. Chan, L. K., Cheng, S. W., and Spiring, F. A. (1988). A New Measure of
     Process Capability: Cpm ` Journal of Quality Teclmology ,20,162-175.
     3. Chou, Y. M. and Owen, D. B. (1989). On The Distributions of The Estimated
     Process Capability Indices. Conuuun. Statist. - Theory Meth. )8,4549-4560.
     4. Franklin, L. A. and ,Vassennan, G. S. (1992). Bootstrap Lower Corrfidence
     Limits for Capability Indices. Journal of Quality Teclmology ,24,196-209.
     5. Fun, Y. P. and Li, C. C. (1991). Some Discussion and Proposition on Process
     Capability Index. Journal of The Chinese Institute of Industrial Engineers
     ,8,83-89.
     6. Gupta, S.S., and Huang, D.Y. (1981). Multiple Statistical Decision Theory.
     Lecture Notes in Statistics (6), Springer-Verlag, New York.
     7. Gupta, S.S., and Panchapakesan, S. (1979). Multiple Decision Procedures:
     Theory and Methodology of Selecting and Ranking Populatioons. John Wiley
     & Sons, New York.
     8. Haynam, G. E. , Govindarajulu, Z., Leone, F. C., and Siefert, P. (1982, 1983).
     Tables of The Cumulative Noncentral Chi-square Distribution. Parts 1, 2, 3,
     4, 5, and 6. iVIath. Operationsforsch. Statist. Sel`. Statistics 13 and 14.
     9. Johnson, N.L., and Kotz, S. (1970). Continuous Univariate Distributions-2.
     Houghton Mifflin company, Boston.
     10. Johnson, T. (1992). The Relationship of Cpm to Square Error Loss. Journal
     of Quality Technology ,24,211-215.
     11. Kane, V. E. (1986). Process Capability Indices. Journal of Quality Technology
     ,18,41-52.
     12. Kirmani, S. N. U. A., Kocherlakota, K., and Kocherlakota, S. (1991). Estirnation
     of iT and The Process Capability Index Based on Subsamples. Corrunun.
     Statist. - Theory :Meth. ,20,275-291.
     13. Ko cherlakot a, S. (1992). Process Capability Index: Recent developrnents .Sankhyal
     :The Indian Journal of Statistics,54, Series B ,352-369.
     14. Kotz, S. and Jolmson, N. 1. (1993). Process Capability Indices. Chapman &
     Hall.
     15. Kuchler, R. H. and Hurley, P. (1992). Confidence Bounds for Capability Indices.
     Journal of Quality Technology ,24,188-195.
     16. Montgomery, D.e. (1991). Introduction to Statistical Quality Control. 2nd ed.
     John Wiley & Sons, New York.
     17. Peam) W. L.) Kotz) S., and Johnson, N. L. (1992). Distributional and Inferential
     Propertices of Process Capability Indices. Journal of Quality Technology
     ,24,215-231.
     18. Rohatgi, V. K. (1984). Statistical Inference. John Wiley & Sons, New York.
     19. Spiring, F. A. (1991). Assessing Process Capability in The Presence of Sys~
     tematic Assignable Cause. Journal of Quality Technology ,23,125-134.
     20. Tseng, S.T. and Wu, T.Y. (1991). Selecting The Best Manufacturing Process.
     Journal of Quality Technology ,23,53-62.
     21. Wu, T.Y. (1990). A Study of MLR Rule on Sampling Plan. Ph.D. Thesis. Dept
     of Industrial rvlanagement, National Taiwan Institute of Tec1mology, R.O.C.		zh_TW