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題名 二元損失管制圖之設計
Design of the bivariate loss control chart
作者 呂雨築
Lu, Yu Chu
貢獻者 楊素芬
Yang,Su Fen
呂雨築
Lu, Yu Chu
關鍵詞 二元損失管制圖
日期 2010
上傳時間 5-Oct-2011 14:31:56 (UTC+8)
摘要 利用單一二元損失管制圖來偵測製程平均數向量及共變異數矩陣同時偏移。不同於已存在的多元管制圖，本文所提出的管制圖是以二元平均損失函數建構而成的，因此，在監控製程時，我們同時能獲得產品平均損失的資訊。平均連串長度分析結果指出二元損失管制圖在偵測製程小幅度偏移上有不錯的其偵測能力。本文將與現存的多元方法做績效表現的比較，例如：二元管制圖、多元的累積管制圖和多元的指數加權平均管制圖等。結果顯示，二元損失管制圖在偵測程平均數向量及共變異數矩陣同時偏移的情況下有較好的偵測能力。
參考文獻 1. Alt, F. B. (1985), “Multivariate quality control,” In: Kotz, S. and Johnson, N., eds. Encyclopedia of Statistics. 6, John Wiley & Sons, New York, NY, 110-122.
2. Alt, F. B. and Bedewi, G. E. (1986), “SPC for dispersion for multivariate data,” ASQC. Qual. Congress Trans, 248-254.
3. Aparisi F. and Haro, C. L. (2001), “Hotelling T2 control chart with variable sampling intervals,” Int. J. Prod. Res, 39(14), 3127-3140.
4. Chan, L. K. and Zhang, J. (2001), “Cumulative sum control chart for the covariance matrix,” Statist. Sinica, 11, 767-790.
5. Chen Y. K. and Hsieh K. L. (2007), “Hotelling T2 control chart with variable sample size and control limit,” European Journal of Operational Research, 182, 1251 – 1262.
6. Cheng, G. Z. (1995), “A Study of an Application on the Multi-Characteristic Quality Loss Function,” Master’s Thesis, Providence University, Shalu, Taiwan.
7. Cheng, S. W. and Thaga, K. (2005), ”Multivariate Max-CUSUM chart,” Quality Technology & Quantitative Management, 2(2), 221-235.
8. Chou, C. Y., Liu, H. R., Chen, C. H. and Huang, X. R. (2002), “Economic-statistical design of multivariate control charts using quality loss function,” Int J Adv Manuf Technol, 20, 916-924.
9. Costa, A. F. B. and Machado, M. A. G. (2009), “A new chart based on sample variances for monitoring the covariance matrix of multivariate processes,” Int J Adv Manuf Technol, 41, 770-779.
10. Crosier, R. B. (1988), “Multivariate generalizations of cumolative sum quality control schemes,” Technometrics, 30, 291-303.
11. Farebrother, R. W. (1984), “Algorithm AS 204: The distribution of a positive linear combination of random variables,” Journal of the Royal Statistical Society, Series C (Applied Statistics), 33, 332-339.
12. Hawkins, D. M. (1991), “Multivariate quality control based on regression – adjusted variables,” Technometrics, 33, 61-75.
13. Hawkins, D. M. and Maboudou-Tchao, E. M. (2008), “Multivariate exponentially weighted moving covariance matrix,” Technometrics, 50, 155-166.
14. Hawkins, D. M., Qiu, P. and Kang, C. W. (2003), “The changepoint model for statistical process control,” Journal of Quality Technology, 35 (4), 355-366.
15. Hawkins, D. M. and Zamba K. D. (2005), “Statistical process control for shifts in mean or variance using a changepoint formulation,” Technometrics, 47 (2), 164-173.
16. Healy, J. D. (1987), “A note on multivariate quality CUSUM procedures,” Technometrics, 29, 409-412.
17. Imhof, J. P. (1961), “Computing the distribution of quadratic forms in normal variables,” Biometrika, 48(3 and 4), 419-426.
18. Jackson, J. E. (1959), “Quality control methods for several related variables,” Technometrics, 1, 359-377.
19. James, W. and Stein, C. (1961), “Estimation with quadratic loss,” Fourth Berkeley Simpslum, 361-379.
20. Johnson, R. A. and Wichern D. W. (1992), “Applied multivariate statistical analysis,” Englewood Cliffs, N.J. : Prentice Hall
21. Khoo, B. C. (2005), “A new bivariate control chart to monitor the multivariate process mean and variance simultaneously,” Quality Engineering, 17, 109-118.
22. Liu, H., Tang, Y., and Zhang, H. H. (2009), “Computational statistics and data analysis,” Computational Statistics and Data Analysis, 53, 853-856.
23. Liu, R. Y. (1995), “Control charts for multivariate process,” J. Amer. Statist. Assoc, 90, 1380-1387.
24. Lowry, C. A., Woodall, W. H., Champ, C. W. and Rigdon, S. E. (1992), “A multivariate exponentially weighted moving average control chart,” Technometrics, 34, 46-53.
25. Mahmoud, M. A. and Zahran, A. R. (2011), “ A multivariate adaptive exponentially weighted moving average control chart,” Communications in Statistics – Theory and Methods, 39 (4), 606-625.
26. Mohebbi, C. and Hayre, L. (1989), “Multivariate control charts: a loss function approach,” Sequential Analysis, 8, 253-268.
27. Moschopoulous, P. G. and Canada, W. B. (1984), “The distribution function of a linear combination of chi-square,” Comp. & Maths, with Appls., 10, 383-386.
28. Montgomery, D. C. (2001), Introduction to statistical quality control, 4th Ed, John Wiley & Sons, New York, NY.
29. Patnaik, P. B. (1949), “The non-central - and F-distribution and their applications,” Biometrika, 36, 202-232.
30. Pearson, E. S. (1959), “Note on an approximation to the distribution of non-central ,” Biometrika, 46, 364-365.
31. Pignatiello, J. J. and Runger, G. C. (1990), “Comparisons of multivariate CUSUM charts,” J. Qual. Technol, 22, 173-186.
32. Qiu, P. and Hawkins, D. M. (2001), “A rank-based multivariate CUSUM procedure,” Technometrics, 43, 120-132.
33. Reynolds, M. R. and Cho, G. Y. (2006), “Multivariate control charts for monitoring the mean vector and covariance matrix,” J. Qual. Technol, 38(3), 230-253.
34. Spiring, F. A. and Cheng, S. W. (1998), “An alternate variables control chart: the univariate and multivariate case,” Statistica Sinica, 8, 273-287.
35. Stoumbos, Z. G., Reynolds, M. R., Ryan, T. P. and Woodall, W. H. (2000). “The state of statistical process control as we proceed into the 21st century,” J. Amer. Statist. Assoc, 95, 992-998.
36. Tang, P. F. and Barnett, N. S. (1996a), “Dispersion control for multivariate processes,” Aust. N. J. Stat, 38, 235-251.
37. Tang, P. F. and Barnett, N. S. (1996b), “Dispersion control for multivariate processes-some comparisons,” Aust. N. J. Stat, 31, 376-386.
38. Tsui, K. and Woodall, W. H. (1993), “Multivariate control charts based on loss functions,” Sequential Analysis, 12(1), 79-92.
39. Woodall, W. H. and Montgomery D. C. (1999), “Research issues and ideas in statistical process control,” J. Qual. Technol, 31, 376-386.
40. Woodall, W. H. and Nucube, M. M. (1985), “Multivariate CUSUM quality control procedures,” Technometrics, 27, 285-292.
41. Xie, H. (1999). “Contribution to qualimetry,” Ph.D. thesis, University of Manitoba, Winnipeg, Canada.
42. Yang, S. F., Lin, K. J. and Hung, T.C. (2009), “ Improvement in consistency of the metallic film thickness of computer connectors,” Journal of Process Control, 19, 498-505.
43. Yeh, A. B., Huwang, L. and Wu, Y. F. (2004), “A likelihood-ratio-based EWMA control chart for monitoring variability of multivariate normal processes,” IIE Trans, 36, 865-879.
44. Yeh, A. B., Huwang, L. and Wu, C. W. (2005), “A multivariate EWMA control chart for monitoring process variability with individual observations,” IIE Trans, 37, 1023-1035.
45. Yeh, A. B. and Lin, D. K. (2002), “A new variables control chart for simultaneously monitoring multivariate process mean and variability,” Int. J. Reliab. Qual. Saf. Eng, 9 (1). 41-59.
46. Yeh, A. B., Lin, K. J., Zhou, H. H. and Venkataramani, C. (2003), “ A multivariate exponentially weighted moving average control chart for monitoring process variability,” Journal of Applied Statistics, 30(5), 507-536.
47. Zamba, K. D. and Hawkinsm D. M. (2006), “A multivariate change-point model for statistical process control,” Technometrics, 48 (4), 539-548.
48. Zhang, J., Li, Z. and Wang, Z. (2010), “A multivariate control chart for simultaneously monitoring process mean and variability,” Computational Statisitcs and Data Analysis, 54, 2244-2252.
描述 碩士
國立政治大學
統計研究所
98354004
99
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0098354004
資料類型 thesis
dc.contributor.advisor 楊素芬zh_TW
dc.contributor.advisor Yang,Su Fenen_US
dc.contributor.author (Authors) 呂雨築zh_TW
dc.contributor.author (Authors) Lu, Yu Chuen_US
dc.creator (作者) 呂雨築zh_TW
dc.creator (作者) Lu, Yu Chuen_US
dc.date (日期) 2010en_US
dc.date.accessioned 5-Oct-2011 14:31:56 (UTC+8)-
dc.date.available 5-Oct-2011 14:31:56 (UTC+8)-
dc.date.issued (上傳時間) 5-Oct-2011 14:31:56 (UTC+8)-
dc.identifier (Other Identifiers) G0098354004en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/51201-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計研究所zh_TW
dc.description (描述) 98354004zh_TW
dc.description (描述) 99zh_TW
dc.description.abstract (摘要) 利用單一二元損失管制圖來偵測製程平均數向量及共變異數矩陣同時偏移。不同於已存在的多元管制圖，本文所提出的管制圖是以二元平均損失函數建構而成的，因此，在監控製程時，我們同時能獲得產品平均損失的資訊。平均連串長度分析結果指出二元損失管制圖在偵測製程小幅度偏移上有不錯的其偵測能力。本文將與現存的多元方法做績效表現的比較，例如：二元管制圖、多元的累積管制圖和多元的指數加權平均管制圖等。結果顯示，二元損失管制圖在偵測程平均數向量及共變異數矩陣同時偏移的情況下有較好的偵測能力。zh_TW
dc.description.tableofcontents Table of Contents
Chapter 1 INTRODUCTION 1
1.1 The Importance of the Process Control 1
1.2 Research Problem 1
1.3 Research Purpose 2
1.4 Literature Review 2
1.5 Proposed Method and Structure 8
Chapter 2 THE BIVARIATE LOSS CONTROL CHART 9
2.1 Design of the Bivariate Loss Chart 9
2.2 Average Bivariate Loss and its Distribution 9
2.3 The Approximated Distribution of BL 11
2.4 The Control Limits of the BL Chart 13
2.5 The Out-of-control Approximate Distribution of BL 14
2.6 Performance Measurement of the BL Chart 15
2.7 Illustrating Example of the Bivariate Loss Chart 16
2.8 ARL1 of the Bivariate Loss Chart 26
2.9 The Bivariate Loss Chart with Optimal Sample Size and Sampling Interval 42
2.10 ATS1 Comparison of the Specified Bivariate Loss Chart and the Optimal Bivariate Loss Chart 51
Chapter 3 THE VSSI BIVARAITE LOSS CONTROL CHART 56
3.1 Design of the VSSI Bivariate Loss Chart 56
3.2 The Approximate Distribution of BL 57
3.3 The Control Limits of the VSSI BL Chart 58
3.4 The Out-of-control Approximate Distribution of BL 59
3.5 Performance Measurement of the VSSI BL Chart 59
3.6 Example for the VSSI Bivariate Loss Chart 61
Chapter 4 ATS1 ANALYSIS OF THE VSSI BIVARIATE LOSS CHART AND
ATS1 COMPARISON BETWEEN THE BL CHART AND THE
VSSI BL CHART 65
4.1 The Specified ( ) VSSI Bivariate Loss Chart 65
4.2 The VSSI Bivariate Loss Chart With Optimal ( ) 71
4.3 The OptimalVSSI Bivariate Loss Chart 78
Chapter 5 PERFORMANCE COMPARISON WITH SOME EXISTING METHODS 84
5.1 ARL1 Comparison of the BL Chart and Khoo’s Max Bivariate Control Chart 84
5.2 ARL1 Comparison for the BL Chart, MSE Chart, Max-CUSUM Chart and Max- MEWMA Chart 93
5.3 ARL1 Comparison for the Bivariate Loss Chart, EWMA V- Chart, EWMA M-Chart, MEWMA Chart and - Chart 96
Chapter 6 CONCLUSION AND FUTURE RESEARCH 101
Appendices 103
Appendix A 103
Appendix B 106
Appendix C 113
References 116		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0098354004en_US
dc.subject (關鍵詞) 二元損失管制圖zh_TW
dc.title (題名) 二元損失管制圖之設計zh_TW
dc.title (題名) Design of the bivariate loss control charten_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 1. Alt, F. B. (1985), “Multivariate quality control,” In: Kotz, S. and Johnson, N., eds. Encyclopedia of Statistics. 6, John Wiley & Sons, New York, NY, 110-122.zh_TW
dc.relation.reference (參考文獻) 2. Alt, F. B. and Bedewi, G. E. (1986), “SPC for dispersion for multivariate data,” ASQC. Qual. Congress Trans, 248-254.zh_TW
dc.relation.reference (參考文獻) 3. Aparisi F. and Haro, C. L. (2001), “Hotelling T2 control chart with variable sampling intervals,” Int. J. Prod. Res, 39(14), 3127-3140.zh_TW
dc.relation.reference (參考文獻) 4. Chan, L. K. and Zhang, J. (2001), “Cumulative sum control chart for the covariance matrix,” Statist. Sinica, 11, 767-790.zh_TW
dc.relation.reference (參考文獻) 5. Chen Y. K. and Hsieh K. L. (2007), “Hotelling T2 control chart with variable sample size and control limit,” European Journal of Operational Research, 182, 1251 – 1262.zh_TW
dc.relation.reference (參考文獻) 6. Cheng, G. Z. (1995), “A Study of an Application on the Multi-Characteristic Quality Loss Function,” Master’s Thesis, Providence University, Shalu, Taiwan.zh_TW
dc.relation.reference (參考文獻) 7. Cheng, S. W. and Thaga, K. (2005), ”Multivariate Max-CUSUM chart,” Quality Technology & Quantitative Management, 2(2), 221-235.zh_TW
dc.relation.reference (參考文獻) 8. Chou, C. Y., Liu, H. R., Chen, C. H. and Huang, X. R. (2002), “Economic-statistical design of multivariate control charts using quality loss function,” Int J Adv Manuf Technol, 20, 916-924.zh_TW
dc.relation.reference (參考文獻) 9. Costa, A. F. B. and Machado, M. A. G. (2009), “A new chart based on sample variances for monitoring the covariance matrix of multivariate processes,” Int J Adv Manuf Technol, 41, 770-779.zh_TW
dc.relation.reference (參考文獻) 10. Crosier, R. B. (1988), “Multivariate generalizations of cumolative sum quality control schemes,” Technometrics, 30, 291-303.zh_TW
dc.relation.reference (參考文獻) 11. Farebrother, R. W. (1984), “Algorithm AS 204: The distribution of a positive linear combination of random variables,” Journal of the Royal Statistical Society, Series C (Applied Statistics), 33, 332-339.zh_TW
dc.relation.reference (參考文獻) 12. Hawkins, D. M. (1991), “Multivariate quality control based on regression – adjusted variables,” Technometrics, 33, 61-75.zh_TW
dc.relation.reference (參考文獻) 13. Hawkins, D. M. and Maboudou-Tchao, E. M. (2008), “Multivariate exponentially weighted moving covariance matrix,” Technometrics, 50, 155-166.zh_TW
dc.relation.reference (參考文獻) 14. Hawkins, D. M., Qiu, P. and Kang, C. W. (2003), “The changepoint model for statistical process control,” Journal of Quality Technology, 35 (4), 355-366.zh_TW
dc.relation.reference (參考文獻) 15. Hawkins, D. M. and Zamba K. D. (2005), “Statistical process control for shifts in mean or variance using a changepoint formulation,” Technometrics, 47 (2), 164-173.zh_TW
dc.relation.reference (參考文獻) 16. Healy, J. D. (1987), “A note on multivariate quality CUSUM procedures,” Technometrics, 29, 409-412.zh_TW
dc.relation.reference (參考文獻) 17. Imhof, J. P. (1961), “Computing the distribution of quadratic forms in normal variables,” Biometrika, 48(3 and 4), 419-426.zh_TW
dc.relation.reference (參考文獻) 18. Jackson, J. E. (1959), “Quality control methods for several related variables,” Technometrics, 1, 359-377.zh_TW
dc.relation.reference (參考文獻) 19. James, W. and Stein, C. (1961), “Estimation with quadratic loss,” Fourth Berkeley Simpslum, 361-379.zh_TW
dc.relation.reference (參考文獻) 20. Johnson, R. A. and Wichern D. W. (1992), “Applied multivariate statistical analysis,” Englewood Cliffs, N.J. : Prentice Hallzh_TW
dc.relation.reference (參考文獻) 21. Khoo, B. C. (2005), “A new bivariate control chart to monitor the multivariate process mean and variance simultaneously,” Quality Engineering, 17, 109-118.zh_TW
dc.relation.reference (參考文獻) 22. Liu, H., Tang, Y., and Zhang, H. H. (2009), “Computational statistics and data analysis,” Computational Statistics and Data Analysis, 53, 853-856.zh_TW
dc.relation.reference (參考文獻) 23. Liu, R. Y. (1995), “Control charts for multivariate process,” J. Amer. Statist. Assoc, 90, 1380-1387.zh_TW
dc.relation.reference (參考文獻) 24. Lowry, C. A., Woodall, W. H., Champ, C. W. and Rigdon, S. E. (1992), “A multivariate exponentially weighted moving average control chart,” Technometrics, 34, 46-53.zh_TW
dc.relation.reference (參考文獻) 25. Mahmoud, M. A. and Zahran, A. R. (2011), “ A multivariate adaptive exponentially weighted moving average control chart,” Communications in Statistics – Theory and Methods, 39 (4), 606-625.zh_TW
dc.relation.reference (參考文獻) 26. Mohebbi, C. and Hayre, L. (1989), “Multivariate control charts: a loss function approach,” Sequential Analysis, 8, 253-268.zh_TW
dc.relation.reference (參考文獻) 27. Moschopoulous, P. G. and Canada, W. B. (1984), “The distribution function of a linear combination of chi-square,” Comp. & Maths, with Appls., 10, 383-386.zh_TW
dc.relation.reference (參考文獻) 28. Montgomery, D. C. (2001), Introduction to statistical quality control, 4th Ed, John Wiley & Sons, New York, NY.zh_TW
dc.relation.reference (參考文獻) 29. Patnaik, P. B. (1949), “The non-central - and F-distribution and their applications,” Biometrika, 36, 202-232.zh_TW
dc.relation.reference (參考文獻) 30. Pearson, E. S. (1959), “Note on an approximation to the distribution of non-central ,” Biometrika, 46, 364-365.zh_TW
dc.relation.reference (參考文獻) 31. Pignatiello, J. J. and Runger, G. C. (1990), “Comparisons of multivariate CUSUM charts,” J. Qual. Technol, 22, 173-186.zh_TW
dc.relation.reference (參考文獻) 32. Qiu, P. and Hawkins, D. M. (2001), “A rank-based multivariate CUSUM procedure,” Technometrics, 43, 120-132.zh_TW
dc.relation.reference (參考文獻) 33. Reynolds, M. R. and Cho, G. Y. (2006), “Multivariate control charts for monitoring the mean vector and covariance matrix,” J. Qual. Technol, 38(3), 230-253.zh_TW
dc.relation.reference (參考文獻) 34. Spiring, F. A. and Cheng, S. W. (1998), “An alternate variables control chart: the univariate and multivariate case,” Statistica Sinica, 8, 273-287.zh_TW
dc.relation.reference (參考文獻) 35. Stoumbos, Z. G., Reynolds, M. R., Ryan, T. P. and Woodall, W. H. (2000). “The state of statistical process control as we proceed into the 21st century,” J. Amer. Statist. Assoc, 95, 992-998.zh_TW
dc.relation.reference (參考文獻) 36. Tang, P. F. and Barnett, N. S. (1996a), “Dispersion control for multivariate processes,” Aust. N. J. Stat, 38, 235-251.zh_TW
dc.relation.reference (參考文獻) 37. Tang, P. F. and Barnett, N. S. (1996b), “Dispersion control for multivariate processes-some comparisons,” Aust. N. J. Stat, 31, 376-386.zh_TW
dc.relation.reference (參考文獻) 38. Tsui, K. and Woodall, W. H. (1993), “Multivariate control charts based on loss functions,” Sequential Analysis, 12(1), 79-92.zh_TW
dc.relation.reference (參考文獻) 39. Woodall, W. H. and Montgomery D. C. (1999), “Research issues and ideas in statistical process control,” J. Qual. Technol, 31, 376-386.zh_TW
dc.relation.reference (參考文獻) 40. Woodall, W. H. and Nucube, M. M. (1985), “Multivariate CUSUM quality control procedures,” Technometrics, 27, 285-292.zh_TW
dc.relation.reference (參考文獻) 41. Xie, H. (1999). “Contribution to qualimetry,” Ph.D. thesis, University of Manitoba, Winnipeg, Canada.zh_TW
dc.relation.reference (參考文獻) 42. Yang, S. F., Lin, K. J. and Hung, T.C. (2009), “ Improvement in consistency of the metallic film thickness of computer connectors,” Journal of Process Control, 19, 498-505.zh_TW
dc.relation.reference (參考文獻) 43. Yeh, A. B., Huwang, L. and Wu, Y. F. (2004), “A likelihood-ratio-based EWMA control chart for monitoring variability of multivariate normal processes,” IIE Trans, 36, 865-879.zh_TW
dc.relation.reference (參考文獻) 44. Yeh, A. B., Huwang, L. and Wu, C. W. (2005), “A multivariate EWMA control chart for monitoring process variability with individual observations,” IIE Trans, 37, 1023-1035.zh_TW
dc.relation.reference (參考文獻) 45. Yeh, A. B. and Lin, D. K. (2002), “A new variables control chart for simultaneously monitoring multivariate process mean and variability,” Int. J. Reliab. Qual. Saf. Eng, 9 (1). 41-59.zh_TW
dc.relation.reference (參考文獻) 46. Yeh, A. B., Lin, K. J., Zhou, H. H. and Venkataramani, C. (2003), “ A multivariate exponentially weighted moving average control chart for monitoring process variability,” Journal of Applied Statistics, 30(5), 507-536.zh_TW
dc.relation.reference (參考文獻) 47. Zamba, K. D. and Hawkinsm D. M. (2006), “A multivariate change-point model for statistical process control,” Technometrics, 48 (4), 539-548.zh_TW
dc.relation.reference (參考文獻) 48. Zhang, J., Li, Z. and Wang, Z. (2010), “A multivariate control chart for simultaneously monitoring process mean and variability,” Computational Statisitcs and Data Analysis, 54, 2244-2252.zh_TW