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題名 適應性累積和損失管制圖之研究
The Study of Adaptive CUSUM Loss Control Charts
作者 林政憲
貢獻者 楊素芬
林政憲
關鍵詞 累積和管制圖
適應性管制圖
VSI管制圖
VSS管制圖
VSSI管制圖
損失函數
馬可夫鍊
基因演算法
CUSUM control chart
Adaptive control chart
VSI control chart
VSS control chart
VSSI control chart
Loss function
Markov chain
Genetic algorithm
日期 2009
上傳時間 8-Dec-2010 14:54:06 (UTC+8)
摘要 The CUSUM control charts have been widely used in detecting small process shifts since it was first introduced by Page (1954). And recent studies have shown that adaptive charts can improve the efficiency and performance of traditional Shewhart charts. To monitor the process mean and variance in a single chart, the loss function is used as a measure statistic in this article. The loss function can measure the process quality loss while the process mean and/or variance has shifted. This study combines the three features: adaption, CUSUM and the loss function, and proposes the optimal VSSI, VSI, and FP CUSUM Loss chart. The performance of the proposed charts is measured by using Average Time to Signal (ATS) and Average Number of Observations to Signal (ANOS). The ATS and ANOS calculations are based on Markov chain approach. The performance comparisons between the proposed charts and some existing charts, such as X-bar+S^2 charts and CUSUM X-bar+S^2 charts, are illustrated by numerical analyses and some examples. From the results of the numerical analyses, it shows that the optimal VSSI CUSUM Loss chart has better performance than the optimal VSI CUSUM Loss chart, optimal FP CUSUM Loss chart, CUSUM X-bar+S^2 charts and X-bar+S^2 charts. Furthermore, using a single chart to monitor a process is not only easier but more efficient than using two charts simultaneously. Hence, the adaptive CUSUM Loss charts are recommended in real process.
The CUSUM control charts have been widely used in detecting small process shifts since it was first introduced by Page (1954). And recent studies have shown that adaptive charts can improve the efficiency and performance of traditional Shewhart charts. To monitor the process mean and variance in a single chart, the loss function is used as a measure statistic in this article. The loss function can measure the process quality loss while the process mean and/or variance has shifted. This study combines the three features: adaption, CUSUM and the loss function, and proposes the optimal VSSI, VSI, and FP CUSUM Loss chart. The performance of the proposed charts is measured by using Average Time to Signal (ATS) and Average Number of Observations to Signal (ANOS). The ATS and ANOS calculations are based on Markov chain approach. The performance comparisons between the proposed charts and some existing charts, such as X-bar+S^2 charts and CUSUM X-bar+S^2 charts, are illustrated by numerical analyses and some examples. From the results of the numerical analyses, it shows that the optimal VSSI CUSUM Loss chart has better performance than the optimal VSI CUSUM Loss chart, optimal FP CUSUM Loss chart, CUSUM X-bar+S^2 charts and X-bar+S^2 charts. Furthermore, using a single chart to monitor a process is not only easier but more efficient than using two charts simultaneously. Hence, the adaptive CUSUM Loss charts are recommended in real process.
參考文獻 [1] Albin, S. L., Kang, L and Shea, G. (1997), “An X and EWMA chart for individual observations,” Journal of Quality Technology, 29, 41-48
[2] Amin, R. W. and Miller, R. W. (1993), “A Robustness Study of Charts with Variable Sampling Intervals,” Journal of Quality Technology, 25, 36-44
[3] Amin, R. W., Wolff, H., Besenfelder, W. and Baxley R. Jr. (1999), “EWMA control charts for the smallest and largest observations,” Journal of Quality Technology, 31, 189-206
[4] Annadi, H. P., Keats, J. B., Runger, G. C. and Montgomery, D. C. (1995), “An adaptive sample size CUSUM control chart,” International Journal of Production Research, 33, 1605-1616
[5] Arnold, J. C. and Reynolds Jr., M. R. (2001), “CUSUM control charts with variable sample sizes and sampling intervals,” Journal of Quality Technology, 33, 66-81
[6] Braverman, J. D. (1981), “Fundamentals of Statistical Quality Control,” Reston Publishing Company, Reston, VA.
[7] Brook D. and Evans D. A. (1972), “An approach to the probability distribution of cusum run length,” Biometrika, 59, 3, 539-549
[8] Chen, G., Cheng, S. W. and Xie, H. (2001), “Monitoring Process Mean and Variability With One EWMA Chart,” Journal of Quality Technology, 33, 223-233
[9] Costa, A. F. B. (1994), “ charts with Variable Sample Size,” Journal of Quality Technology, 26, 155-163
[10] Costa, A. F. B. (1997), “ charts with Variable Sample Size and Sampling Intervals,” Journal of Quality Technology, 29, 197-204
[11] Costa, A. F. B. (1998), “Joint and R charts with variable parameters,” IIE Transactions, 30, 505-514
[12] Costa, A. F. B. (1999a), “Joint and R charts with variable sample size and sampling intervals,” Journal of Quality Technology, 31, 387-397
[13] Costa, A. F. B. (1999b), “ charts with variable parameters,” Journal of Quality Technology, 31, 408-416
[14] Costa, A. F. B. and Magalhaes S. (2006), “An Adaptive Chart for Monitoring the Process Mean and Variance,” Quality and Reliability Engineering International, 23, 821-831
[15] Costa, A. F. B. and Rahim M. A. (2006), “A Single EWMA Chart for Monitoring Process Mean and Variance,” Quality Technology and Quantitative Management, 3, 295-305
[16] DeVor, R. E., Chang, T. and Sutherland, J. W. (1992), “Statistical quality design and control : contemporary concepts and methods”
[17] Hawkins, D. M. (1992), “A Fast Approximation for Average Run Lengths of CUSUM Control Charts,” Journal of Quality Technology, 24, 37-43
[18] Hawkins, D. M. (1993), “Cumulative Sum Control Charting: An Underutilized SPC Tool,” Quality Engineering, 5(3), 463-477
[19] IMSL (1991), Users Manual, Math/Library, Vol. 2, IMSL, Inc., Houstin, Texas
[20] Luceno, A. and Puig-Pey, J. (2002), “Computing the Run Length Probability Distribution for CUSUM Charts,” Journal of Quality Technology, 34, 209-215
[21] Luo, Y., Li, Z. and Wang Z. (2009), “Adaptive CUSUM control chart with variable sampling intervals,” Computational Statistics and Data Analysis, 53, 2693-2701
[22] Montgomery D. C. (2009), “Statistical Quality Control 6th Edition”, Aptara, Inc.
[23] Patnaik P. B. (1949), “The Non-central Chi-square and F-distributions and Their Applications,” Biometrika, 36, 1/2, 202-232
[24] Reynolds, M. R., Jr., Amin, R. W., Arnold, J. C. and Nachlas, J. A. (1988), “ Charts With Variable Sampling Intervals,” Technometrics, 30, 181-192
[25] Reynolds, M. R., Jr., Amin, R. W. and Arnold, J. C. (1990), “CUSUM charts with variable sampling intervals,” Technometrics, 32, 371-384
[26] Reynolds, M. R., Jr. and Arnold J. C. (1989), “Optimal one-sided Shewhart control charts with variable sampling intervals,” Sequential Analysis, 8, 51-77
[27] Wu, Z. and Yu, T. (2006), “Weighted-loss-function control charts,” The International Journal of Advanced Manufacturing Technology, 31, 107-115
[28] Wu, Z., Zhang, S. and Wang, P (2007), “A CUSUM Scheme with Variable Sample Sizes and Sampling Intervals for Monitoring the Process Mean and Variance,” Quality and Reliability Engineering International, 23, 157-170
[29] Zhang, S. and Wu, Z. (2006), “Monitoring the process mean and variance using a weighted loss function CUSUM scheme with variable sampling intervals,” IIE Transactions, 38, 377-387
[30] Zhang, S. and Wu, Z. (2007), “A CUSUM scheme with variable sample sizes for monitoring process shifts,” The International Journal of Advanced Manufacturing Technology, 33, 977-987
描述 碩士
國立政治大學
統計研究所
97354001
98
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097354001
資料類型 thesis
dc.contributor.advisor 楊素芬zh_TW
dc.contributor.author (Authors) 林政憲zh_TW
dc.creator (作者) 林政憲zh_TW
dc.date (日期) 2009en_US
dc.date.accessioned 8-Dec-2010 14:54:06 (UTC+8)-
dc.date.available 8-Dec-2010 14:54:06 (UTC+8)-
dc.date.issued (上傳時間) 8-Dec-2010 14:54:06 (UTC+8)-
dc.identifier (Other Identifiers) G0097354001en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/49600-
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) 97354001zh_TW
dc.description (描述) 98zh_TW
dc.description.abstract (摘要) The CUSUM control charts have been widely used in detecting small process shifts since it was first introduced by Page (1954). And recent studies have shown that adaptive charts can improve the efficiency and performance of traditional Shewhart charts. To monitor the process mean and variance in a single chart, the loss function is used as a measure statistic in this article. The loss function can measure the process quality loss while the process mean and/or variance has shifted. This study combines the three features: adaption, CUSUM and the loss function, and proposes the optimal VSSI, VSI, and FP CUSUM Loss chart. The performance of the proposed charts is measured by using Average Time to Signal (ATS) and Average Number of Observations to Signal (ANOS). The ATS and ANOS calculations are based on Markov chain approach. The performance comparisons between the proposed charts and some existing charts, such as X-bar+S^2 charts and CUSUM X-bar+S^2 charts, are illustrated by numerical analyses and some examples. From the results of the numerical analyses, it shows that the optimal VSSI CUSUM Loss chart has better performance than the optimal VSI CUSUM Loss chart, optimal FP CUSUM Loss chart, CUSUM X-bar+S^2 charts and X-bar+S^2 charts. Furthermore, using a single chart to monitor a process is not only easier but more efficient than using two charts simultaneously. Hence, the adaptive CUSUM Loss charts are recommended in real process.zh_TW
dc.description.abstract (摘要) The CUSUM control charts have been widely used in detecting small process shifts since it was first introduced by Page (1954). And recent studies have shown that adaptive charts can improve the efficiency and performance of traditional Shewhart charts. To monitor the process mean and variance in a single chart, the loss function is used as a measure statistic in this article. The loss function can measure the process quality loss while the process mean and/or variance has shifted. This study combines the three features: adaption, CUSUM and the loss function, and proposes the optimal VSSI, VSI, and FP CUSUM Loss chart. The performance of the proposed charts is measured by using Average Time to Signal (ATS) and Average Number of Observations to Signal (ANOS). The ATS and ANOS calculations are based on Markov chain approach. The performance comparisons between the proposed charts and some existing charts, such as X-bar+S^2 charts and CUSUM X-bar+S^2 charts, are illustrated by numerical analyses and some examples. From the results of the numerical analyses, it shows that the optimal VSSI CUSUM Loss chart has better performance than the optimal VSI CUSUM Loss chart, optimal FP CUSUM Loss chart, CUSUM X-bar+S^2 charts and X-bar+S^2 charts. Furthermore, using a single chart to monitor a process is not only easier but more efficient than using two charts simultaneously. Hence, the adaptive CUSUM Loss charts are recommended in real process.en_US
dc.description.tableofcontents 1. INTRODUCTION 1
2. DESCRIPTION OF IN-CONTROL AND OUT-OF-CONTROL PROCESS QUALITY VARIABLES 3
3. OPTIMAL FP CUSUM LOSS CHART 4
3.1 Description of the optimal FP CUSUM Loss chart 4
3.2 Design of the optimal FP CUSUM Loss chart 6
3.2.1 The Performance Measurement 6
3.2.2 ARL calculation based on Markov chain approach 6
3.2.3 Computing the upper control limit H under a specified k 9
3.2.4 The procedure of acquiring the optimal reference value k and upper control limit H 9
3.3 Numerical analyses for the optimal FP CUSUM Loss chart 10
3.4 Example for the optimal FP CUSUM Loss Chart 16
4. OPTIMAL VSI CUSUM LOSS CHART 19
4.1 Description of the optimal VSI CUSUM Loss chart 19
4.2 Design of the optimal VSI CUSUM Loss chart 21
4.2.1 The performance measurement 21
4.2.2 ATS calculation based on Markov chain approach 22
4.2.3 Computing the warning control limit W under k and H 24
4.2.4 The procedure of acquiring the optimal process parameters 24
4.3 Numerical analyses for the optimal VSI CUSUM Loss chart 25
4.4 Example for the optimal VSI CUSUM Loss Chart 29
5. OPTIMAL VSSI CUSUM LOSS CHART 32
5.1 Description of the optimal VSSI CUSUM Loss chart 32
5.2 Design of the optimal VSSI CUSUM Loss chart 35
5.2.1 The performance measurement 35
5.2.2 ATS and ANOS calculations based on Markov chain approach 36
5.2.3 Computing the warning control limit W under k and H 38
5.2.4 Computing the long sampling interval t1 38
5.2.5 The procedure of acquiring the optimal process parameters 39
5.3 Numerical analyses for the optimal VSSI CUSUM Loss chart 40
5.4 Example for the optimal VSSI CUSUM Loss Chart 44
6. CONCLUSION AND FUTURE STUDY 47
REFERENCES 48
APPENDIX 51		zh_TW
dc.format.extent 875650 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0097354001en_US
dc.subject (關鍵詞) 累積和管制圖zh_TW
dc.subject (關鍵詞) 適應性管制圖zh_TW
dc.subject (關鍵詞) VSI管制圖zh_TW
dc.subject (關鍵詞) VSS管制圖zh_TW
dc.subject (關鍵詞) VSSI管制圖zh_TW
dc.subject (關鍵詞) 損失函數zh_TW
dc.subject (關鍵詞) 馬可夫鍊zh_TW
dc.subject (關鍵詞) 基因演算法zh_TW
dc.subject (關鍵詞) CUSUM control charten_US
dc.subject (關鍵詞) Adaptive control charten_US
dc.subject (關鍵詞) VSI control charten_US
dc.subject (關鍵詞) VSS control charten_US
dc.subject (關鍵詞) VSSI control charten_US
dc.subject (關鍵詞) Loss functionen_US
dc.subject (關鍵詞) Markov chainen_US
dc.subject (關鍵詞) Genetic algorithmen_US
dc.title (題名) 適應性累積和損失管制圖之研究zh_TW
dc.title (題名) The Study of Adaptive CUSUM Loss Control Chartsen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] Albin, S. L., Kang, L and Shea, G. (1997), “An X and EWMA chart for individual observations,” Journal of Quality Technology, 29, 41-48zh_TW
dc.relation.reference (參考文獻) [2] Amin, R. W. and Miller, R. W. (1993), “A Robustness Study of Charts with Variable Sampling Intervals,” Journal of Quality Technology, 25, 36-44zh_TW
dc.relation.reference (參考文獻) [3] Amin, R. W., Wolff, H., Besenfelder, W. and Baxley R. Jr. (1999), “EWMA control charts for the smallest and largest observations,” Journal of Quality Technology, 31, 189-206zh_TW
dc.relation.reference (參考文獻) [4] Annadi, H. P., Keats, J. B., Runger, G. C. and Montgomery, D. C. (1995), “An adaptive sample size CUSUM control chart,” International Journal of Production Research, 33, 1605-1616zh_TW
dc.relation.reference (參考文獻) [5] Arnold, J. C. and Reynolds Jr., M. R. (2001), “CUSUM control charts with variable sample sizes and sampling intervals,” Journal of Quality Technology, 33, 66-81zh_TW
dc.relation.reference (參考文獻) [6] Braverman, J. D. (1981), “Fundamentals of Statistical Quality Control,” Reston Publishing Company, Reston, VA.zh_TW
dc.relation.reference (參考文獻) [7] Brook D. and Evans D. A. (1972), “An approach to the probability distribution of cusum run length,” Biometrika, 59, 3, 539-549zh_TW
dc.relation.reference (參考文獻) [8] Chen, G., Cheng, S. W. and Xie, H. (2001), “Monitoring Process Mean and Variability With One EWMA Chart,” Journal of Quality Technology, 33, 223-233zh_TW
dc.relation.reference (參考文獻) [9] Costa, A. F. B. (1994), “ charts with Variable Sample Size,” Journal of Quality Technology, 26, 155-163zh_TW
dc.relation.reference (參考文獻) [10] Costa, A. F. B. (1997), “ charts with Variable Sample Size and Sampling Intervals,” Journal of Quality Technology, 29, 197-204zh_TW
dc.relation.reference (參考文獻) [11] Costa, A. F. B. (1998), “Joint and R charts with variable parameters,” IIE Transactions, 30, 505-514zh_TW
dc.relation.reference (參考文獻) [12] Costa, A. F. B. (1999a), “Joint and R charts with variable sample size and sampling intervals,” Journal of Quality Technology, 31, 387-397zh_TW
dc.relation.reference (參考文獻) [13] Costa, A. F. B. (1999b), “ charts with variable parameters,” Journal of Quality Technology, 31, 408-416zh_TW
dc.relation.reference (參考文獻) [14] Costa, A. F. B. and Magalhaes S. (2006), “An Adaptive Chart for Monitoring the Process Mean and Variance,” Quality and Reliability Engineering International, 23, 821-831zh_TW
dc.relation.reference (參考文獻) [15] Costa, A. F. B. and Rahim M. A. (2006), “A Single EWMA Chart for Monitoring Process Mean and Variance,” Quality Technology and Quantitative Management, 3, 295-305zh_TW
dc.relation.reference (參考文獻) [16] DeVor, R. E., Chang, T. and Sutherland, J. W. (1992), “Statistical quality design and control : contemporary concepts and methods”zh_TW
dc.relation.reference (參考文獻) [17] Hawkins, D. M. (1992), “A Fast Approximation for Average Run Lengths of CUSUM Control Charts,” Journal of Quality Technology, 24, 37-43zh_TW
dc.relation.reference (參考文獻) [18] Hawkins, D. M. (1993), “Cumulative Sum Control Charting: An Underutilized SPC Tool,” Quality Engineering, 5(3), 463-477zh_TW
dc.relation.reference (參考文獻) [19] IMSL (1991), Users Manual, Math/Library, Vol. 2, IMSL, Inc., Houstin, Texaszh_TW
dc.relation.reference (參考文獻) [20] Luceno, A. and Puig-Pey, J. (2002), “Computing the Run Length Probability Distribution for CUSUM Charts,” Journal of Quality Technology, 34, 209-215zh_TW
dc.relation.reference (參考文獻) [21] Luo, Y., Li, Z. and Wang Z. (2009), “Adaptive CUSUM control chart with variable sampling intervals,” Computational Statistics and Data Analysis, 53, 2693-2701zh_TW
dc.relation.reference (參考文獻) [22] Montgomery D. C. (2009), “Statistical Quality Control 6th Edition”, Aptara, Inc.zh_TW
dc.relation.reference (參考文獻) [23] Patnaik P. B. (1949), “The Non-central Chi-square and F-distributions and Their Applications,” Biometrika, 36, 1/2, 202-232zh_TW
dc.relation.reference (參考文獻) [24] Reynolds, M. R., Jr., Amin, R. W., Arnold, J. C. and Nachlas, J. A. (1988), “ Charts With Variable Sampling Intervals,” Technometrics, 30, 181-192zh_TW
dc.relation.reference (參考文獻) [25] Reynolds, M. R., Jr., Amin, R. W. and Arnold, J. C. (1990), “CUSUM charts with variable sampling intervals,” Technometrics, 32, 371-384zh_TW
dc.relation.reference (參考文獻) [26] Reynolds, M. R., Jr. and Arnold J. C. (1989), “Optimal one-sided Shewhart control charts with variable sampling intervals,” Sequential Analysis, 8, 51-77zh_TW
dc.relation.reference (參考文獻) [27] Wu, Z. and Yu, T. (2006), “Weighted-loss-function control charts,” The International Journal of Advanced Manufacturing Technology, 31, 107-115zh_TW
dc.relation.reference (參考文獻) [28] Wu, Z., Zhang, S. and Wang, P (2007), “A CUSUM Scheme with Variable Sample Sizes and Sampling Intervals for Monitoring the Process Mean and Variance,” Quality and Reliability Engineering International, 23, 157-170zh_TW
dc.relation.reference (參考文獻) [29] Zhang, S. and Wu, Z. (2006), “Monitoring the process mean and variance using a weighted loss function CUSUM scheme with variable sampling intervals,” IIE Transactions, 38, 377-387zh_TW
dc.relation.reference (參考文獻) [30] Zhang, S. and Wu, Z. (2007), “A CUSUM scheme with variable sample sizes for monitoring process shifts,” The International Journal of Advanced Manufacturing Technology, 33, 977-987zh_TW