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題名 利用調適性管制技術同時監控製程平均數和變異數
Joint Monitoring of Process Means and Variances by Using Adaptive Control Schemes
作者 陳琬昀
貢獻者 楊素芬
陳琬昀
關鍵詞 管制圖
變動參數
相依製程
選控圖
馬可夫鏈
Control Charts
Variable Parameters
Dependent Process Steps
Cause-Selecting Control Chart
Markov Chain
日期 2007
上傳時間 17-Sep-2009 18:47:19 (UTC+8)
摘要 　　由近期的研究中發現變動所有參數的管制圖在偵測小幅度偏移時的速度比起傳統的舒華特管制圖來的快，許多文獻也討論到利用調適性管制技術同時監控製程的平均數和變異數。而在這份研究中，為了改善現有管制圖的偵測效率，依序提出了U-V管制圖以及Max-M管制圖來偵測單一製程與兩相依製程的平均數和變異數。採用AATS及ANOS來衡量管制圖的偵測績效，並利用馬可夫鏈推導計算得之。透過兩階段的範例來介紹所提出的管制圖的應用方法並將VP U-V管制圖、VP Max-M管制圖與FP Z(X-bar)-Z(Sx^2)管制圖加以比較。從所研究的數值分析中發現VP Max-M管制圖比另兩種管制圖的表現來的好，再加上只需要單一管制圖在使用上對工程師來說也較為簡便，因此建議Max-M管制圖値得在實務上被使用。
Recent studies have shown that the variable parameters (VP) charts detect small process shifts faster than the traditional Shewhart charts. There have been many papers discussed adaptive control schemes to monitor process mean and variance simultaneously. In the study, to improve the efficiency and performance of the existing control charts, the U-V control charts and Max-M control charts are respectively proposed to monitor the process mean and variance for a single process and two dependent process steps. The performance of the proposed control charts is measured by using adjusted average time to signal (AATS) and average number of observations to signal (ANOS). The calculation of AATS and ANOS is derived by Markov chain approach. The application of the proposed control charts is illustrated by a numerical example for two dependent process steps, and the performance of VP U-V control charts, VP Max-M control charts and FP Z(X-bar)-Z(Sx^2) control charts is compared. From the results of data analyses, it shows that the VP Max-M control charts have better performance than VP U-V control charts and FP Z(X-bar)-Z(Sx^2) control charts. Furthermore, using a single chart to monitor a process is easier than using two charts for engineers. Hence, Max-M control charts are recommended in real industrial process.
參考文獻 [1]Amin, R. W. and Miller, R. W. (1993), “A Robustness Study of X-bar Charts with Variable Sampling Intervals,” Journal of Quality Technology 25, 36-44.
[2]Chen, G. and Cheng, S. W. (1998), “Max Chart: Combining X-bar Chart and S Chart,” Statistic Sinica 8, 263-271.
[3]Chengalur, I. N., Arnold, J. C. and Reynolds, M. R., JR. (1989), “Variable Sampling Intervals for Multiparameter Shewhart Charts,” Communications in Statistics - Theory and Methods 18, 1769-1792.
[4]Cinlar, E. (1975), Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, N.J.
[5]Constable, G. K., Cleary, M. J., Tickel, C. and Zhang, G. X. (1988), “Use of Cause-Selecting Charts in the Auto Industry,” ASQC Quality Congress Transactions. American Society for Quality Control, 597-602.
[6]Costa, A. F. B. (1994), “ X-bar Charts with Variable Sample Size,” Journal of Quality Technology 26, 155-163.
[7]Costa, A. F. B. (1997), “ X-bar Charts with Variable Sample Size and Sampling Intervals,” Journal of Quality Technology 29, 197-204.
[8]Costa, A. F. B. (1998), “Joint X-bar and R Charts with Variable Parameters,” IIE Transactions 30, 505-514.
[9]Costa, A. F. B. (1999a), “Joint X-bar and R Charts with Variable Sample Size and Sampling Intervals,” Journal of Quality Technology 31, 387-397.
[10]Costa, A. F. B. (1999b), “ X-bar Charts with Variable Parameters,” Journal of Quality Technology 31, 408-416.
[11]Daudin, J. J. (1992), “Double Sampling X-bar Charts,” Journal of Quality Technology 24, 78-87.
[12]Fiocca, A. (1988), Some unpublished works of Ludovico Ferrari (Italian), Boll. Storia Sci. Mat. 8 (2), 239-305.
[13]IMSL (1991), Users Manual, Math/Library, Vol.2, IMSL, Inc., Houstin, Texas.
[14]Kang, L. and Albin, S. L. (2000), “On-Line Monitoring When the Process Yields a Linear Profile,” Journal of Quality Technology 32, 418-426.
[15]Mandel, B. J. (1969), “The Regression Control Chart,” Journal of Quality Technology 1, 1-9.
[16]Prabhu, S. S., Montgomery, D. C. and Runger, G. C. (1994), “A Combined Adaptive Sample Size and Sampling Interval X-bar Control Scheme,” Journal of Quality Technology 26, 164-176.
[17]Prabhu, S. S., Runger, G. C. and Keats, J. B. (1993), “An Adaptive Sample Size X-bar Chart,” International Journal of Production Research 31, 2895-2909.
[18]Reynolds, M. R., JR. (1989), “Optimal Variable Sampling Interval Control Charts,” Sequential Analysis 8, 361-379.
[19]Reynolds, M. R., JR. (1995), “Evaluating Properties of Variable Sampling Interval Control Charts,” Sequential Analysis 14, 59-97.
[20]Reynolds, M. R., JR. (1996), “Variable-Sampling-Interval Control Charts with Sampling at Fixed Times,” IIE Transactions 28, 497-510.
[21]Reynolds, M. R., JR., Amin, R. W., Arnold, J. C. and Nachlas, J. A. (1988), “ X-bar Charts with Variable Sampling Intervals,” Technometrics 30, 181-192.
[22]Reynolds, M. R., JR. and Arnold, J. C. (1989), “Optimal One-Sized Shewhart Control Charts with Variable Sampling Intervals,” Sequential Analysis 8, 51-77.
[23]Reynolds, M. R., JR., Arnold, J. C. and Baik, J. W. (1996), “Variable Sampling Interval X-bar Charts in the Presence of Correlation,” Journal of Quality Technology 28, 12-30.
[24]Runger, G. C. and Montgomery, D. C. (1993), “Adaptive Sampling Enhancements for Shewhart Control Charts,” IIE Transactions 25, 41-51.
[25]Runger, G. C. and Pignatiello, J. J., JR. (1991), “Adaptive Sampling for Process Control,” Journal of Quality Technology 23, 135-155.
[26]Tagaras, G. (1998), “A Survey of Recent Developments in the Design of Adaptive Control Charts,” Journal of Quality Technology 30, 212-231.
[27]Wade, M. R. and Woodall, W. H. (1993), “A Review and Analysis of Cause-Selecting Control Charts,” Journal of Quality Technology 25, 161-169.
[28]Yang, S. (2005), “Dependent Processes Control for Over-adjusted Means,” International Journal of Advanced Manufacturing Technology, 109-116.
[29]Yang, S. and Su, H. (2006), “Controlling-dependent Process Steps Using Variable Sample Size Control Charts,” Applied stochastic model in business and industry, Vol. 22, 503-517.
[30]Yang, S. and Su, H. (2007a), “Adaptive Sampling Interval for Two Dependent Process Steps Control,” International Journal of Advanced Manufacturing Technology, Vol. 31, 1169-1180.
[31]Yang, S. and Su, H. (2007b), “Adaptive Control Scheme for Dependent Process Steps,” International Journal of Loss Prevention and Industrial Process, Vol. 20, 15-25.
[32]Yang, S. and Yang, C. (2006), “An Approach to Controlling Two Dependent Process Steps with Autocorrelated Observations,” International Journal of Advanced Manufacturing Technology, Vol. 29, 170-177.
[33]Yang, S. and Chen, W. (2007a), “Controlling Incorrect Adjustment Processes Using Optimum VSI Control Charts,” International Statistical Conference, ISI 56, Lisbon, Portugal.
[34]Yang, S. and Chen, W. (2007b), “Variable Sampling Interval Control Charts,” International Conference of Multiple Decision Theory, in honor of Dr. Den-Yung Hwang, Taiwan.
[35]Zhang, G. X. (1984), “A New Type of Control Charts and a Theory of Diagnosis with Control Charts,” World Quality Congress Transactions. American Society for Quality Control, 175-185.
描述 碩士
國立政治大學
統計研究所
95354020
96
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0095354020
資料類型 thesis
dc.contributor.advisor 楊素芬zh_TW
dc.contributor.author (Authors) 陳琬昀zh_TW
dc.creator (作者) 陳琬昀zh_TW
dc.date (日期) 2007en_US
dc.date.accessioned 17-Sep-2009 18:47:19 (UTC+8)-
dc.date.available 17-Sep-2009 18:47:19 (UTC+8)-
dc.date.issued (上傳時間) 17-Sep-2009 18:47:19 (UTC+8)-
dc.identifier (Other Identifiers) G0095354020en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/33910-
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) 95354020zh_TW
dc.description (描述) 96zh_TW
dc.description.abstract (摘要) 　　由近期的研究中發現變動所有參數的管制圖在偵測小幅度偏移時的速度比起傳統的舒華特管制圖來的快，許多文獻也討論到利用調適性管制技術同時監控製程的平均數和變異數。而在這份研究中，為了改善現有管制圖的偵測效率，依序提出了U-V管制圖以及Max-M管制圖來偵測單一製程與兩相依製程的平均數和變異數。採用AATS及ANOS來衡量管制圖的偵測績效，並利用馬可夫鏈推導計算得之。透過兩階段的範例來介紹所提出的管制圖的應用方法並將VP U-V管制圖、VP Max-M管制圖與FP Z(X-bar)-Z(Sx^2)管制圖加以比較。從所研究的數值分析中發現VP Max-M管制圖比另兩種管制圖的表現來的好，再加上只需要單一管制圖在使用上對工程師來說也較為簡便，因此建議Max-M管制圖値得在實務上被使用。zh_TW
dc.description.abstract (摘要) Recent studies have shown that the variable parameters (VP) charts detect small process shifts faster than the traditional Shewhart charts. There have been many papers discussed adaptive control schemes to monitor process mean and variance simultaneously. In the study, to improve the efficiency and performance of the existing control charts, the U-V control charts and Max-M control charts are respectively proposed to monitor the process mean and variance for a single process and two dependent process steps. The performance of the proposed control charts is measured by using adjusted average time to signal (AATS) and average number of observations to signal (ANOS). The calculation of AATS and ANOS is derived by Markov chain approach. The application of the proposed control charts is illustrated by a numerical example for two dependent process steps, and the performance of VP U-V control charts, VP Max-M control charts and FP Z(X-bar)-Z(Sx^2) control charts is compared. From the results of data analyses, it shows that the VP Max-M control charts have better performance than VP U-V control charts and FP Z(X-bar)-Z(Sx^2) control charts. Furthermore, using a single chart to monitor a process is easier than using two charts for engineers. Hence, Max-M control charts are recommended in real industrial process.en_US
dc.description.tableofcontents 1 INTRODUCTION.............................................1
2 DESCRIPTION OF TWO DEPENDENT PROCESS STEPS...............7
3 JOINT VP U-V CONTROL CHARTS FOR ONE STEP AND TWO DEPENDENT STEPS...........................................10
3.1 Description of the Joint VP U-V Control Charts for One Step....................................................11
3.2 Description of the Joint VP U-V Control Charts for Two Dependent Steps...................................................13
3.2.1 The distributions of the U and V statistics under in-control and out-of-control process......................13
3.2.2 Design of the VP U-V control charts...............15
3.2.3 Initial probability calculation...................17
3.2.4 Determination of the warning limit................20
3.2.5 Performance measurement...........................23
4 VP MAX-M CONTROL CHARTS FOR ONE STEP AND TWO DEPENDENT STEPS.....................................................29
4.1 Description of the VP Max-M Control Chart for One Step....................................................29
4.2 Description of the VP Max-M Control Charts for Two Dependent Steps.........................................30
4.2.1 The distributions of the M statistics under in-control and out-of-control process......................30
4.2.2 Design of the VP Max-M control charts.............31
4.2.3 Initial probability calculation...................33
4.2.4 Determination of the warning limit................34
4.2.5 Performance measurement...........................37
5 NUMERICAL ANALYSES FOR THE PROPOSED CONTROL CHARTS......41
5.1 A Real Example of Using FP U-V and FP Max-M Control Charts..................................................41
5.2 Performance Comparisons and Sensitivity Analyses of the FP U-V, FP Max-M and FP Z(X-bar)-Z(Sx^2) Control Charts.49
5.2.1 The effects of parameters on AATS.................49
5.2.2 The effects of parameters on AATS and ANOS........55
5.3 A Real Example of Using VP U-V and VP Max-M Control Charts..................................................57
5.4 Performance Comparisons and Sensitivity Analyses of the VP U-V, VP Max-M and FP Z(X-bar)-Z(Sx^2) Control Charts.65
6 SUMMARY AND FUTURE RESEARCH.............................73
REFERENCES................................................74
APPENDICES................................................78		zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0095354020en_US
dc.subject (關鍵詞) 管制圖zh_TW
dc.subject (關鍵詞) 變動參數zh_TW
dc.subject (關鍵詞) 相依製程zh_TW
dc.subject (關鍵詞) 選控圖zh_TW
dc.subject (關鍵詞) 馬可夫鏈zh_TW
dc.subject (關鍵詞) Control Chartsen_US
dc.subject (關鍵詞) Variable Parametersen_US
dc.subject (關鍵詞) Dependent Process Stepsen_US
dc.subject (關鍵詞) Cause-Selecting Control Charten_US
dc.subject (關鍵詞) Markov Chainen_US
dc.title (題名) 利用調適性管制技術同時監控製程平均數和變異數zh_TW
dc.title (題名) Joint Monitoring of Process Means and Variances by Using Adaptive Control Schemesen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1]Amin, R. W. and Miller, R. W. (1993), “A Robustness Study of X-bar Charts with Variable Sampling Intervals,” Journal of Quality Technology 25, 36-44.zh_TW
dc.relation.reference (參考文獻) [2]Chen, G. and Cheng, S. W. (1998), “Max Chart: Combining X-bar Chart and S Chart,” Statistic Sinica 8, 263-271.zh_TW
dc.relation.reference (參考文獻) [3]Chengalur, I. N., Arnold, J. C. and Reynolds, M. R., JR. (1989), “Variable Sampling Intervals for Multiparameter Shewhart Charts,” Communications in Statistics - Theory and Methods 18, 1769-1792.zh_TW
dc.relation.reference (參考文獻) [4]Cinlar, E. (1975), Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, N.J.zh_TW
dc.relation.reference (參考文獻) [5]Constable, G. K., Cleary, M. J., Tickel, C. and Zhang, G. X. (1988), “Use of Cause-Selecting Charts in the Auto Industry,” ASQC Quality Congress Transactions. American Society for Quality Control, 597-602.zh_TW
dc.relation.reference (參考文獻) [6]Costa, A. F. B. (1994), “ X-bar Charts with Variable Sample Size,” Journal of Quality Technology 26, 155-163.zh_TW
dc.relation.reference (參考文獻) [7]Costa, A. F. B. (1997), “ X-bar Charts with Variable Sample Size and Sampling Intervals,” Journal of Quality Technology 29, 197-204.zh_TW
dc.relation.reference (參考文獻) [8]Costa, A. F. B. (1998), “Joint X-bar and R Charts with Variable Parameters,” IIE Transactions 30, 505-514.zh_TW
dc.relation.reference (參考文獻) [9]Costa, A. F. B. (1999a), “Joint X-bar and R Charts with Variable Sample Size and Sampling Intervals,” Journal of Quality Technology 31, 387-397.zh_TW
dc.relation.reference (參考文獻) [10]Costa, A. F. B. (1999b), “ X-bar Charts with Variable Parameters,” Journal of Quality Technology 31, 408-416.zh_TW
dc.relation.reference (參考文獻) [11]Daudin, J. J. (1992), “Double Sampling X-bar Charts,” Journal of Quality Technology 24, 78-87.zh_TW
dc.relation.reference (參考文獻) [12]Fiocca, A. (1988), Some unpublished works of Ludovico Ferrari (Italian), Boll. Storia Sci. Mat. 8 (2), 239-305.zh_TW
dc.relation.reference (參考文獻) [13]IMSL (1991), Users Manual, Math/Library, Vol.2, IMSL, Inc., Houstin, Texas.zh_TW
dc.relation.reference (參考文獻) [14]Kang, L. and Albin, S. L. (2000), “On-Line Monitoring When the Process Yields a Linear Profile,” Journal of Quality Technology 32, 418-426.zh_TW
dc.relation.reference (參考文獻) [15]Mandel, B. J. (1969), “The Regression Control Chart,” Journal of Quality Technology 1, 1-9.zh_TW
dc.relation.reference (參考文獻) [16]Prabhu, S. S., Montgomery, D. C. and Runger, G. C. (1994), “A Combined Adaptive Sample Size and Sampling Interval X-bar Control Scheme,” Journal of Quality Technology 26, 164-176.zh_TW
dc.relation.reference (參考文獻) [17]Prabhu, S. S., Runger, G. C. and Keats, J. B. (1993), “An Adaptive Sample Size X-bar Chart,” International Journal of Production Research 31, 2895-2909.zh_TW
dc.relation.reference (參考文獻) [18]Reynolds, M. R., JR. (1989), “Optimal Variable Sampling Interval Control Charts,” Sequential Analysis 8, 361-379.zh_TW
dc.relation.reference (參考文獻) [19]Reynolds, M. R., JR. (1995), “Evaluating Properties of Variable Sampling Interval Control Charts,” Sequential Analysis 14, 59-97.zh_TW
dc.relation.reference (參考文獻) [20]Reynolds, M. R., JR. (1996), “Variable-Sampling-Interval Control Charts with Sampling at Fixed Times,” IIE Transactions 28, 497-510.zh_TW
dc.relation.reference (參考文獻) [21]Reynolds, M. R., JR., Amin, R. W., Arnold, J. C. and Nachlas, J. A. (1988), “ X-bar Charts with Variable Sampling Intervals,” Technometrics 30, 181-192.zh_TW
dc.relation.reference (參考文獻) [22]Reynolds, M. R., JR. and Arnold, J. C. (1989), “Optimal One-Sized Shewhart Control Charts with Variable Sampling Intervals,” Sequential Analysis 8, 51-77.zh_TW
dc.relation.reference (參考文獻) [23]Reynolds, M. R., JR., Arnold, J. C. and Baik, J. W. (1996), “Variable Sampling Interval X-bar Charts in the Presence of Correlation,” Journal of Quality Technology 28, 12-30.zh_TW
dc.relation.reference (參考文獻) [24]Runger, G. C. and Montgomery, D. C. (1993), “Adaptive Sampling Enhancements for Shewhart Control Charts,” IIE Transactions 25, 41-51.zh_TW
dc.relation.reference (參考文獻) [25]Runger, G. C. and Pignatiello, J. J., JR. (1991), “Adaptive Sampling for Process Control,” Journal of Quality Technology 23, 135-155.zh_TW
dc.relation.reference (參考文獻) [26]Tagaras, G. (1998), “A Survey of Recent Developments in the Design of Adaptive Control Charts,” Journal of Quality Technology 30, 212-231.zh_TW
dc.relation.reference (參考文獻) [27]Wade, M. R. and Woodall, W. H. (1993), “A Review and Analysis of Cause-Selecting Control Charts,” Journal of Quality Technology 25, 161-169.zh_TW
dc.relation.reference (參考文獻) [28]Yang, S. (2005), “Dependent Processes Control for Over-adjusted Means,” International Journal of Advanced Manufacturing Technology, 109-116.zh_TW
dc.relation.reference (參考文獻) [29]Yang, S. and Su, H. (2006), “Controlling-dependent Process Steps Using Variable Sample Size Control Charts,” Applied stochastic model in business and industry, Vol. 22, 503-517.zh_TW
dc.relation.reference (參考文獻) [30]Yang, S. and Su, H. (2007a), “Adaptive Sampling Interval for Two Dependent Process Steps Control,” International Journal of Advanced Manufacturing Technology, Vol. 31, 1169-1180.zh_TW
dc.relation.reference (參考文獻) [31]Yang, S. and Su, H. (2007b), “Adaptive Control Scheme for Dependent Process Steps,” International Journal of Loss Prevention and Industrial Process, Vol. 20, 15-25.zh_TW
dc.relation.reference (參考文獻) [32]Yang, S. and Yang, C. (2006), “An Approach to Controlling Two Dependent Process Steps with Autocorrelated Observations,” International Journal of Advanced Manufacturing Technology, Vol. 29, 170-177.zh_TW
dc.relation.reference (參考文獻) [33]Yang, S. and Chen, W. (2007a), “Controlling Incorrect Adjustment Processes Using Optimum VSI Control Charts,” International Statistical Conference, ISI 56, Lisbon, Portugal.zh_TW
dc.relation.reference (參考文獻) [34]Yang, S. and Chen, W. (2007b), “Variable Sampling Interval Control Charts,” International Conference of Multiple Decision Theory, in honor of Dr. Den-Yung Hwang, Taiwan.zh_TW
dc.relation.reference (參考文獻) [35]Zhang, G. X. (1984), “A New Type of Control Charts and a Theory of Diagnosis with Control Charts,” World Quality Congress Transactions. American Society for Quality Control, 175-185.zh_TW