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題名 適應性加權損失管制圖之研究
The Study of Adaptive Weighted Loss Control Charts for Dependent Process Steps
作者 林亮妤
Lin,Liang Yu
貢獻者 楊素芬
Yang,Su Fen
林亮妤
Lin,Liang Yu
關鍵詞 管制圖
變動參數
相依製程
損失函數
最佳化技術
馬可夫鏈
Control charts
Variable parameters
Dependent process steps
Loss function
Optimization technique
Markov chain
日期 2009
上傳時間 5-Sep-2013 15:10:33 (UTC+8)
摘要 近年來有許多研究發現，適應性管制圖在偵測製程或產品幅度偏移時的速度比傳統的舒華特管制圖來的快，許多文獻也討論到利用適應性管制技術同時監控製程的平均數和變異數。隨著科技的發達，許多產品在製造上更加精密，現今普遍使用的固定參數管制圖並無法有效率的偵測出製程失控，導致巨大的成本損失。為了改善現有管制圖的偵測效率與有效控制製程失控下的損失，我們提出了三種適應性加權損失管制圖，包括變動抽樣間隔(VSI)、變動樣本數與抽樣間隔(VSI)、變動管制參數(VP)來偵測單一製程與兩相依製程的平均數和變異數。採用製程發生變動後到管制圖偵測出異常訊息所需的平均時間(AATS)與所需的總觀測數(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。從數值分析中發現，適應性加權損失管制圖在「偵測小偏移幅度時的偵測效率」與「成本的控制」明顯比傳統管制圖表現的更好，再加上每一個製程僅需採用單一管制圖，對使用者也較為簡便並且容易理解，因此適應性加權損失管制圖在實務上是值得被推薦使用的。
Recent research has shown that control charts with adaptive features detect process shifts faster than traditional Shewhart charts. In this article, we propose three kinds of adaptive weighted loss (WL) control charts, variable sampling intervals (VSI) WL control charts , variable sample sizes and sampling intervals (VSSI) WL control charts and variable parameters (VP) WL control charts, to monitor the target and variance on a single process step and two dependent process steps simultaneously. These adaptive WL control charts may effectively distinguish which process step is out-of-control. We use the Markov chain approach to calculate the adjusted average time to signal (AATS) and average number of observations to signal (ANOS) in order to measure the performance of the proposed control charts. From the numerical examples and data analyses, we find the adaptive WL control charts have better detection abilities and performance than fixed parameters (FP) WL control charts and FP Z(X-bar)-Z(Sx^2) and Z(e-bar)-Z(Se^2) control charts. We also proposed the optimal adaptive WL control charts using an optimization technique to minimize AATS when users cannot specify the values of the variable parameters. In addition, we discuss the impact of misusing weighted loss of outgoing quality control chart. In conclusion, using a single chart to monitor a process is inherently easier than using two charts. The WL control charts are easy to understand for the users, and have better performance and detection abilities than the other charts, thus, we recommend the use of WL control charts in the 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]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.
[3]Chen, G., Cheng, S. W. and Xie, H. (2001), “Monitoring process mean and variability with one EWMA chart,” Journal of Quality Technology 33(2), 223-233.
[4]Chengular, 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.
[5]Cinlar, E. (1975), Introduction to stochastic process. Englewood Cliffs, NJ:Prentice-Hall.
[6]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.
[7]Costa, A. F. B. (1994), “X-bar Charts with variable sample size,” Journal of Quality Technology 26(3), 155-163.
[8]Costa, A. F. B. (1997), “X-bar Charts with variable sample size and sampling intervals,” Journal of Quality Technology 29(2), 197-204.
[9]Costa, A. F. B. (1998), “Joint X-bar and R Charts with variable parameters,” IIE Transactions 30(4), 505-514
[10]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.
[11]Costa, A. F. B. (1999b), “X-bar Charts with variable parameters,” Journal of Quality Technology 31, 408-416.
[12]Cyrus, D. (1997), Statistical Aspects of Quality Control Academic Press, London.
[13]Daudin, J. J. (1992), “Double sampling X-bar Charts,” Journal of Quality Technology 24, 78-87.
[14]Grabov, P. and Ingman, D. (1996), “Adaptive control limits for bivariate process monitoring,” Journal of Quality Technology 28, 320-330.
[15]Mandel, B. J. (1969), “The Regression Control Chart,” Journal of Quality Technology 1, 1-9.
[16]Penrose, K., Nelson, A. and Fisher, A. (1985), “Generalized body composition prediction equation for men using simple measurement techniques” Medicine and Science in Sports and Exercise,17(2), 189.
[17]Prabhu, S. S., Montgomery, D. C. and Runger, G. G. (1994), “ A combine dadaptive sample size and sampling interval control scheme,” Journal of Quality Technology, 26(3), 164–176.
[18]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.
[19]Reynolds, M. R., JR. (1996), “Variable-sampling-interval control charts with
Sampling at Fixed Times,” IIE Transactions 28, 497-510.
[20]Reynolds, M. R., JR. and Glosh, B. K. (1981), “Designing control charts for means and variances,” ASQC Quality Congress Transactions, American Society for Quality Control ,San Francisco ,400-407.
[21]Reynolds, M. R., JR., Amin, R. W., Arnold, J. C. and Nachlas, J. A (1988), “ charts with variable sampling intervals,” Technometrics 30(2), 181-192.
[22]Reynolds, M. R., JR. and Arnold, J. C., (1989), “ Optimal one-sided Shewhart control chart with variable sampling intervals,” Sequential Analysis 8, 51-77.
[23]Reynolds, M. R., JR., Arnold, J. C. and Baik (1996), “ Variable sampling interval X-bar Charts in the presence of Correlation,” Journal of Quality Technology 28, 1-28.
[24]Reynolds, M. R., JR. and Stoumbos, Z. G. (2001), “ Monitoring the process mean and variance using individual observations and variable sampling intervals,” Journal of Quality Technology 33, 181–205.
[25]Runger, G. C. and Montgomery, D. C. (1993), “Adaptive sampling enhancements for Shewhart control charts,” IIE Transactions 25, 41-51.
[26]Runger, G. C. and Pignatiello, J. J., JR. (1991), “Adaptive sampling for process control,” Journal of Quality Technology 23, 135-155.
[27]Shewhart, W. A. (1931), Economic Control of Quality of Manufactured Product, D. Van Nostrand Co., New York.
[28]Spiring, F. A. and Yeung, A. S. (1998), “A general class of loss functions with individual applications,” Journal of Quality Technology 30, 152-162.
[29]Sullivan, J. H. and Woodall, W. H. (1996), “A control chart for preliminary analysis of individual observations,” Journal of Quality Technology 28, 265-278.
[30]Tagaras, G. (1998), “A survey of recent developments in the design of adaptive control charts”, Journal of Quality Technology 30, 212-231.
[31]Taguchi, G. (1986), Introduction to Quality Engineering, Asian Productivity Organization, Tokyo.
[32]Wade, M. R. and Woodall, W. H. (1993), “A review and analysis of cause-selecting control charts,” Journal of Quality Technology 25(2), 161-169.
[33]Wu, Z. and Tian, Y. (2006) “Weighted-loss-function control charts,” International Journal of Production Research, 31, 107–115.
[34]Yang, S. and Su, H. (2007), “Adaptive Control Scheme for Dependent Process Steps,” International Journal of Loss Prevention and Industrial Process, Vol. 20,15-25.
[35]Zhang, G. X. (1984), “A new type of control charts and a theory of diagnosis with control chats,” 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
97354008
98
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097354008
資料類型 thesis
dc.contributor.advisor 楊素芬zh_TW
dc.contributor.advisor Yang,Su Fenen_US
dc.contributor.author (Authors) 林亮妤zh_TW
dc.contributor.author (Authors) Lin,Liang Yuen_US
dc.creator (作者) 林亮妤zh_TW
dc.creator (作者) Lin,Liang Yuen_US
dc.date (日期) 2009en_US
dc.date.accessioned 5-Sep-2013 15:10:33 (UTC+8)-
dc.date.available 5-Sep-2013 15:10:33 (UTC+8)-
dc.date.issued (上傳時間) 5-Sep-2013 15:10:33 (UTC+8)-
dc.identifier (Other Identifiers) G0097354008en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/60431-
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) 97354008zh_TW
dc.description (描述) 98zh_TW
dc.description.abstract (摘要) 近年來有許多研究發現，適應性管制圖在偵測製程或產品幅度偏移時的速度比傳統的舒華特管制圖來的快，許多文獻也討論到利用適應性管制技術同時監控製程的平均數和變異數。隨著科技的發達，許多產品在製造上更加精密，現今普遍使用的固定參數管制圖並無法有效率的偵測出製程失控，導致巨大的成本損失。為了改善現有管制圖的偵測效率與有效控制製程失控下的損失，我們提出了三種適應性加權損失管制圖，包括變動抽樣間隔(VSI)、變動樣本數與抽樣間隔(VSI)、變動管制參數(VP)來偵測單一製程與兩相依製程的平均數和變異數。採用製程發生變動後到管制圖偵測出異常訊息所需的平均時間(AATS)與所需的總觀測數(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。從數值分析中發現，適應性加權損失管制圖在「偵測小偏移幅度時的偵測效率」與「成本的控制」明顯比傳統管制圖表現的更好，再加上每一個製程僅需採用單一管制圖，對使用者也較為簡便並且容易理解，因此適應性加權損失管制圖在實務上是值得被推薦使用的。zh_TW
dc.description.abstract (摘要) Recent research has shown that control charts with adaptive features detect process shifts faster than traditional Shewhart charts. In this article, we propose three kinds of adaptive weighted loss (WL) control charts, variable sampling intervals (VSI) WL control charts , variable sample sizes and sampling intervals (VSSI) WL control charts and variable parameters (VP) WL control charts, to monitor the target and variance on a single process step and two dependent process steps simultaneously. These adaptive WL control charts may effectively distinguish which process step is out-of-control. We use the Markov chain approach to calculate the adjusted average time to signal (AATS) and average number of observations to signal (ANOS) in order to measure the performance of the proposed control charts. From the numerical examples and data analyses, we find the adaptive WL control charts have better detection abilities and performance than fixed parameters (FP) WL control charts and FP Z(X-bar)-Z(Sx^2) and Z(e-bar)-Z(Se^2) control charts. We also proposed the optimal adaptive WL control charts using an optimization technique to minimize AATS when users cannot specify the values of the variable parameters. In addition, we discuss the impact of misusing weighted loss of outgoing quality control chart. In conclusion, using a single chart to monitor a process is inherently easier than using two charts. The WL control charts are easy to understand for the users, and have better performance and detection abilities than the other charts, thus, we recommend the use of WL control charts in the real industrial process.en_US
dc.description.tableofcontents 1.INTRODUCTION.............................................1
2.DESIGN OF ADAPTIVE WEIGHTED LOSS CONTROL CHART FOR A SINGLE PROCESS STEP........................................5
2.1 The Weighted Loss Function.............................5
2.2 The Adaptive Weighted Loss Control Chart for a Single Process Step...............................................7
3.DESCRIPTION OF TWO DEPENDENT PROCESS STEPS...............8
4.VARIABLE SAMPLING INTERVALS WEIGHTED LOSS CONTROL CHARTS....................................................10
4.1 The Distributions of the VSI Weighted Loss Statistics.10
4.2 Design of the VSI Weighted Loss Control Charts........13
4.3 Performance Measurement for VSI Weighted Loss Control Charts....................................................16
4.4 An example of VSI Weighted Loss Control Charts........19
4.5 Performance Comparison for VSI Weighted Loss Control Charts....................................................25
5.VARIABLE SAMPLE SIZES AND SAMPLING INTERVALS WEIGHTED LOSS CONTROL CHARTS.......................................29
5.1 The Distributions of the VSSI Weighted Loss Statistics................................................29
5.2 Design of the VSSI Weighted Loss Control Charts.......32
5.3 Performance Measurement for VSSI Weighted Loss Control Charts....................................................36
5.4 An example of VSSI Weighted Loss Control Charts.......39
5.5 Performance Comparison for VSSI Weighted Loss Control Charts....................................................43
6.VARIABLE PARAMETERS WEIGHTED LOSS CONTROL CHARTS........49
6.1 The Distributions of the VP Weighted Loss Statistics..49
6.2 Design of the VP Weighted Loss Control Charts.........52
6.3 Performance Measurement for VP Weighted Loss Control Charts....................................................57
6.4 An Example and Impact of Misusing Control Chart.......60
6.5 Performance Comparison for VP Weighted Loss Control Charts....................................................70
7.CONCLUSIONS.............................................86
REFERENCES................................................88
APPENDICES................................................91
Appendix 1：The Calculation of Transition Probabilities for VP Weighted Loss Control Charts...........................91
Appendix 2：The Calculation of AATS, ANOS and Out-Of-Control Average Loss per unit product for FP
Z(X-bar)-Z(Sx^2) and Z(e-bar)-Z(Se^2)Control Charts.......98		zh_TW
dc.format.extent 1067099 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/#G0097354008en_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) 損失函數zh_TW
dc.subject (關鍵詞) 最佳化技術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) Loss functionen_US
dc.subject (關鍵詞) Optimization techniqueen_US
dc.subject (關鍵詞) Markov chainen_US
dc.title (題名) 適應性加權損失管制圖之研究zh_TW
dc.title (題名) The Study of Adaptive Weighted Loss Control Charts for Dependent Process Stepsen_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.
[2]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.
[3]Chen, G., Cheng, S. W. and Xie, H. (2001), “Monitoring process mean and variability with one EWMA chart,” Journal of Quality Technology 33(2), 223-233.
[4]Chengular, 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.
[5]Cinlar, E. (1975), Introduction to stochastic process. Englewood Cliffs, NJ:Prentice-Hall.
[6]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.
[7]Costa, A. F. B. (1994), “X-bar Charts with variable sample size,” Journal of Quality Technology 26(3), 155-163.
[8]Costa, A. F. B. (1997), “X-bar Charts with variable sample size and sampling intervals,” Journal of Quality Technology 29(2), 197-204.
[9]Costa, A. F. B. (1998), “Joint X-bar and R Charts with variable parameters,” IIE Transactions 30(4), 505-514
[10]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.
[11]Costa, A. F. B. (1999b), “X-bar Charts with variable parameters,” Journal of Quality Technology 31, 408-416.
[12]Cyrus, D. (1997), Statistical Aspects of Quality Control Academic Press, London.
[13]Daudin, J. J. (1992), “Double sampling X-bar Charts,” Journal of Quality Technology 24, 78-87.
[14]Grabov, P. and Ingman, D. (1996), “Adaptive control limits for bivariate process monitoring,” Journal of Quality Technology 28, 320-330.
[15]Mandel, B. J. (1969), “The Regression Control Chart,” Journal of Quality Technology 1, 1-9.
[16]Penrose, K., Nelson, A. and Fisher, A. (1985), “Generalized body composition prediction equation for men using simple measurement techniques” Medicine and Science in Sports and Exercise,17(2), 189.
[17]Prabhu, S. S., Montgomery, D. C. and Runger, G. G. (1994), “ A combine dadaptive sample size and sampling interval control scheme,” Journal of Quality Technology, 26(3), 164–176.
[18]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.
[19]Reynolds, M. R., JR. (1996), “Variable-sampling-interval control charts with
Sampling at Fixed Times,” IIE Transactions 28, 497-510.
[20]Reynolds, M. R., JR. and Glosh, B. K. (1981), “Designing control charts for means and variances,” ASQC Quality Congress Transactions, American Society for Quality Control ,San Francisco ,400-407.
[21]Reynolds, M. R., JR., Amin, R. W., Arnold, J. C. and Nachlas, J. A (1988), “ charts with variable sampling intervals,” Technometrics 30(2), 181-192.
[22]Reynolds, M. R., JR. and Arnold, J. C., (1989), “ Optimal one-sided Shewhart control chart with variable sampling intervals,” Sequential Analysis 8, 51-77.
[23]Reynolds, M. R., JR., Arnold, J. C. and Baik (1996), “ Variable sampling interval X-bar Charts in the presence of Correlation,” Journal of Quality Technology 28, 1-28.
[24]Reynolds, M. R., JR. and Stoumbos, Z. G. (2001), “ Monitoring the process mean and variance using individual observations and variable sampling intervals,” Journal of Quality Technology 33, 181–205.
[25]Runger, G. C. and Montgomery, D. C. (1993), “Adaptive sampling enhancements for Shewhart control charts,” IIE Transactions 25, 41-51.
[26]Runger, G. C. and Pignatiello, J. J., JR. (1991), “Adaptive sampling for process control,” Journal of Quality Technology 23, 135-155.
[27]Shewhart, W. A. (1931), Economic Control of Quality of Manufactured Product, D. Van Nostrand Co., New York.
[28]Spiring, F. A. and Yeung, A. S. (1998), “A general class of loss functions with individual applications,” Journal of Quality Technology 30, 152-162.
[29]Sullivan, J. H. and Woodall, W. H. (1996), “A control chart for preliminary analysis of individual observations,” Journal of Quality Technology 28, 265-278.
[30]Tagaras, G. (1998), “A survey of recent developments in the design of adaptive control charts”, Journal of Quality Technology 30, 212-231.
[31]Taguchi, G. (1986), Introduction to Quality Engineering, Asian Productivity Organization, Tokyo.
[32]Wade, M. R. and Woodall, W. H. (1993), “A review and analysis of cause-selecting control charts,” Journal of Quality Technology 25(2), 161-169.
[33]Wu, Z. and Tian, Y. (2006) “Weighted-loss-function control charts,” International Journal of Production Research, 31, 107–115.
[34]Yang, S. and Su, H. (2007), “Adaptive Control Scheme for Dependent Process Steps,” International Journal of Loss Prevention and Industrial Process, Vol. 20,15-25.
[35]Zhang, G. X. (1984), “A new type of control charts and a theory of diagnosis with control chats,” World Quality Congress Transactions. American Society for Quality Control, 175-185.		zh_TW