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題名 適應性計數值損失函數管制圖之設計
Design of the Adaptive Loss Function Control Chart for Binomial Data作者 李宜臻
Lee,I Chen貢獻者 楊素芬<br>蔡紋琦
Yang,Su Fen<br>Tsai,Wen Chi
李宜臻
Lee,I Chen關鍵詞 計數值管制圖
田口損失函數
變動抽樣區間
變動樣本數
變動參數
馬可夫鏈
Attribute Control Chart
Taguchi Loss Function
Variable Sampling Intervals
Variable Sample Sizes
Variable Parameters
Markov Chain日期 2009 上傳時間 28-Jun-2013 13:59:32 (UTC+8) 摘要
This article proposes the algorithm of a new control chart (loss function control chart) based on the Taguchi loss function with an adaptive scheme for binomial data. The loss function control chart is able to monitor cost variation from the process by applying loss function in the design. This new angle economically explores production cost. This research provides designs of the loss function control chart with specified VSI, optimal VSI, VSS and VP, respectively. Numerical analyses show that the specified VSI loss function chart, the optimal VSI loss function chart, the optimal VSS loss function chart and the optimal VP loss function chart outperform the Fp loss function chart significantly and show costs can be controlled systematically.參考文獻 [1] Alexander, S.M., Dillman, M.A., Usher, J.S. and Damodaran, B. (1995),“Economic Design of Control Charts using the Taguchi Loss Function,” Computers & Industrial Engineering 28, 671-679.[2] Calabrese, J.M. (1995),“Bayesian process control for attributes,” Management Science 41,637-645.[3] Serel, D.A. (2009),“Economic design of EWMA control charts based on loss function,” Mathematical and Computer Modelling 49, 745-759.[4] Epprecht, E.K. and Costa, A.F.B. (2001),“Adaptive Sample Size Control Chartsfor Attributes,” Quality Engineering 13, 465-473. [5] Epprecht, E.K., Costa, A.F.B. and Mendes, F.C.T. (2003),“Adaptive control charts for attributes,” IEE Transaction 35, 567-582.[6] Luo, H. and Wu, Z. (2002),“Optimal np Control Charts with Variable Sample Sizes or Variable Sampling Intervals,” Economic Quality Control 17, 39-61.[7] Luo, H. and Wu, Z. (2004),“Optimal Design of the Adaptive Sample Size and Sampling Interval np Control Chart,” Quality Reliability Engineering International 20, 553–570. [8] Koo, T. and Lin, L. (1992),“Economic design of chart when Taguchi’s loss function is considered,” Proceedings of Asian Quality Control Symposium, South Korea, 166-178.[9] Lorenzen, T.J. and Vance, L.C. (1986),“The Economic Design of Control Charts: A Unified Approach,” Technometrics 28, 3-10.[10] Montgomery, D.C. (1980),“The economic design of control charts: a review and literature survey”, Journal of Quality Technology 12, 75-87.[12] Montgomery, D.C. (2009), Introduction to Statistical Quality Control, 6th ed.John Wiley & Sons, New York.[13] Porteus, E.L. and Angelus, A. (1997),“Opportunities for improved statistical process control,” Management Science 43, 1214-1228.[14] Rendtel, U. (1987),”The Use of Generalized CUSUM-Schemes to Control the Percent Defective of a Continuous Production Process,” Frontiers in Statistical Quality Control, 3rd ed. H.J. Lenz et al. Physica-Verlag, Heidelberg.[15] Reynolds, M.R., Amin, R.W., Arnold, J.C. and Nachlas, J.A. (1988),“ Charts with Variable Sampling Intervals,” Technometrics 30,181-192.[16] Rendtel, U. (1990),”CUSUM-schemes with variable sampling intervals and sample sizes,” Statistical Papers 31, 103-118.[17] Saniga, E.M., Davis, D.J. and McWilliams, T. P. (1995),“Economic, Statistical, and Economic-Statistical Design of Attribute Charts,” Journal of Quality Technology 27, 56-73.[18] Taguchi, G. (1984),“The role of metrological control for quality control,” Proceedings of the international Symposium on Metrology for Quality Control in Production, 1-7.[19] Tagaras, G. (1998),“A survey of recent developments in the design of adaptive control charts,” Journal of Quality Technology 30, 212-231. [20] Vaughan, T.S. (1993),”Variable sampling interval np process control chart,” Communications in Statistics—Theory and Methods 22, 147-167.[21] Woodall, W.H. (1986),“Weaknesses of the Economic Design of Control Charts, Technometrics 28, 408-410.[22] Wu, Z. and Pan, E.S. (2004),“Optimization design of control charts based on Taguchi’s loss function and random process shifts,” International Journal of Production Research 42, 379–390.[23] Wu, Z. and Luo, H. (2004),“Optimal Design of the Adaptive Sample Size and Sampling Interval,” Quality and Reliability Engineering International 20, 553-570.[24] Yang, S. (1997),”An optimal design of joint and S control charts using quadratic loss function,” International Journal of Quality & Reliability Management 14, 948-966. 描述 碩士
國立政治大學
統計研究所
97354003
98資料來源 http://thesis.lib.nccu.edu.tw/record/#G0973540031 資料類型 thesis dc.contributor.advisor 楊素芬<br>蔡紋琦 zh_TW dc.contributor.advisor Yang,Su Fen<br>Tsai,Wen Chi en_US dc.contributor.author (Authors) 李宜臻 zh_TW dc.contributor.author (Authors) Lee,I Chen en_US dc.creator (作者) 李宜臻 zh_TW dc.creator (作者) Lee,I Chen en_US dc.date (日期) 2009 en_US dc.date.accessioned 28-Jun-2013 13:59:32 (UTC+8) - dc.date.available 28-Jun-2013 13:59:32 (UTC+8) - dc.date.issued (上傳時間) 28-Jun-2013 13:59:32 (UTC+8) - dc.identifier (Other Identifiers) G0973540031 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/58598 - 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) 97354003 zh_TW dc.description (描述) 98 zh_TW dc.description.abstract (摘要) zh_TW dc.description.abstract (摘要) This article proposes the algorithm of a new control chart (loss function control chart) based on the Taguchi loss function with an adaptive scheme for binomial data. The loss function control chart is able to monitor cost variation from the process by applying loss function in the design. This new angle economically explores production cost. This research provides designs of the loss function control chart with specified VSI, optimal VSI, VSS and VP, respectively. Numerical analyses show that the specified VSI loss function chart, the optimal VSI loss function chart, the optimal VSS loss function chart and the optimal VP loss function chart outperform the Fp loss function chart significantly and show costs can be controlled systematically. en_US dc.description.tableofcontents 1.Introduction 12.Distribution of the Loss Function for binomial data 43.Design of the VSI Loss Function Chart for binomial data 6 3.1 Construction of the VSI Loss Function Chart for binomial data 6 3.2 Performance Measurment 9 3.3 Determination of the UCL, WCL of the Specified VSI Loss Function Chart 11 3.4 Determination of the UCL, WCL of the Optimal VSI Loss Function Chart 12 3.5 Performance Comparisons 15 3.5.1 Specified VSI Loss Function Chart for binomial data 15 3.5.2 Optimal VSI Loss Function Chart for binomial data 17 3.6 Example 224.Design of the VSS Loss Function Chart for binomial data 27 4.1 Construction of the VSS Loss Function Chart for binomial data 27 4.2 Performance Measurement 30 4.3 Determination of the UCLi, WCLi of the Optimal VSS Loss Function Chart 32 4.4 Performance Comparisons 35 4.5 Example 395.Design of the VP Loss Function Chart for binomial data 43 5.1 Construction of the VP Loss Function Chart for binomial data 43 5.2 Performance Measurement 46 5.3 Determination of the UCLi, WCLi of the Optimal VP Loss Function Chart 48 5.4 Performance Comparisons 52 5.5 Example 566. Conclusion and Future Study 60References 61Appendix 63 zh_TW dc.format.extent 5121656 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/#G0973540031 en_US dc.subject (關鍵詞) 計數值管制圖 zh_TW dc.subject (關鍵詞) 田口損失函數 zh_TW dc.subject (關鍵詞) 變動抽樣區間 zh_TW dc.subject (關鍵詞) 變動樣本數 zh_TW dc.subject (關鍵詞) 變動參數 zh_TW dc.subject (關鍵詞) 馬可夫鏈 zh_TW dc.subject (關鍵詞) Attribute Control Chart en_US dc.subject (關鍵詞) Taguchi Loss Function en_US dc.subject (關鍵詞) Variable Sampling Intervals en_US dc.subject (關鍵詞) Variable Sample Sizes en_US dc.subject (關鍵詞) Variable Parameters en_US dc.subject (關鍵詞) Markov Chain en_US dc.title (題名) 適應性計數值損失函數管制圖之設計 zh_TW dc.title (題名) Design of the Adaptive Loss Function Control Chart for Binomial Data en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) [1] Alexander, S.M., Dillman, M.A., Usher, J.S. and Damodaran, B. (1995),“Economic Design of Control Charts using the Taguchi Loss Function,” Computers & Industrial Engineering 28, 671-679.[2] Calabrese, J.M. (1995),“Bayesian process control for attributes,” Management Science 41,637-645.[3] Serel, D.A. (2009),“Economic design of EWMA control charts based on loss function,” Mathematical and Computer Modelling 49, 745-759.[4] Epprecht, E.K. and Costa, A.F.B. (2001),“Adaptive Sample Size Control Chartsfor Attributes,” Quality Engineering 13, 465-473. [5] Epprecht, E.K., Costa, A.F.B. and Mendes, F.C.T. (2003),“Adaptive control charts for attributes,” IEE Transaction 35, 567-582.[6] Luo, H. and Wu, Z. (2002),“Optimal np Control Charts with Variable Sample Sizes or Variable Sampling Intervals,” Economic Quality Control 17, 39-61.[7] Luo, H. and Wu, Z. (2004),“Optimal Design of the Adaptive Sample Size and Sampling Interval np Control Chart,” Quality Reliability Engineering International 20, 553–570. [8] Koo, T. and Lin, L. (1992),“Economic design of chart when Taguchi’s loss function is considered,” Proceedings of Asian Quality Control Symposium, South Korea, 166-178.[9] Lorenzen, T.J. and Vance, L.C. (1986),“The Economic Design of Control Charts: A Unified Approach,” Technometrics 28, 3-10.[10] Montgomery, D.C. (1980),“The economic design of control charts: a review and literature survey”, Journal of Quality Technology 12, 75-87.[12] Montgomery, D.C. (2009), Introduction to Statistical Quality Control, 6th ed.John Wiley & Sons, New York.[13] Porteus, E.L. and Angelus, A. (1997),“Opportunities for improved statistical process control,” Management Science 43, 1214-1228.[14] Rendtel, U. (1987),”The Use of Generalized CUSUM-Schemes to Control the Percent Defective of a Continuous Production Process,” Frontiers in Statistical Quality Control, 3rd ed. H.J. Lenz et al. Physica-Verlag, Heidelberg.[15] Reynolds, M.R., Amin, R.W., Arnold, J.C. and Nachlas, J.A. (1988),“ Charts with Variable Sampling Intervals,” Technometrics 30,181-192.[16] Rendtel, U. (1990),”CUSUM-schemes with variable sampling intervals and sample sizes,” Statistical Papers 31, 103-118.[17] Saniga, E.M., Davis, D.J. and McWilliams, T. P. (1995),“Economic, Statistical, and Economic-Statistical Design of Attribute Charts,” Journal of Quality Technology 27, 56-73.[18] Taguchi, G. (1984),“The role of metrological control for quality control,” Proceedings of the international Symposium on Metrology for Quality Control in Production, 1-7.[19] Tagaras, G. (1998),“A survey of recent developments in the design of adaptive control charts,” Journal of Quality Technology 30, 212-231. [20] Vaughan, T.S. (1993),”Variable sampling interval np process control chart,” Communications in Statistics—Theory and Methods 22, 147-167.[21] Woodall, W.H. (1986),“Weaknesses of the Economic Design of Control Charts, Technometrics 28, 408-410.[22] Wu, Z. and Pan, E.S. (2004),“Optimization design of control charts based on Taguchi’s loss function and random process shifts,” International Journal of Production Research 42, 379–390.[23] Wu, Z. and Luo, H. (2004),“Optimal Design of the Adaptive Sample Size and Sampling Interval,” Quality and Reliability Engineering International 20, 553-570.[24] Yang, S. (1997),”An optimal design of joint and S control charts using quadratic loss function,” International Journal of Quality & Reliability Management 14, 948-966. zh_TW
