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題名 設計EWMA管制圖以監控相依製程
作者 余翊寧
貢獻者 楊素芬
余翊寧
關鍵詞 管制圖
相依製程
馬可夫鏈
EWMA
日期 2007
上傳時間 18-Sep-2009 20:10:22 (UTC+8)
摘要 
Control charts are used to effectively monitor and determine whether a process is in-control or out-of-control. The properties of EWMA control charts on a single process have been discussed by many researchers. They have proved that EWMA control charts detect small shifts in means or variances more quickly than the traditional Shewhart control charts. However, many products are currently produced in several dependent process steps. In this article, (1) we propose three kinds of EWMA control charts, - , - , and a combined control charts, to monitor the process mean and variance for a single process step, and (2) extend the three kinds of EWMA control charts in (1) to control two dependent steps. The performance of the proposed control charts is measured by using the Markov chain approach. The application of the proposed control charts is illustrated by using some numerical examples, and the performance of the proposed charts is compared by using some numerical examples. The adjusted average time to signal (AATS) and the adjusted average samples to signal (ANOS) are calculated to measure the performance of the proposed EWMA control charts by Markov chain approach. A data set consisting of the measurements of the inside diameter of the cylinder bores in an engine block example illustrates the applications of the three kinds of EWMA control charts for a single step and a empirical automobile braking system example illustrates the applications of the three kinds of EWMA control charts for two dependent steps. Moreover, their performances are compared by some numerical analysis results.
參考文獻 [1] Box G. E. P., Hunter W., and Hunter J. (1978). Statistics for Experiments. John Wiley & Sons, New York, NY.
[2] Crowder, S. V. (1987a), “A Simple Method for Studying Run Length Distributions of Exponentially Weighted Moving Average Charts,”Technometrics 29, 401-407.
[3] Crowder, S. V. (1987b),”Average Run Lengths of Exponentially Weighted Moving Average Charts,” Journal of Quality Technology 18, pp. 203-210.
[4] Costa, A. F. B. and Rahim, M. A. (2006), “ A Single EWMA Chart for Monitoring Process Mean and Process Variance,” Quality Technology & Quantitative Management, pp.295-305
[5] Castagliola, P. (2005a), “A New S2-EWMA Control Chart for Monitoring the Process Variance,” Quality and Reliability Engineering International, Vol. 21, pp.781-794
[6] Castagliola, P. (2005b), “A R-EWMA Control Chart for Monitoring the Process Range,” Quality and Safety Engineering, Vol. 12(1), pp.31-49
[7] Montgomery, D. C. (2005). Introduction to Statistical Quality Control, 5th ed. John Wiley & Sons, New York, NY.
[8] Gan, F. F. (1995), “ Joint monitoring of process mean and variance using exponentially weighted moving average control charts,” Technometrics 33, pp. 446-453
[9] Chen, G., Cheng, S. W., and Xie, H. (2001), “Monitoring Process Mean and Variability with One EWMA Chart,” Journal of Quality Technology Vol.33, No.2
[10] Chen, G., Cheng, S. W., and Xie, H. (2004), “A New EWMA Control Chart for Monitoring Both Location and Dispersion,” Quality Technology & Quantitative Management, pp.217-231
[11] Wade, M. R., and Woodall, W. H. (1993), “A Review and Analysis of Cause-Selecting Control Charts,” Journal of Quality Technology 25, No.3, pp. 161-169
[12] MacGregor, J.F. and Harris, T.J. (1993), “The Exponentially Weighted Moving Variance,” Journal of Quality Technology, Vol. 25(2), pp. 106-118
[13] Quesenberry C. P. (1991), “SPC Q charts for Start-Up Process and Short or Long Runs,” Journal of Quality Technology 23, pp. 213-224
[14] Quesenberry C. P. (1995), “On Properties of Q charts Variables,” Journal of Quality Technology 27, pp. 184-203
[15] Roberts, S. W. (1959), “Control Chart Tests Based on Geometric Moving Averages,” Technometrics 1, pp. 239-250
[16] Crowder, S. V., and Hamilton, M. D. (1992), “An EWMA for Monitoring a Process Standard Deviation,” Journal of Quality Technology 24, No.1, pp. 12-21
[17] Shewhart, W. A. (1931), Economic Control of Quality of Manufactured Product, D. Van Nostrand Co., New York.
[18] 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, pp. 175-185.
描述 碩士
國立政治大學
統計研究所
95354017
96
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0095354017
資料類型 thesis
dc.contributor.advisor 楊素芬zh_TW
dc.contributor.author (Authors) 余翊寧zh_TW
dc.creator (作者) 余翊寧zh_TW
dc.date (日期) 2007en_US
dc.date.accessioned 18-Sep-2009 20:10:22 (UTC+8)-
dc.date.available 18-Sep-2009 20:10:22 (UTC+8)-
dc.date.issued (上傳時間) 18-Sep-2009 20:10:22 (UTC+8)-
dc.identifier (Other Identifiers) G0095354017en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/36925-
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) 95354017zh_TW
dc.description (描述) 96zh_TW
dc.description.abstract (摘要) zh_TW
dc.description.abstract (摘要) Control charts are used to effectively monitor and determine whether a process is in-control or out-of-control. The properties of EWMA control charts on a single process have been discussed by many researchers. They have proved that EWMA control charts detect small shifts in means or variances more quickly than the traditional Shewhart control charts. However, many products are currently produced in several dependent process steps. In this article, (1) we propose three kinds of EWMA control charts, - , - , and a combined control charts, to monitor the process mean and variance for a single process step, and (2) extend the three kinds of EWMA control charts in (1) to control two dependent steps. The performance of the proposed control charts is measured by using the Markov chain approach. The application of the proposed control charts is illustrated by using some numerical examples, and the performance of the proposed charts is compared by using some numerical examples. The adjusted average time to signal (AATS) and the adjusted average samples to signal (ANOS) are calculated to measure the performance of the proposed EWMA control charts by Markov chain approach. A data set consisting of the measurements of the inside diameter of the cylinder bores in an engine block example illustrates the applications of the three kinds of EWMA control charts for a single step and a empirical automobile braking system example illustrates the applications of the three kinds of EWMA control charts for two dependent steps. Moreover, their performances are compared by some numerical analysis results.en_US
dc.description.tableofcontents 1.INTRODUCTION............................................1
2.DESIGN OF THREE KINDS OF EWMA CONTROL CHARTS FOR A SINGLE PROCESS STEP .............................................3
2.1 Description of the EWMAZx-bar-EWMAZlnSx^2 Control Charts for a Single Process Step .........................4
2.1.1 The distributions of the plotted statistics under in-control and out-of-control process........................4
2.1.2 The structure of the EWMAZx-bar-EWMAZlnSx^2 control charts ...................................................6
2.1.3 Performance measurement of the EWMAZx-bar-EWMAZlnSx^2 control charts ...........................................6
2.2 Description of the EWMAUx-bar-EWMAVx-bar Control Charts for a Single Process Step ...............................10
2.2.1 The distributions of the plotted statistics under in-control and out-of-control process ......................10
2.2.2 The structure of the EWMAUx-bar-EWMAVx-bar control charts ..................................................12
2.2.3 Performance measurement of the EWMAUx-bar-EWMAVx-bar control charts ..........................................13
2.3 Description of the EWMAMx-bar Control Chart for a Single Process Step .....................................16
2.3.1 The distributions of the plotted statistics under in-control and out-of-control process ......................16
2.3.2 The structure of the EWMAMx-bar control charts ....18
2.3.3 Performance measurement of the EWMAMx-bar control charts ..................................................18
2.4 Numerical Analyses for a Single Process Step ........21
2.4.1 A real example of using three kinds of EWMA control charts ..................................................21
2.4.2 Performance comparisons for the three kinds of EWMA control charts ...........................................27
3.DESIGN OF THREE KINDS OF EWMA CONTROL CHARTS FOR TWO DEPENDENT PROCESS STEPS ..................................33
3.1 Description of the EWMAZx-bar-EWMAZlnSx^2 and EWMAZe-bar-EWMAZlnSe^2 Control Charts Under Two Dependent Steps..34
3.1.1 The distributions of the plotted statistics under in-control and out-of-control process .......................34
3.1.2 The structure of the EWMAZx-bar-EWMAZlnSx^2 and EWMAZe-bar-EWMAZlnSe^2 control charts ....................37
3.1.3 Performance measurement of the EWMAZx-bar-EWMAZlnSx^2 and EWMAZe-bar-EWMAZlnSe^2 control charts ................37
3.2 Description of the EWMAUx-bar-EWMAVx-bar and EWMAUe-bar-EWMAVe-bar Control Charts under Two Dependent Steps.......43
3.2.1 The distributions of the plotted statistics under in-control and out-of-control process .......................43
3.2.2 The structure of the EWMAUx-bar-EWMAVx-bar and EWMAUe-bar-EWMAVe-bar control charts ............................45
3.2.3 Performance measurement of the EWMAUx-bar-EWMAVx-bar and EWMAUe-bar-EWMAVe-bar control charts .................46
3.3 Description of the EWMAMx-bar and EWMAMe-bar Control Charts Under Two Dependent Steps .........................52
3.3.1 The distributions of the plotted statistics under in-control and out-of- control process ......................52
3.3.2 The structure of the EWMAMx-bar and EWMAMe-bar control charts ...........................................53
3.3.3 Performance measurement of the EWMAMx-bar and EWMAMe-bar control charts .......................................54
3.4 Numerical Analyses for Two Dependent Steps ...........58
3.4.1 A real example of using three kinds of EWMA control charts ...................................................56
3.4.2 Performance comparisons for the three kinds of EWMA control charts ..........................................69
4.CONCLUTION…………………………………………………………………..71
REFERENCE ………………………………………………………………………72
APPENDICES ..............................................74
Appendix 1: The calculation of all transition probabilities of EWMAZx-bar-EWMAZlnSx^2 and EWMAZe-bar-EWMAZlnSe^2 control charts ..........................................74
Appendix 2: The calculation of all transition probabilities of EWMAUx-bar-EWMAVx-bar control charts .................81
Appendix 3: The calculation of all transition probabilities of EWMAMx-bar and EWMAMe-bar control charts .............88		zh_TW
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dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0095354017en_US
dc.subject (關鍵詞) 管制圖zh_TW
dc.subject (關鍵詞) 相依製程zh_TW
dc.subject (關鍵詞) 馬可夫鏈zh_TW
dc.subject (關鍵詞) EWMAen_US
dc.title (題名) 設計EWMA管制圖以監控相依製程zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] Box G. E. P., Hunter W., and Hunter J. (1978). Statistics for Experiments. John Wiley & Sons, New York, NY.zh_TW
dc.relation.reference (參考文獻) [2] Crowder, S. V. (1987a), “A Simple Method for Studying Run Length Distributions of Exponentially Weighted Moving Average Charts,”Technometrics 29, 401-407.zh_TW
dc.relation.reference (參考文獻) [3] Crowder, S. V. (1987b),”Average Run Lengths of Exponentially Weighted Moving Average Charts,” Journal of Quality Technology 18, pp. 203-210.zh_TW
dc.relation.reference (參考文獻) [4] Costa, A. F. B. and Rahim, M. A. (2006), “ A Single EWMA Chart for Monitoring Process Mean and Process Variance,” Quality Technology & Quantitative Management, pp.295-305zh_TW
dc.relation.reference (參考文獻) [5] Castagliola, P. (2005a), “A New S2-EWMA Control Chart for Monitoring the Process Variance,” Quality and Reliability Engineering International, Vol. 21, pp.781-794zh_TW
dc.relation.reference (參考文獻) [6] Castagliola, P. (2005b), “A R-EWMA Control Chart for Monitoring the Process Range,” Quality and Safety Engineering, Vol. 12(1), pp.31-49zh_TW
dc.relation.reference (參考文獻) [7] Montgomery, D. C. (2005). Introduction to Statistical Quality Control, 5th ed. John Wiley & Sons, New York, NY.zh_TW
dc.relation.reference (參考文獻) [8] Gan, F. F. (1995), “ Joint monitoring of process mean and variance using exponentially weighted moving average control charts,” Technometrics 33, pp. 446-453zh_TW
dc.relation.reference (參考文獻) [9] Chen, G., Cheng, S. W., and Xie, H. (2001), “Monitoring Process Mean and Variability with One EWMA Chart,” Journal of Quality Technology Vol.33, No.2zh_TW
dc.relation.reference (參考文獻) [10] Chen, G., Cheng, S. W., and Xie, H. (2004), “A New EWMA Control Chart for Monitoring Both Location and Dispersion,” Quality Technology & Quantitative Management, pp.217-231zh_TW
dc.relation.reference (參考文獻) [11] Wade, M. R., and Woodall, W. H. (1993), “A Review and Analysis of Cause-Selecting Control Charts,” Journal of Quality Technology 25, No.3, pp. 161-169zh_TW
dc.relation.reference (參考文獻) [12] MacGregor, J.F. and Harris, T.J. (1993), “The Exponentially Weighted Moving Variance,” Journal of Quality Technology, Vol. 25(2), pp. 106-118zh_TW
dc.relation.reference (參考文獻) [13] Quesenberry C. P. (1991), “SPC Q charts for Start-Up Process and Short or Long Runs,” Journal of Quality Technology 23, pp. 213-224zh_TW
dc.relation.reference (參考文獻) [14] Quesenberry C. P. (1995), “On Properties of Q charts Variables,” Journal of Quality Technology 27, pp. 184-203zh_TW
dc.relation.reference (參考文獻) [15] Roberts, S. W. (1959), “Control Chart Tests Based on Geometric Moving Averages,” Technometrics 1, pp. 239-250zh_TW
dc.relation.reference (參考文獻) [16] Crowder, S. V., and Hamilton, M. D. (1992), “An EWMA for Monitoring a Process Standard Deviation,” Journal of Quality Technology 24, No.1, pp. 12-21zh_TW
dc.relation.reference (參考文獻) [17] Shewhart, W. A. (1931), Economic Control of Quality of Manufactured Product, D. Van Nostrand Co., New York.zh_TW
dc.relation.reference (參考文獻) [18] 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, pp. 175-185.zh_TW