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題名 捲積管制圖之設計
The design of the convolution chart
作者 鄭鈞遠
Cheng, Chun-Yuan
貢獻者 楊素芬
鄭鈞遠
Cheng, Chun-Yuan
關鍵詞 管制圖
高良率製程
量測誤差
捲積
control chart
high yield process
measurement error
convolution
日期 2010
上傳時間 5-Sep-2013 15:12:07 (UTC+8)
摘要 量測誤差是工業製程中影響產品值常見的因素。大的量測誤差會使得產品的量測值偏離實際值，並引導監控者至錯誤的結論。本文提出一種新的捲積管制圖。提出指數分配形式的時間間隔型資料，並加上量測誤差的考量，應用在指數加權移動平均管制圖上。此外，假設量測誤差為常態或是指數分配。研究顯示出，在兩種不同分配的量測誤差之下，管制圖的表現都會顯著的受到影響。
Measurement error is an important factor in industry that influences the outcome of a process. Large measurement error would cause the observation measure deviate from the true value and consequently lead to a wrong decision. In this project, we propose a convolution control chart. We then design the EWMA ‘time between events’ (TBE) control chart with the measurement error, with the assumption that the observations are exponentially distributed. In addition, we assumed the measurement error follows a normal distribution or an exponential distribution. We showed that, in two cases of the measurement error, the performance of the proposed chart monitoring the process mean is greatly affected.
參考文獻 Reference
1. Borror, C. M., Champ, C. W. and Rigdon, S.E. Poisson EWMA control charts. Journal of Quality Technology, 1998, 30, 352-361.
2. Canan Pehl Van. Controlling high quality manufacturing processesa robustness study of the lower-sided tbe EWMA procedure. The graduate school of natural and applied sciences of middle east technical university.
3. Capizzi, G. and Masarotto, G. An adaptive exponentially weighted moving average control chart. Technometrics. 2003, 45, 3.
4. Champ, C. W and Woodal, W. H. Exact results for Shewhart control charts with supplementary run rules. Technometrics, 1987, 29, 4, 393-399.
5. Chan, L. Y., Xie, M. and Goh, T. N. Cumulative quantity control charts for monitoring production process. International Journal of Production Research. 2000, 38, 2, 397-408.
6. Gan, F. F. Designs of one- and two-sided exponential ewma charts. Journal of Quality Technology, 1998, 30, 55-69.
7. Glushkovsky, E.A. On-line G-control chart for attribute data. Quality and Reliability Engineering International. 1994, 10, 3, 217-227.
8. Kuralmani, V., Xie, M., Goh, T. N. and Gan, F. F. A conditional decision procedure for high yield processes. IIE Transactions, 2002, 34, 1021-2030.
9. Lacouture, Y. and Cousineau, D. How to use Matlab to fit the ex‐Gaussian and other probability functions to a distribution of response times. Tutorials in Quantitative Methods for Psychology. 2008, 4, 1, 35‐45.
10. Liu, J. Y., Xie, M., and Goh, T. N. CUSUM chart with transformed exponential data. Communications in Statistics—Theory and Methods. 2006, 35, 1829–1843.
11. Liu, J. Y., Xie, M., Goh, T. N and Sharma, P. R. A Comparative study of exponential time between events charts. Quality Technology of Quantitative Management. 2006, 3, 3, 347-359.
12. Liu, J. Y., Xie, M., Goh, T. N and Chan, L. Y. A study of EWMA chart with transformed exponential data. International Journal of Production Research. 2007, 45, 3, 1, 743-763.
13. Linna, K. W. and Woodall, W. H. Effect of measurement error on shewhart control charts. Journal of Quality Technology. 2001, 33, 2.
14. Luce, R. D. Response Times [electronic resource]：Their role in inferring elementary mental organization. 1991, New York：Oxford University Press.
15. Maravelakis, P. E., Panaretosand, J. and Psarakis, S. EWMA chart and measurement error. Journal of Applied Statistics. 2004, 31, 4, 445-455.
16. Montgomery. Statistical process control – A modern introduction. Sixth edition, Wiley, Asia.
17. Serel, D. A. Economic design of EWMA control charts based on loss function. Mathematical and Computer Modeling. 2009, 49, 745-759.
18. Sharma, P. R. A study of properties and applications of control charts for high yield processes. 2003, Department of industrial & systems engineering the national university of Singapore.
19. Shewhart, W. A. The application of statistics as an aid in maintaining quality of a manufactured product. Journal of the American Statistical Association. 1925, 20, 546-548.
20. Yang, S., Ho, H. and Rahim, M.A. Effects of measurement error on controlling two dependent process steps., Economic Quality Control, 2007, 22, 1, 127-139.
描述 碩士
國立政治大學
統計研究所
98354003
99
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0098354003
資料類型 thesis
dc.contributor.advisor 楊素芬zh_TW
dc.contributor.author (Authors) 鄭鈞遠zh_TW
dc.contributor.author (Authors) Cheng, Chun-Yuanen_US
dc.creator (作者) 鄭鈞遠zh_TW
dc.creator (作者) Cheng, Chun-Yuanen_US
dc.date (日期) 2010en_US
dc.date.accessioned 5-Sep-2013 15:12:07 (UTC+8)-
dc.date.available 5-Sep-2013 15:12:07 (UTC+8)-
dc.date.issued (上傳時間) 5-Sep-2013 15:12:07 (UTC+8)-
dc.identifier (Other Identifiers) G0098354003en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/60438-
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) 98354003zh_TW
dc.description (描述) 99zh_TW
dc.description.abstract (摘要) 量測誤差是工業製程中影響產品值常見的因素。大的量測誤差會使得產品的量測值偏離實際值，並引導監控者至錯誤的結論。本文提出一種新的捲積管制圖。提出指數分配形式的時間間隔型資料，並加上量測誤差的考量，應用在指數加權移動平均管制圖上。此外，假設量測誤差為常態或是指數分配。研究顯示出，在兩種不同分配的量測誤差之下，管制圖的表現都會顯著的受到影響。zh_TW
dc.description.abstract (摘要) Measurement error is an important factor in industry that influences the outcome of a process. Large measurement error would cause the observation measure deviate from the true value and consequently lead to a wrong decision. In this project, we propose a convolution control chart. We then design the EWMA ‘time between events’ (TBE) control chart with the measurement error, with the assumption that the observations are exponentially distributed. In addition, we assumed the measurement error follows a normal distribution or an exponential distribution. We showed that, in two cases of the measurement error, the performance of the proposed chart monitoring the process mean is greatly affected.en_US
dc.description.tableofcontents Table of Contents
Chapter 1. Introduction……………………………………...………………...…….1
1.1 Controlling High Yield Manufacturing Processes………………………...…….1
1.2 Motivation and Objectives…………………………………………………..….2
1.3 Literature Review……………………………………………………………….3
Chapter 2. Performance Comparison Among the C Chart, CQC Chart, Transformed EWMA Chart and CQC EWMA Chart………………10
2.1 Control Limits of Cumulative Quantity Control Chart, Transformed EWMA
Chart and Cumulative Quantity Control EWMA Chart….……………………10
2.2 An Example of the Cumulative Quantity Control Charts, Cumulative Quantity Control EWMA and Transformed EWMA Chart……………………………...12
2.3 Average Run Length Analysis…………………………………………………15
Chapter 3. The Design of the Convolution EWMA Chart with Normal Measurement Error…………………………………………………....18
3.1 Measurement Error with Normal Distribution…………………………..…….18
3.2 Design of the Exponential - Normal EWMA Convolution Chart……………..21
3.3 Average Run Length of the Chart………………………………………..…….21
3.4 Average Run Length Calculation………………………………………….......23
3.5 The Impact of the Mistaking of the Chart……………………………….…….47
Chapter 4. The Design of the EWMA Convolution Chart with Exponential Measurement Error……………………………………………….......51
4.1 Measurement Error with Exponential Distribution…………………..………..51
4.2 Design of the Exponential - Exponential EWMA Convolution Chart…..…….52
4.3 Average Run Length of the Exponential-Exponential EWMA Convolution
Chart …………………………………………………………………………..53
4.4 The Impact of the Mistaking of the Chart……………………………………..77
Chapter 5. Conclusion and Future Researches…………………...………………83
Reference…………………………………………………………………………….85		zh_TW
dc.format.extent 1529857 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/#G0098354003en_US
dc.subject (關鍵詞) 管制圖zh_TW
dc.subject (關鍵詞) 高良率製程zh_TW
dc.subject (關鍵詞) 量測誤差zh_TW
dc.subject (關鍵詞) 捲積zh_TW
dc.subject (關鍵詞) control charten_US
dc.subject (關鍵詞) high yield processen_US
dc.subject (關鍵詞) measurement erroren_US
dc.subject (關鍵詞) convolutionen_US
dc.title (題名) 捲積管制圖之設計zh_TW
dc.title (題名) The design of the convolution charten_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Reference
1. Borror, C. M., Champ, C. W. and Rigdon, S.E. Poisson EWMA control charts. Journal of Quality Technology, 1998, 30, 352-361.
2. Canan Pehl Van. Controlling high quality manufacturing processesa robustness study of the lower-sided tbe EWMA procedure. The graduate school of natural and applied sciences of middle east technical university.
3. Capizzi, G. and Masarotto, G. An adaptive exponentially weighted moving average control chart. Technometrics. 2003, 45, 3.
4. Champ, C. W and Woodal, W. H. Exact results for Shewhart control charts with supplementary run rules. Technometrics, 1987, 29, 4, 393-399.
5. Chan, L. Y., Xie, M. and Goh, T. N. Cumulative quantity control charts for monitoring production process. International Journal of Production Research. 2000, 38, 2, 397-408.
6. Gan, F. F. Designs of one- and two-sided exponential ewma charts. Journal of Quality Technology, 1998, 30, 55-69.
7. Glushkovsky, E.A. On-line G-control chart for attribute data. Quality and Reliability Engineering International. 1994, 10, 3, 217-227.
8. Kuralmani, V., Xie, M., Goh, T. N. and Gan, F. F. A conditional decision procedure for high yield processes. IIE Transactions, 2002, 34, 1021-2030.
9. Lacouture, Y. and Cousineau, D. How to use Matlab to fit the ex‐Gaussian and other probability functions to a distribution of response times. Tutorials in Quantitative Methods for Psychology. 2008, 4, 1, 35‐45.
10. Liu, J. Y., Xie, M., and Goh, T. N. CUSUM chart with transformed exponential data. Communications in Statistics—Theory and Methods. 2006, 35, 1829–1843.
11. Liu, J. Y., Xie, M., Goh, T. N and Sharma, P. R. A Comparative study of exponential time between events charts. Quality Technology of Quantitative Management. 2006, 3, 3, 347-359.
12. Liu, J. Y., Xie, M., Goh, T. N and Chan, L. Y. A study of EWMA chart with transformed exponential data. International Journal of Production Research. 2007, 45, 3, 1, 743-763.
13. Linna, K. W. and Woodall, W. H. Effect of measurement error on shewhart control charts. Journal of Quality Technology. 2001, 33, 2.
14. Luce, R. D. Response Times [electronic resource]：Their role in inferring elementary mental organization. 1991, New York：Oxford University Press.
15. Maravelakis, P. E., Panaretosand, J. and Psarakis, S. EWMA chart and measurement error. Journal of Applied Statistics. 2004, 31, 4, 445-455.
16. Montgomery. Statistical process control – A modern introduction. Sixth edition, Wiley, Asia.
17. Serel, D. A. Economic design of EWMA control charts based on loss function. Mathematical and Computer Modeling. 2009, 49, 745-759.
18. Sharma, P. R. A study of properties and applications of control charts for high yield processes. 2003, Department of industrial & systems engineering the national university of Singapore.
19. Shewhart, W. A. The application of statistics as an aid in maintaining quality of a manufactured product. Journal of the American Statistical Association. 1925, 20, 546-548.
20. Yang, S., Ho, H. and Rahim, M.A. Effects of measurement error on controlling two dependent process steps., Economic Quality Control, 2007, 22, 1, 127-139.		zh_TW