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| 研究生： |
鄭鈞遠 Cheng, Chun-Yuan |
|---|---|
| 論文名稱： |
捲積管制圖之設計 The design of the convolution chart |
| 指導教授： | 楊素芬 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 統計學系 Department of Statistics |
| 論文出版年： | 2011 |
| 畢業學年度： | 99 |
| 語文別： | 英文 |
| 論文頁數： | 85 |
| 中文關鍵詞： | 管制圖 、高良率製程 、量測誤差 、捲積 |
| 外文關鍵詞： | control chart, high yield process, measurement error, convolution |
| 相關次數： | 點閱：332 下載：8 |
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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.
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
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.
