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研究生:楊榮欽
論文名稱:雙邊規格製程能力指標Spk的信賴下界
論文名稱(外文):Lower confidence bound for two sided process capability index Spk
指導教授:彭文理彭文理引用關係
學位類別:碩士
校院名稱:國立交通大學
系所名稱:工業工程與管理學系
學門:工程學門
學類:工業工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:41
中文關鍵詞:製程良率製程能力指標信賴下界拔靴法
外文關鍵詞:production yieldprocess capability indexlower boundbootstrap method
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在製造工廠內,製程良率被當成標準的衡量準則已經很久。製程能力指標 可以精確地衡量常態性分配製程的良率。然而,欲以精確的數學方式推論得到 的自然估計之抽樣分配卻相當困難,因為該抽樣分配非常複雜。因此,多種近似估計方法都被開發,試圖解決以上難題。Pearn et al. (2010)利用二階條件泰勒展開式推導出一個近似估計量,他們利用臨界值(critical value)深入探討該近似估計量的性質。Chen (2005)則是利用拔靴法,模擬產生四種不同的信賴下界(the standard bootstrap (SB), the percentile bootstrap (PB), the biased-corrected percentile bootstrap (BCPB), and the bias-corrected and accelerated bootstrap (BCa))。Chen(2005)認為SB信賴下界比起其他三個信賴下界具有更高的涵蓋率,也就是說,SB信賴下界的績效優於其他三種拔靴法。這篇碩士論文中,我們比較Pearn et al. (2010)的近似估計量所產生的信賴下界,還有四種拔靴法(SB, PB, BCPB, and bootstrap-t (BT) methods)產生的信賴下界。實驗結果顯示Pearn et al. (2010)所產生的信賴下界有幾個優點:(1)在五種信賴下界中,其具有最高的涵蓋率,這也是最重要的優點,(2)Pearn et al. (2010)提出的是一種可解析函式(analytical function),由此可知,由此法產生的信賴下界所存在的誤差能夠被衡量,但是拔靴法地信賴下界卻無法衡量誤差(3)Pearn et al. (2010)提供唯一的信賴下界,但是拔靴法提供振動的信賴下界且無法預測。綜合以上理由,我們認為由Pearn et al. (2010)所產生的信賴下界比起拔靴法更優良。
Process yield has been a common and standard criterion in manufacturing industry for a long time. The yield index provides an exact measure on the production yield of normal processes. However, the sampling distribution of estimated is analytically intractable, therefore the approximating approach is considered. Chen (2005) applied the famous boot-strap method, a nonparametric but effective simulation technique, to deal with the intractabil-ity. Chen (2005) utilized four bootstrap methods to conduct lower confidence bound (LCB) and noted that the standard bootstrap (SB) method outperforms the other three in coverage proportion. Moreover, Pearn et al. (2010) used the convolution method based upon the se-cond-order approximation by Taylor expansion to estimate the yield index . In this thesis, we compared coverage proportions and LCBs based on the convolution and the bootstrap approximation. The results revealed that the CP incurred by the LCB obtained from the convolution approximation outperforms the one from the bootstrap method.
中文摘要 i
Abstract ii
誌謝 iii
Contents iv
List of Tables v
List of Figures vi
1. Introduction 1
2. Literature review 4
3. Convolution method for the estimated 8
3.1 The estimator 8
3.2 Determine the minimal required sample size 9
3.3 Lower confidence bounds and coverage proportion 17
4 Bootstrap methodology 19
4.1 Lower confidence bounds of bootstrap methodology 20
A. Standard Bootstrap (SB) method 20
B. Percentile Bootstrap (PB) method 20
C. Bias-Corrected Percentile Bootstrap (BCPB) method 21
D. Bootstrap-t (BT) method 21
4.2 Lower confidence bounds and coverage proportions based on the bootstrap method 22
5 Performance comparisons of convolution and bootstrapping methods 26
Reference 35
Appendix 38
1. Boyles, R. A. (1991). The Taguchi capability index. Journal of Quality Technology, 23(1), 17-26.
2. Boyles, R. A. (1994). Process capability with asymmetric tolerances. Communications in Statistics-Simulation and Computation, 23(3), 615-643.
3. Chan, L. K., Cheng, S. W. and Spiring, F. A. (1988). A new measure of process capability Cpm. Journal of Quality Technology, 20(3), 162-175.
4. Chen, S. M. and Hsu, N. F. (2005). The asymptotic distribution of the process capability index Cpmk. Communications in Statistics: Theory and Methods. 24(5), 1279-1291.
5. Chen, J. P. and Tong, L. I. (2003). Bootstrap confidence interval of the difference between two process capability indices. International Journal of Advanced Manufacturing Technology, 21, 249-256.
6. Chen, J. P. (2005). Comparing four lower confidence limits for process yield index . International Journal of Advanced Manufacturing Technology. 26(5), 609-614.
7. Choi, K. C., Nam, K. H. and Park, D. H. (1996). Estimation of capability index based on bootstrap method. Microelectronics Reliability, 36(9), 1141-1153.
8. Efron, B. (1979). Bootstrap methods: another look at the Jackknife. The Annals of Statis-tics, 7, 1-26.
9. Efron, B. (1981). Nonparametric standard errors and confidence intervals. Canadian Journal of Statistics. 9, 139-172.
10. Efron, B. (1982). The Jackknife, the bootstrap and other resampling plans. Society for In-dustrial and Applied Mathematics, Philadelphia, PA.
11. Efron, B. and Tibshirani, R. J. (1986). Bootstrap methods for standard errors, confidence interval, and other measures of statistical accuracy. Statistical Science, 1, 54-77.
12. Franklin, L. A. and Wasserman, G. S. (1992). Bootstrap lower confidence limits for capa-bility indices. Journal of Quality Technology, 24(4), 196-210.
13. Hsiang, T. C. and Taguchi, G. (1985). A tutorial on quality control and assurance – the Taguchi methods. ASA Annual Meeting, Las Vegas, Nevada.
14. Kane, V. E. (1986). Process capability indices. Journal of Quality Technology, 18(1), 41-52.
15. Lee, J. C., Hung, H. N., Pearn, W. L. and Kueng, T. L. (2002). On the distribution of the estimated process yield index . Quality and Reliability Engineering International, 18(2), 111-116.
16. Pearn, W. L., Kotz, S. and Johnson, N. L. (1992). Distributional and inferential properties of process capability indices. Journal of Quality Technology, 24(4), 216-231.
17. Pearn, W. L., Lin, G. H. and Chen, K. S. (1998). Distributional and inferential properties of the process accuracy and process precision indices. Communications in Statistics: Theory and Methods, 27(4), 985-1000.
18. Pearn, W. L. and Lin, P. C. (2002). Computer program for calculating the p-value in test-ing process capability index Cpmk. Quality and Reliability Engineering International, 18(4), 333-342.
19. Pearn, W. L. and Shu, M. H. (2003). Lower confidence bounds with sample size infor-mation for Cpm with application to production yield assurance. International Journal of Production Research, 41(15), 3581-3599.
20. Pearn, W. L., Lin, G. H. and Wang, K. H. (2004a). Normal approximation to the distribu-tion of the estimated yield index . Quality and Quantity, 38(1), 95-111.
21. Pearn, W. L., Wu, C. /W. and Lin, H. C. (2004b). Procedure supplier selection based on Cpm applied to super twisted nematic liquid crystal display processes. International Journal of Production Research, 42(13), 2719-2734.
22. Pearn, W. L., Wu, C. W. and Wang, K. H. (2005). Capability measure for asymmetric tol-erance non-normal processes applied to speaker driver manufacturing. The International Journal of Advanced Manufacturing Technology, 25(5-6), 506-515.
23. Pearn, W. L., Chang, Y. C. and Wu, C. W. (2005). Bootstrap approach for estimating pro-cess quality yield with application to light emitting diodes. The International Journal of Advanced Manufacturing Technology, 25(5-6), 560-570.
24. Pearn, W. L. and Cheng, Y. C. (2007). Estimating process yield based on for multi-ple samples. International Journal of Production Research, 45(1), 49-64.
25. Pearn, W. L., Hui, N. H., Ya, C. C. and Gu, H. L. (2010). Procedure of convolution meth-od for estimating production yield with sample size information. International Journal of Production Research, 48(5), 1245-1265.
26. Wright, P. A. (1998). The probability density function of process capability index Cpmk. Communications in Statistics – Theory and Methods, 27(7), 1781-1789.
27. Wu, C. W., Shu, M. H., Pearn, W. L. and Liu, K. H. (2008). Bootstrap approach for sup-plier selection based on production yield. International Journal of Production Research, 46(18), 5211-5230.
28. Wu, C. W. and Liao, M. Y. (2012). Generalized inference for measuring process yield with the contamination of measurement errors – quality control for silicon wafer manufacturing processes in semiconductor industry. IEEE Transactions on semiconductor manufacturing, 25(2), 272-283.

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