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題名 用拔靴法建構無母數剖面資料監控之信賴帶
Nonparametric profile monitoring via bootstrap percentile confidence bands
作者 謝至芬
貢獻者 洪英超
謝至芬
關鍵詞 無母數剖面資料監控
B-spline
區塊拔靴法
信賴帶
曲線深度
Nonparametric profile monitoring
B-spline
block bootstrap
confidence band
curve depth
日期 2010
上傳時間 5-Sep-2013 15:14:31 (UTC+8)
摘要 近年來剖面資料的監控在統計製程控制中有很大範圍的應用。在這篇論文裡，我們針對監控無母數剖面資料提出一個實務上的操作方法。這個操作方法有下列這些重要的特色：(1)使用一個靈活且有計算效率的無母數模型B-spline來描述反應變數與解釋變數的關係；(2)一般迴歸模型中之殘差結構假設是不需要的；(3)允許剖面資料內之觀測值間具有相關性之結構。最後，我們利用一個無線偵測器的實際資料來評估所提出方法的效率。
Profile monitoring has received increasingly attention in a wide range of applications in statistical process control (SPC). In this work, we propose a practical proposed guide which has the following important features: (i) a flexible and computationally efficient smoothing technique, called the B-spline, is employed to describe the relationship between the response variable and the explanatory variable(s); (ii) the usual structural assumptions on the residuals are not require; and (iii) the dependence structure for the within-profile observations is appropriately accommodated. Finally, a real data set from a wireless sensor is used to evaluate the efficiency of our proposed method.
參考文獻 [1] S. Basu, M. Meckesheimer, Automatic outlier detection for time series: an application to sensor data, Knowl. Inf. Syst. 11 (2007) 137-154.
[2] Carl de Boor, A Practical Guide to Splines, Springer-Verlag, 1978.
[3] Carl de Boor, A Practical Guide to Splines, Revised Edition, Springer-Verlag, 2001.
[4] L. Breima, Fitting additive models to regression data, Comput. Statist. Data Anal. 15 (1993) 13-46.
[5] Peter Bühlmann, H.R. Künsch, Block length selection in the bootstrap for time series, Comput. Statist. Data Anal. 31 (1999) 295-310.
[6] I. Chang, G.C. Tiao, C. Chen, Estimation of time series parameters in the presence of outliers, Technometrics 30 (1988) 193-204.
[7] M.R. Chernick, Bootstrap Methods, A practitioner’s guide, Wiley Series in Probability and Statistics, 1999.
[8] B.M. Colosime, M. Pacella, On the Use of Principal Component Analysis to Identify Systimatic Patterns in Foundness Profiles, Qual. Reliab. Eng. Int. 23 (2007) 707-725.
[9] A.C. Davison, D. Hinkley, Bootstrap Methods and their Application, 8th ed., Cambridge: Cambridge Series in Statistical and Probabilistic Mathematics, 2006.
[10] D.G.T. Denison, B.K. Mallick, A.F. Smith, Automatic Bayesian curve fitting, J. Roy. Statist. Soc. B 60 (1998) 333-350.
[11] Y. Ding, L. Zeng, S. Zhou, Phase I Analysis for Monitoring Nonlinear Profiles in Manufacturing Processes, J. Qual. Technol. 38 (2006) 199-216.
[12] J.H. Friedman, B.W. Silverman, Flexible parsimonious smoothing and additive modeling (with discussion), Technometrics 31 (1989) 3-39.
[13] P.J. Green, B.W. Silverman, Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, Chapman and Hall, 1994.
[14] P. Hall, J.L. Horowitz, B-Y. Jing, On blocking rules for the bootstrap with dependent data, Biometrika 82 (1995) 561-674.
[15] T.J. Hasite, R.J. Tibshirani, Generalized Additive Models, Chapman and Hall, 1990.
[16] W.A. Jensen, J.B. Birch, Progile Monitoring via Nonlinear Mixed Models, J. Qual. Technol. 41 (2009) 18-34.
[17] W.A. Jensen, J.B. Birch, W.H. Woodall, Monitoring correlation within linear profiles using mixed models, J. Qual. Technol. 40 (2008) 167-183.
[18] L. Kang, S.L. Albin, On-Line Monitoring When the Process Yields a Linear Profile, J. Qual. Technol. 32 (2000) 418-426.
[19] R.B. Kazemzadeh, R. Noorossana, A. Amiri, Phase I Monitoring of Polynomial Profiles, Comm. Statist. Theor. Meth. 37 (2008) 1671-1686.
[20] K. Kim, M.A. Mahmoud, W.H. Woodall, On the monitoring of Linear Profiles, J. Qual. Technol. 35 (2003) 317-328.
[21] W.H. Kruskal, W.A. Wallis, Use of Ranks in One-Criterion Variance Analysis, J. Amer. Statist. Assoc. 47 (1952) 583-621.
[22] H.R. Künsch, The Jackknife and the Bootstrap for General Stationary Observations, Ann. Statist. 17 (1989) 1217-1241.
[23] E.K. Lada, J.-C. Lu, J.R. Wilson, A Wavelet-Based Procedure for Process Fault Detection, IEEE. Trans. Semicond. Manuf. 15 (2002) 79-90.
[24] S.N. Lahiri, Theoretical comparisons of block bootstrap methods, Ann. Statist. 27 (1999) 386-404.
[25] S.N. Lahiri, K. Furukawa, Y.-D. Lee, A nonparametric plug-in rule for selecting optimal block lengths for block bootstrap methods, Statist. Methodol. 4 (2007) 292-321.
[26] D. Lolive, N. Barbot, O. Boeffard, Melodic contour estimation with B-spline models using a MDL criterion, Proceedings of the 11th International Conference on Speech and Computer (SPECOM), Saint Petersburg, Russia, 2006, pp. 333-338.
[27] M.A. Mahmoud, W.H. Woodall, Phase I Analysis of Linear Profiles With Calibration Applications, Technometrics 46 (2004) 380-391.
[28] S. Mignani, R. Rose, Markov Chain Monte Carlo in Statistical Mechanics: the Problem of Accuracy, Technometrics 43 (2001) 347-355.
[29] N. Molinari, J.F. Durand, R. Sabtier, Bounded optimal knots for regression splines, Comput. Statist. Data Anal. 45 (2004) 159-178.
[30] D. Pena, Outliers, influential observations, and missing data, In: A course in time series analysis, Wiley, New York, 2001, pp. 136-170.
[31] D.N. Politis, J.P. Romano, The Stationary Bootstrap, J. Amer. Statist. Assoc. 89 (1994) 1303-1313.
[32] P. Qiu, C. Zou, Z. Wang, Nonparametric Profile Monitoring by Mixed Effects Modeling, Technometrics 52 (2010) 265-277.
[33] G. Wahba, Spline Models for Observational Data, SIAM, Philadelphia, 1990.
[34] J.D. Williams, W.H. Woodall, J.B. Birch, Statistical Monitoring of Nonlinear Product and Process Quality Profiles, Qual. Reliab. Eng. Int. 23 (2007) 925-941.
[35] J.D. Williams, J.B. Birch, W.H. Woodall, N.M. Ferry, Statistical Monitoring of Heteroscedastic Dose-Response Profiles From High-Throughput Screening, J. Agric. Biol. Envir. Statist. 12 (2007) 216-235.
[36] W.H. Woodall, D.J. Spitzner, D.C. Montgomery, S. Gupta, Using Control Charts to Monitor Process and Product Quality Profiles, J. Qual. Technol. 36 (2004) 309-320.
[37] W.H. Woodall, Current Research on Profile Monitoring, Revista Producão 17 (2004) 309-320.
[38] A.B. Yeh, Bootstrap percentile confidence bands based on the concept of curve depth, Comm. Statist. Simulat. Comput. 25 (1996) 905-922.
[39] C. Zou, Y. Zhang, Z. Wang, Control Chart Based on Change-Point Model for Monitoring Linear Profiles, IIE Trans. 38 (2006) 1093-1103.
[40] C. Zou, F. Tsung, Z. Wang, Monitoring General Linear Profiles Using Multivariate EWMA Schemes, Technometrics 49 (2007) 395-408.
[41] C. Zou, F. Tsung, Z. Wang, Monitoring Profiles Based on Nonparametric Regression Methods, Technometrics 20 (2008) 512-526.
[42] P. Hall, Resampling a coverage process, Stoch. Proces. Applic. 20 (1985) 231-246.
描述 碩士
國立政治大學
統計研究所
98354009
99
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0983540092
資料類型 thesis
dc.contributor.advisor 洪英超zh_TW
dc.contributor.author (Authors) 謝至芬zh_TW
dc.creator (作者) 謝至芬zh_TW
dc.date (日期) 2010en_US
dc.date.accessioned 5-Sep-2013 15:14:31 (UTC+8)-
dc.date.available 5-Sep-2013 15:14:31 (UTC+8)-
dc.date.issued (上傳時間) 5-Sep-2013 15:14:31 (UTC+8)-
dc.identifier (Other Identifiers) G0983540092en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/60450-
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) 98354009zh_TW
dc.description (描述) 99zh_TW
dc.description.abstract (摘要) 近年來剖面資料的監控在統計製程控制中有很大範圍的應用。在這篇論文裡，我們針對監控無母數剖面資料提出一個實務上的操作方法。這個操作方法有下列這些重要的特色：(1)使用一個靈活且有計算效率的無母數模型B-spline來描述反應變數與解釋變數的關係；(2)一般迴歸模型中之殘差結構假設是不需要的；(3)允許剖面資料內之觀測值間具有相關性之結構。最後，我們利用一個無線偵測器的實際資料來評估所提出方法的效率。zh_TW
dc.description.abstract (摘要) Profile monitoring has received increasingly attention in a wide range of applications in statistical process control (SPC). In this work, we propose a practical proposed guide which has the following important features: (i) a flexible and computationally efficient smoothing technique, called the B-spline, is employed to describe the relationship between the response variable and the explanatory variable(s); (ii) the usual structural assumptions on the residuals are not require; and (iii) the dependence structure for the within-profile observations is appropriately accommodated. Finally, a real data set from a wireless sensor is used to evaluate the efficiency of our proposed method.en_US
dc.description.tableofcontents 第一章 導論 1
第二章 無母數剖面資料監控方法 3
第一節 資料清潔 (Data Cleaning) 4
第二節 配適B-spline模型 6
第三節 區塊拔靴法 (Block Bootstrap) 9
第四節 利用曲線深度建立信賴帶 11
第五節 演算法 13
第三章 績效評估：無線感應器的實例 14
第一節 Babyfinder－無線感應器之介紹 14
第二節 操作方法的套用 18
第三節 測試檢定力 (Power) 29
第四章 結論與建議 32
附錄 33
參考文獻 51		zh_TW
dc.format.extent 1496148 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/#G0983540092en_US
dc.subject (關鍵詞) 無母數剖面資料監控zh_TW
dc.subject (關鍵詞) B-splinezh_TW
dc.subject (關鍵詞) 區塊拔靴法zh_TW
dc.subject (關鍵詞) 信賴帶zh_TW
dc.subject (關鍵詞) 曲線深度zh_TW
dc.subject (關鍵詞) Nonparametric profile monitoringen_US
dc.subject (關鍵詞) B-splineen_US
dc.subject (關鍵詞) block bootstrapen_US
dc.subject (關鍵詞) confidence banden_US
dc.subject (關鍵詞) curve depthen_US
dc.title (題名) 用拔靴法建構無母數剖面資料監控之信賴帶zh_TW
dc.title (題名) Nonparametric profile monitoring via bootstrap percentile confidence bandsen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] S. Basu, M. Meckesheimer, Automatic outlier detection for time series: an application to sensor data, Knowl. Inf. Syst. 11 (2007) 137-154.
[2] Carl de Boor, A Practical Guide to Splines, Springer-Verlag, 1978.
[3] Carl de Boor, A Practical Guide to Splines, Revised Edition, Springer-Verlag, 2001.
[4] L. Breima, Fitting additive models to regression data, Comput. Statist. Data Anal. 15 (1993) 13-46.
[5] Peter Bühlmann, H.R. Künsch, Block length selection in the bootstrap for time series, Comput. Statist. Data Anal. 31 (1999) 295-310.
[6] I. Chang, G.C. Tiao, C. Chen, Estimation of time series parameters in the presence of outliers, Technometrics 30 (1988) 193-204.
[7] M.R. Chernick, Bootstrap Methods, A practitioner’s guide, Wiley Series in Probability and Statistics, 1999.
[8] B.M. Colosime, M. Pacella, On the Use of Principal Component Analysis to Identify Systimatic Patterns in Foundness Profiles, Qual. Reliab. Eng. Int. 23 (2007) 707-725.
[9] A.C. Davison, D. Hinkley, Bootstrap Methods and their Application, 8th ed., Cambridge: Cambridge Series in Statistical and Probabilistic Mathematics, 2006.
[10] D.G.T. Denison, B.K. Mallick, A.F. Smith, Automatic Bayesian curve fitting, J. Roy. Statist. Soc. B 60 (1998) 333-350.
[11] Y. Ding, L. Zeng, S. Zhou, Phase I Analysis for Monitoring Nonlinear Profiles in Manufacturing Processes, J. Qual. Technol. 38 (2006) 199-216.
[12] J.H. Friedman, B.W. Silverman, Flexible parsimonious smoothing and additive modeling (with discussion), Technometrics 31 (1989) 3-39.
[13] P.J. Green, B.W. Silverman, Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, Chapman and Hall, 1994.
[14] P. Hall, J.L. Horowitz, B-Y. Jing, On blocking rules for the bootstrap with dependent data, Biometrika 82 (1995) 561-674.
[15] T.J. Hasite, R.J. Tibshirani, Generalized Additive Models, Chapman and Hall, 1990.
[16] W.A. Jensen, J.B. Birch, Progile Monitoring via Nonlinear Mixed Models, J. Qual. Technol. 41 (2009) 18-34.
[17] W.A. Jensen, J.B. Birch, W.H. Woodall, Monitoring correlation within linear profiles using mixed models, J. Qual. Technol. 40 (2008) 167-183.
[18] L. Kang, S.L. Albin, On-Line Monitoring When the Process Yields a Linear Profile, J. Qual. Technol. 32 (2000) 418-426.
[19] R.B. Kazemzadeh, R. Noorossana, A. Amiri, Phase I Monitoring of Polynomial Profiles, Comm. Statist. Theor. Meth. 37 (2008) 1671-1686.
[20] K. Kim, M.A. Mahmoud, W.H. Woodall, On the monitoring of Linear Profiles, J. Qual. Technol. 35 (2003) 317-328.
[21] W.H. Kruskal, W.A. Wallis, Use of Ranks in One-Criterion Variance Analysis, J. Amer. Statist. Assoc. 47 (1952) 583-621.
[22] H.R. Künsch, The Jackknife and the Bootstrap for General Stationary Observations, Ann. Statist. 17 (1989) 1217-1241.
[23] E.K. Lada, J.-C. Lu, J.R. Wilson, A Wavelet-Based Procedure for Process Fault Detection, IEEE. Trans. Semicond. Manuf. 15 (2002) 79-90.
[24] S.N. Lahiri, Theoretical comparisons of block bootstrap methods, Ann. Statist. 27 (1999) 386-404.
[25] S.N. Lahiri, K. Furukawa, Y.-D. Lee, A nonparametric plug-in rule for selecting optimal block lengths for block bootstrap methods, Statist. Methodol. 4 (2007) 292-321.
[26] D. Lolive, N. Barbot, O. Boeffard, Melodic contour estimation with B-spline models using a MDL criterion, Proceedings of the 11th International Conference on Speech and Computer (SPECOM), Saint Petersburg, Russia, 2006, pp. 333-338.
[27] M.A. Mahmoud, W.H. Woodall, Phase I Analysis of Linear Profiles With Calibration Applications, Technometrics 46 (2004) 380-391.
[28] S. Mignani, R. Rose, Markov Chain Monte Carlo in Statistical Mechanics: the Problem of Accuracy, Technometrics 43 (2001) 347-355.
[29] N. Molinari, J.F. Durand, R. Sabtier, Bounded optimal knots for regression splines, Comput. Statist. Data Anal. 45 (2004) 159-178.
[30] D. Pena, Outliers, influential observations, and missing data, In: A course in time series analysis, Wiley, New York, 2001, pp. 136-170.
[31] D.N. Politis, J.P. Romano, The Stationary Bootstrap, J. Amer. Statist. Assoc. 89 (1994) 1303-1313.
[32] P. Qiu, C. Zou, Z. Wang, Nonparametric Profile Monitoring by Mixed Effects Modeling, Technometrics 52 (2010) 265-277.
[33] G. Wahba, Spline Models for Observational Data, SIAM, Philadelphia, 1990.
[34] J.D. Williams, W.H. Woodall, J.B. Birch, Statistical Monitoring of Nonlinear Product and Process Quality Profiles, Qual. Reliab. Eng. Int. 23 (2007) 925-941.
[35] J.D. Williams, J.B. Birch, W.H. Woodall, N.M. Ferry, Statistical Monitoring of Heteroscedastic Dose-Response Profiles From High-Throughput Screening, J. Agric. Biol. Envir. Statist. 12 (2007) 216-235.
[36] W.H. Woodall, D.J. Spitzner, D.C. Montgomery, S. Gupta, Using Control Charts to Monitor Process and Product Quality Profiles, J. Qual. Technol. 36 (2004) 309-320.
[37] W.H. Woodall, Current Research on Profile Monitoring, Revista Producão 17 (2004) 309-320.
[38] A.B. Yeh, Bootstrap percentile confidence bands based on the concept of curve depth, Comm. Statist. Simulat. Comput. 25 (1996) 905-922.
[39] C. Zou, Y. Zhang, Z. Wang, Control Chart Based on Change-Point Model for Monitoring Linear Profiles, IIE Trans. 38 (2006) 1093-1103.
[40] C. Zou, F. Tsung, Z. Wang, Monitoring General Linear Profiles Using Multivariate EWMA Schemes, Technometrics 49 (2007) 395-408.
[41] C. Zou, F. Tsung, Z. Wang, Monitoring Profiles Based on Nonparametric Regression Methods, Technometrics 20 (2008) 512-526.
[42] P. Hall, Resampling a coverage process, Stoch. Proces. Applic. 20 (1985) 231-246.		zh_TW