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題名 多元製程之共變數矩陣追蹤研究
The study of Multivariate Process Dispersion Control Chart作者 劉宴伶
Liu, Yen-Ling貢獻者 楊素芬
劉宴伶
Liu, Yen-Ling關鍵詞 多元統計過程控制
共變異數矩陣
資料深度
無分佈假設
指數加權移動平均
變動維度
Multivariate statistical process control
Covariance matrix
Data depth
Distribution-free
Exponentially weighted moving average
Variable dimension日期 2021 上傳時間 4-Aug-2021 14:41:33 (UTC+8) 摘要 近年來，在工業製造過程中同時監控兩個上的相關品質變數非常重要，因此多元統計過程控制 (MSPC) 成為研究人員的熱門研究領域。由於許多數據資料不服從多元常態分佈，因此無分配假設的管制圖更是一個相當重要的工具來監控產品品質。本文建構了兩種新的指數加權移動平均 (EWMA) 管制圖。一種是基於Hotelling T^2二次式來監控資料服從多元常態分佈的共變異數矩陣。另一個則是結合資料深度 (data depth) 和符號方法 (sign method) 的無分佈假設的管制圖來監控過程的分散程度。此外，我們添加了變動維度 (VD) 技巧來建構新的變動維度的管制圖，用於監控過程具有 s_2 個變量的共變異數矩陣。在 s_2 個變量中，其中一些衡量容易或只需要較少的測量成本，而其餘的變量衡量困難或需要昂貴的測量成本。當共變異矩陣的變異數有變化時，所提出的管制圖比文獻中現有的管制圖表現更好。此外，我們通過使用半導體數據說明了所提出的管制圖的應用。因此，我們建議採用提出的管制圖來檢測過程分散的變化。
Today it is important to monitor more than two correlated quality variables at the same time in the industrial manufacturing process, so the multivariate statistical process control (MSPC) becomes a popular research area for the researchers. Since many data do not follow a multivariate normal distribution, the study of distribution-free control chart is very important.This paper constructs two kinds of new exponentially weighted moving average (EWMA) control charts. One is based on the Hotelling T^2 quadratic form to monitor the covariance matrix for a process following a multivariate normal distribution. Another is a distribution-free control chart based on the data depth and the sign method to monitor process dispersion. In addition, we add the technique of variable dimension (VD) to build new VD-type control charts for monitoring covariance matrix of a process with s_2 variables. Some of them are easy or need less cost to measure and the remaining variables are difficult or need expensive cost to measure.The proposed control charts performs better than the existing control charts in literature when the covariance matrix has changes in variances. Furthermore, we illustrate the application of the proposed control charts by using the semiconductor data. Hence, we suggest adopting the proposed control charts to detect the shifts in process dispersion.參考文獻 [1] Alt, F. B. (1985). Multivariate quality control. The Encyclopedia of Statistical Sciences, 110-122.[2] Aparisi, F., Epprecht, E. K., & Ruiz, O. (2012). T2 control chart with variable dimension. Journal of Quality Technology, 44(4), 375-393.[3] Bell, R. C., Jones-Farmer, L. A., & Billor, N. (2014). A distribution-free multivariate phase I location control chart for subgrouped data from elliptical distributions. Technometrics, 56(4), 528-538.[4] Chaven, A. R., & Shirke, D. T. (2020). Nonparametric two sample tests for scale parameters of multivariate distributions. Communications for Statistical Applications and Methods, 27(4), 397-412.[5] Chen, N., Zi, X., & Zou, C. (2016). A distribution-free multivariate control chart. Technometrics, 58(4), 448-459.[6] Crosier, R. B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3), 291-303.[7] Epprecht, E. K., Aparisi, F., & Ruiz, O. (2018). Optimum variable-dimension EWMA chart for multivariate statistical process control. Quality Engineering, 30(2), 268-282.[8] Epprecht, E. K., Aparisi, F., Ruiz, O., & Veiga, A. (2013). Reducing sampling costs in multivariate SPC with a double-dimension T2 control chart. International Journal of Production Economics, 144(1), 90-104.[9] Farokhnia, M., & Niaki, S. T. A. (2019). Principal component analysis-based control charts using support vector machines for multivariate non-normal distributions. Communications in Statistics-Simulation and Computation, 1-24.[10] Hawkins, D. M. (1991). Multivariate quality control based on regression-adjusted variables. Technometrics, 33(1), 61-75.[11] Hawkins, D. M., & Maboudou-Tchao, E. M. (2008). Multivariate exponentially weighted moving covariance matrix. Technometrics, 50, 155-166.[12] Hotelling, H. A. R. O. L. D. (1947). Multivariate quality control. Techniques of statistical analysis. McGraw-Hill, New York.[13] Huwang, L., Lin, L. W., & Yu, C. T. (2019). A spatial rank-based multivariate EWMA chart for monitoring process shape matrices. Quality and Reliability Engineering International, 1-19.[14] Huwang, L., Lin, P. C., Chang, C. H., Lin, L. W., & Tee, Y. S. (2017). An EWMA chart for monitoring the covariance matrix of a multivariate process based on dissimilarity index. Quality and Reliability Engineering International, 33, 2089-2104.[15] Huwang, L., Yeh, A. B., & Wu, C. V. (2007). Monitoring multivariate process variability for individual observations. Journal of Quality Technology, 39, 258-278.[16] Kim, J., Abdella, G. M., Kim, S., Al-Khalifa, K. N., & Hamouda, A. M. (2019). Control charts for variability monitoring in high-dimensional processes. Computers & Industrial Engineering, 130, 309-316.[17] Li, B., Wang, K., & Yeh, A. B. (2013). Monitoring the covariance matrix via penalized likelihood estimation. IIE Transactions, 45, 132-146.[18] Li, Z., Zou, C., Wang, Z. and Huwang, L. (2013). A multivariate sign chart for monitoring process shape parameters. Journal of Quality Technology, 45(2), 149-165.[19] Liang, W., Xiang, D., Pu, X., Li, Y., & Jin, L. (2019). A robust multivariate sign control chart for detecting shifts in covariance matrix under the elliptical directions distributions, Quality Technology & Quantitative Management, 16(1), 113-127.[20] Liu, R. Y. (1995). Control charts for multivariate processes. Journal of the American Statistical Association, 90(432), 1380-1387.[21] Lowry, C. A., & Montgomery, D. C. (1995). A review of multivariate control charts. HE transactions, 27(6), 800-810.[22] Luca Scrucca. (2021). Package ‘GA’. Retrieved June 9, 2021, from https://cran.r-project.org/web/packages/GA/GA.pdf[23] MacGregor, J. F., & Kourti, T. (1995). Statistical process control of multivariate processes. Control Engineering Practice, 3(3), 403-414.[24] McCann M., & Johnston A. (2008). SECOM Data Set Center for Machine Learning and Intelligent Systems. Irvine, CA: University of California. Retrieved June 9, 2021, from https://archive.ics.uci.edu/ml/datasets.php[25] Melo, M. S., Ho, L. L., & Medeiros, P. G. (2017). M a x D: an attribute control chart to monitor a bivariate process mean. The International Journal of advanced Manufacturing Technology. 90, 489-498.[26] Montgomery, D. C., & Wadsworth, H. M. (1972, May). Some techniques for multivariate quality control applications. In ASQC Technical Conference Transactions, Washington, D. C (pp. 427-435).[27] Qiu, P. (2008). Distribution-free multivariate process control based on log-linear modeling. IIE Transactions, 40(7), 664-677.[28] Reynold, M. R., Jr., Amin, R. W., Arnold, J. C., & Nachlas, J. A. (1988). X ̅ charts with variable sampling intervals. Technometrics, 30(2), 181-192.[29] Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 1(3), 239-250.[30] Wang, S. & Reynolds, M. R. (2013). A GLR Control Chart for Monitoring the Mean Vector of a Multivariate Normal Process. Journal of Quality Technology, 45(1), 18-33.[31] Shen, X., Tsung, F., & Zou, C. (2014). A new multivariate EWMA scheme for monitoring covariance matrices. International Journal of Production Research, 52, 2834-2850.[32] Shewhart, W. A. (1924). Some applications of statistical methods to the analysis of physical and engineering data. Bell System Technical Journal, 3(1), 43-87.[33] Yang, S. F., Lin, Y. C., & Yeh, A. B. (2021). A phase Ⅱ depth-based variable dimension EWMA control chart for monitoring process mean. Quality and Reliability Engineering International, 1-15.[34] Yeh, A. B., Huwang, L., & Wu, Y. F. (2004). A likelihood-ratio-based EWMA control chart for monitoring variability of multivariate normal processes. IIE Transactions, 36(9), 865-879.[35] Yeh, A. B., Li, B., & Wang, K. (2012). Monitoring multivariate process variability with individual observations via penalized likelihood estimation. International Journal of Production Research, 50, 6624-6638.[36] Yen, C. L., & Shiau, J. J. H. (2010). A multivariate control chart for detecting increases in process dispersion. Statistica Sinica, 20, 1683-1707.[37] Zou, C., & Tsung, F. (2011). A multivariate sign EWMA control chart. Technometrics, 53(1), 84-97. 描述 碩士
國立政治大學
統計學系
108354010資料來源 http://thesis.lib.nccu.edu.tw/record/#G0108354010 資料類型 thesis dc.contributor.advisor 楊素芬 zh_TW dc.contributor.author (Authors) 劉宴伶 zh_TW dc.contributor.author (Authors) Liu, Yen-Ling en_US dc.creator (作者) 劉宴伶 zh_TW dc.creator (作者) Liu, Yen-Ling en_US dc.date (日期) 2021 en_US dc.date.accessioned 4-Aug-2021 14:41:33 (UTC+8) - dc.date.available 4-Aug-2021 14:41:33 (UTC+8) - dc.date.issued (上傳時間) 4-Aug-2021 14:41:33 (UTC+8) - dc.identifier (Other Identifiers) G0108354010 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/136316 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 108354010 zh_TW dc.description.abstract (摘要) 近年來，在工業製造過程中同時監控兩個上的相關品質變數非常重要，因此多元統計過程控制 (MSPC) 成為研究人員的熱門研究領域。由於許多數據資料不服從多元常態分佈，因此無分配假設的管制圖更是一個相當重要的工具來監控產品品質。本文建構了兩種新的指數加權移動平均 (EWMA) 管制圖。一種是基於Hotelling T^2二次式來監控資料服從多元常態分佈的共變異數矩陣。另一個則是結合資料深度 (data depth) 和符號方法 (sign method) 的無分佈假設的管制圖來監控過程的分散程度。此外，我們添加了變動維度 (VD) 技巧來建構新的變動維度的管制圖，用於監控過程具有 s_2 個變量的共變異數矩陣。在 s_2 個變量中，其中一些衡量容易或只需要較少的測量成本，而其餘的變量衡量困難或需要昂貴的測量成本。當共變異矩陣的變異數有變化時，所提出的管制圖比文獻中現有的管制圖表現更好。此外，我們通過使用半導體數據說明了所提出的管制圖的應用。因此，我們建議採用提出的管制圖來檢測過程分散的變化。 zh_TW dc.description.abstract (摘要) Today it is important to monitor more than two correlated quality variables at the same time in the industrial manufacturing process, so the multivariate statistical process control (MSPC) becomes a popular research area for the researchers. Since many data do not follow a multivariate normal distribution, the study of distribution-free control chart is very important.This paper constructs two kinds of new exponentially weighted moving average (EWMA) control charts. One is based on the Hotelling T^2 quadratic form to monitor the covariance matrix for a process following a multivariate normal distribution. Another is a distribution-free control chart based on the data depth and the sign method to monitor process dispersion. In addition, we add the technique of variable dimension (VD) to build new VD-type control charts for monitoring covariance matrix of a process with s_2 variables. Some of them are easy or need less cost to measure and the remaining variables are difficult or need expensive cost to measure.The proposed control charts performs better than the existing control charts in literature when the covariance matrix has changes in variances. Furthermore, we illustrate the application of the proposed control charts by using the semiconductor data. Hence, we suggest adopting the proposed control charts to detect the shifts in process dispersion. en_US dc.description.tableofcontents Chapter 1. Introduction 11.1 Literature Review 11.2 Study Motivation 31.3 Research Method 3Chapter 2. Using A New EWMA Chart to Monitor Process Dispersion under A Multivariate Normal Distribution 42.1 Design of the new EWMA chart 42.1.1 The one-sided ZEWMAC chart to monitor the upward process dispersion 52.1.2 The two-sided ZEWMAC chart to monitor the upward or downward process dispersion 62.1.3 The one-sided ZEWMAC chart to monitor the downward process dispersion 72.2 The detection performance of the proposed ZEWMAC chart for an in-control process with identity covariance matrix 182.3 The detection performance of the proposed ZEWMAC chart for an in-control process with non-identity covariance matrix 252.4 Performance comparison of the proposed ZEWMAC chart and existing control charts for an in-control process with identity covariance matrix 322.4.1 Performance comparison between the ZEWMAC chart and one-sided LRT chart 322.4.2 Performance comparison among the ZEWMAC, HMT, MaxNorm, and MEWMC-based PLR charts 342.4.3 Performance comparison between the ZEWMAC and RPLR charts 382.5 A numerical example of using the ZEWMAC chart 42Chapter 3. Using the Variable Dimension ZEWMAC Chart to Monitor Process Dispersion under a Multivariate Normal Distribution 503.1 Design the variable dimension ZEWMAC chart 503.1.1 The one-sided VD ZEWMAC chart to monitor the upward process dispersion 513.1.2 The one-sided VD ZEWMAC chart to monitor the downward process dispersion 543.2 The detection performance of the proposed VD ZEWMAC chart for an in-control process with identity covariance matrix 643.3 The detection performance of the proposed VD ZEWMAC chart for an in-control process with non-identity covariance matrix 693.4 Performance comparison of the VD ZEWMAC chart and ZEWMAC chart 733.5 The cost of sampling and detection performance of the VD ZEWMAC chart 773.6 A numerical example of using the VD ZEWMAC chart 81Chapter 4. A New Data-depth based EWMA Dispersion Chart for an Unknown Distributed Multivariate Process Data 924.1 Design of the new EWMA chart 924.1.1 The one-sided ZEWMAD chart to monitor the upward process dispersion 944.1.2 The one-sided ZEWMAD chart to monitor the downward process dispersion 954.2 The detection performance of the proposed ZEWMAD chart for an in-control process with identity covariance matrix 984.3 The detection performance of the proposed ZEWMAD chart for an in-control process with non-identity covariance matrix 1074.4 Performance comparison of the proposed one-sided ZEWMAD chart and existing control charts 1104.4.1 Performance comparison among the ZEWMAD, SMaxNorm, and MaxNorm charts 1104.4.2 Performance comparison between the ZEWMAD and MSRE charts 1144.5 A numerical example of using the ZEWMAD chart 118Chapter 5. Using the Variable Dimension ZEWMAD Chart to Monitor the Process Dispersion for A Process with An Unknown Distribution 1225.1 Design the variable dimension ZEWMAD chart 1225.1.1 The one-sided VD ZEWMAD chart to monitor the upward process dispersion 1245.1.2 The one-sided VD ZEWMAD chart to monitor the downward process dispersion 1265.2 The detection performance of the proposed VD ZEWMAD chart and performance comparison of the VD and FD ZEWMAD charts for an in-control process with identity covariance matrix 1315.3 The detection performance of the proposed VD ZEWMAD chart for an in-control process with non-identity covariance matrix 1445.4 The cost of sampling and detection performance of the VD ZEWMAD chart 1495.5 A numerical example of using the VD ZEWMAD chart 152Chapter 6. Summary and Future Study 160References 161 zh_TW dc.format.extent 8669065 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0108354010 en_US dc.subject (關鍵詞) 多元統計過程控制 zh_TW dc.subject (關鍵詞) 共變異數矩陣 zh_TW dc.subject (關鍵詞) 資料深度 zh_TW dc.subject (關鍵詞) 無分佈假設 zh_TW dc.subject (關鍵詞) 指數加權移動平均 zh_TW dc.subject (關鍵詞) 變動維度 zh_TW dc.subject (關鍵詞) Multivariate statistical process control en_US dc.subject (關鍵詞) Covariance matrix en_US dc.subject (關鍵詞) Data depth en_US dc.subject (關鍵詞) Distribution-free en_US dc.subject (關鍵詞) Exponentially weighted moving average en_US dc.subject (關鍵詞) Variable dimension en_US dc.title (題名) 多元製程之共變數矩陣追蹤研究 zh_TW dc.title (題名) The study of Multivariate Process Dispersion Control Chart en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Alt, F. B. (1985). Multivariate quality control. The Encyclopedia of Statistical Sciences, 110-122.[2] Aparisi, F., Epprecht, E. K., & Ruiz, O. (2012). T2 control chart with variable dimension. Journal of Quality Technology, 44(4), 375-393.[3] Bell, R. C., Jones-Farmer, L. A., & Billor, N. (2014). A distribution-free multivariate phase I location control chart for subgrouped data from elliptical distributions. Technometrics, 56(4), 528-538.[4] Chaven, A. R., & Shirke, D. T. (2020). Nonparametric two sample tests for scale parameters of multivariate distributions. Communications for Statistical Applications and Methods, 27(4), 397-412.[5] Chen, N., Zi, X., & Zou, C. (2016). A distribution-free multivariate control chart. Technometrics, 58(4), 448-459.[6] Crosier, R. B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3), 291-303.[7] Epprecht, E. K., Aparisi, F., & Ruiz, O. (2018). Optimum variable-dimension EWMA chart for multivariate statistical process control. Quality Engineering, 30(2), 268-282.[8] Epprecht, E. K., Aparisi, F., Ruiz, O., & Veiga, A. (2013). Reducing sampling costs in multivariate SPC with a double-dimension T2 control chart. International Journal of Production Economics, 144(1), 90-104.[9] Farokhnia, M., & Niaki, S. T. A. (2019). Principal component analysis-based control charts using support vector machines for multivariate non-normal distributions. Communications in Statistics-Simulation and Computation, 1-24.[10] Hawkins, D. M. (1991). Multivariate quality control based on regression-adjusted variables. Technometrics, 33(1), 61-75.[11] Hawkins, D. M., & Maboudou-Tchao, E. M. (2008). Multivariate exponentially weighted moving covariance matrix. Technometrics, 50, 155-166.[12] Hotelling, H. A. R. O. L. D. (1947). Multivariate quality control. Techniques of statistical analysis. McGraw-Hill, New York.[13] Huwang, L., Lin, L. W., & Yu, C. T. (2019). A spatial rank-based multivariate EWMA chart for monitoring process shape matrices. Quality and Reliability Engineering International, 1-19.[14] Huwang, L., Lin, P. C., Chang, C. H., Lin, L. W., & Tee, Y. S. (2017). An EWMA chart for monitoring the covariance matrix of a multivariate process based on dissimilarity index. Quality and Reliability Engineering International, 33, 2089-2104.[15] Huwang, L., Yeh, A. B., & Wu, C. V. (2007). Monitoring multivariate process variability for individual observations. Journal of Quality Technology, 39, 258-278.[16] Kim, J., Abdella, G. M., Kim, S., Al-Khalifa, K. N., & Hamouda, A. M. (2019). Control charts for variability monitoring in high-dimensional processes. Computers & Industrial Engineering, 130, 309-316.[17] Li, B., Wang, K., & Yeh, A. B. (2013). Monitoring the covariance matrix via penalized likelihood estimation. IIE Transactions, 45, 132-146.[18] Li, Z., Zou, C., Wang, Z. and Huwang, L. (2013). A multivariate sign chart for monitoring process shape parameters. Journal of Quality Technology, 45(2), 149-165.[19] Liang, W., Xiang, D., Pu, X., Li, Y., & Jin, L. (2019). A robust multivariate sign control chart for detecting shifts in covariance matrix under the elliptical directions distributions, Quality Technology & Quantitative Management, 16(1), 113-127.[20] Liu, R. Y. (1995). Control charts for multivariate processes. Journal of the American Statistical Association, 90(432), 1380-1387.[21] Lowry, C. A., & Montgomery, D. C. (1995). A review of multivariate control charts. HE transactions, 27(6), 800-810.[22] Luca Scrucca. (2021). Package ‘GA’. Retrieved June 9, 2021, from https://cran.r-project.org/web/packages/GA/GA.pdf[23] MacGregor, J. F., & Kourti, T. (1995). Statistical process control of multivariate processes. Control Engineering Practice, 3(3), 403-414.[24] McCann M., & Johnston A. (2008). SECOM Data Set Center for Machine Learning and Intelligent Systems. Irvine, CA: University of California. Retrieved June 9, 2021, from https://archive.ics.uci.edu/ml/datasets.php[25] Melo, M. S., Ho, L. L., & Medeiros, P. G. (2017). M a x D: an attribute control chart to monitor a bivariate process mean. The International Journal of advanced Manufacturing Technology. 90, 489-498.[26] Montgomery, D. C., & Wadsworth, H. M. (1972, May). Some techniques for multivariate quality control applications. In ASQC Technical Conference Transactions, Washington, D. C (pp. 427-435).[27] Qiu, P. (2008). Distribution-free multivariate process control based on log-linear modeling. IIE Transactions, 40(7), 664-677.[28] Reynold, M. R., Jr., Amin, R. W., Arnold, J. C., & Nachlas, J. A. (1988). X ̅ charts with variable sampling intervals. Technometrics, 30(2), 181-192.[29] Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 1(3), 239-250.[30] Wang, S. & Reynolds, M. R. (2013). A GLR Control Chart for Monitoring the Mean Vector of a Multivariate Normal Process. Journal of Quality Technology, 45(1), 18-33.[31] Shen, X., Tsung, F., & Zou, C. (2014). A new multivariate EWMA scheme for monitoring covariance matrices. International Journal of Production Research, 52, 2834-2850.[32] Shewhart, W. A. (1924). Some applications of statistical methods to the analysis of physical and engineering data. Bell System Technical Journal, 3(1), 43-87.[33] Yang, S. F., Lin, Y. C., & Yeh, A. B. (2021). A phase Ⅱ depth-based variable dimension EWMA control chart for monitoring process mean. Quality and Reliability Engineering International, 1-15.[34] Yeh, A. B., Huwang, L., & Wu, Y. F. (2004). A likelihood-ratio-based EWMA control chart for monitoring variability of multivariate normal processes. IIE Transactions, 36(9), 865-879.[35] Yeh, A. B., Li, B., & Wang, K. (2012). Monitoring multivariate process variability with individual observations via penalized likelihood estimation. International Journal of Production Research, 50, 6624-6638.[36] Yen, C. L., & Shiau, J. J. H. (2010). A multivariate control chart for detecting increases in process dispersion. Statistica Sinica, 20, 1683-1707.[37] Zou, C., & Tsung, F. (2011). A multivariate sign EWMA control chart. Technometrics, 53(1), 84-97. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202100926 en_US
