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題名 以主成分分析方法建立多元製程位置管制圖之研究
Design of Multivariate Location Control Chart Using Principal Component Analysis Method作者 林健宏
Lin, Chian-Hung貢獻者 楊素芬
林健宏
Lin, Chian-Hung關鍵詞 多維度管制圖
主成分分析
變動樣本
平均連串長度
multivariate control chart
principal component analysis
variable sample size
average run length日期 2019 上傳時間 7-Aug-2019 16:00:47 (UTC+8) 摘要 在監測產品或服務品質的方法中，管制圖是常使用的方法。傳統管制圖受限於常態分佈假設，因此許多學者投入研究非常態或是無母數管制圖的研究。另外，為了改善多變量製程之產品或服務品質，許多學者投入研究多變量管制圖。本文提出一個監控製程的管制圖。在母體分佈未知或非常態情況下，使用主成分分析方法結合符號平均值管制圖方法建立多元製程位置管制圖，EWMA-PM 管制圖，以監測未知多維度母體變數平均值向量。本文以平均連串長度 (ARL) 為指標評估此管制圖的偵測能力。本文以數值分析方法比較EWMA-PM 管制圖與其它文獻管制圖的偵測能力，結果顯示EWMA-PM 管制圖在樣本數大於5時、製程平均發生小幅度偏移時有較好的偵測效果。接著以半導體製程資料演示EWMA-PM管制圖的建立流程。此外，本文進一步建立變動樣本的標準多元製程位置管制圖，VSS EWMA-SM 管制圖，藉此提升偵測能力及降低抽樣成本。本文以抽樣的樣本期望值 (EN)、平均連串長度 (ARL) 和管制圖偵測出異常訊息所需平均抽樣的觀測值總數 (ANOS) 評估VSS EWMA-SM管制圖的偵測能力。
The control chart is a common tool to monitor industrial product process. Traditional Shewhart control charts are limited by the assumption of normal distribution. Furthermore, multivariate data are more common. For monitoring non-parametric multivariate quality variables, we propose a new phase II control chart. We propose multivariate exponentially weighted moving average (EWMA) location control chart, EWMA-PM control chart, that combines the methods of the principal component analysis method and sign control chart to efficiently detect an out-of-control process mean vector.We use the average run length (ARL) to measure the detection performance of the EWMA-PM chart. Comparing the EWMA-PM chart with other existing control charts, the EWMA-PM chart shows the superior detection performance for mean vectors in a small shift when sample size is larger than 5. Then, we use semiconductor process data to illustrate the application of the EWMA-PM chart.We also propose the EWMA-PM control chart with variables sample size (VSS) scheme, VSS EWMA-SM control chart, to monitor process mean vector, for enhancing the process detection ability and reduce the sampling cost. We use average expected number of samples (EN), ARL and average number of observations till the first signal (ANOS) to measure the detection performance of the VSS EWMA-SM chart.參考文獻 [1] Abid, M., Nazir, H. Z., Riaz, M., & Lin, Z. (2017). An Efficient Nonparametric EWMA Wilcoxon Signed‐Rank Chart for Monitoring Location. Quality and Reliability Engineering International, 33(3), 669-685.[2] Amin, R. W., Reynolds Jr, M. R., & Saad, B. (1995). Nonparametric quality control charts based on the sign statistic. Communications in Statistics-Theory and Methods, 24(6), 1597-1623.[3] Amiri, A., Nedaie, A., & Alikhani, M. (2014). A new adaptive variable sample size approach in EWMA control chart. Communications in Statistics-Simulation and Computation, 43(4), 804-812.[4] Bakir, S. T. (2004). A distribution-free Shewhart quality control chart based on signed-ranks. Quality Engineering, 16(4), 613-623.[5] Bakir, S. T. (2006). Distribution-free quality control charts based on signed-rank-like statistics. Communications in Statistics-Theory and Methods, 35(4), 743-757.[6] Bakir, S. T., & Reynolds, M. R. (1979). A nonparametric procedure for process control based on within-group ranking. Technometrics, 21(2), 175-183.[7] Castagliola, P. (2005). A new S2‐EWMA control chart for monitoring the process variance. Quality and Reliability Engineering International, 21(8), 781-794.[8] Castagliola, P., Celano, G., Fichera, S., & Giuffrida, F. (2006). A variable sampling interval S2-EWMA control chart for monitoring the process variance. International Journal of Technology Management, 37(1-2), 125-146.[9] Chen, N., Zi, X., & Zou, C. (2016). A distribution-free multivariate control chart. Technometrics, 58(4), 448-459.[10] Costa, A. F. (1994). X charts with variable sample size. Journal of quality technology, 26(3), 155-163.[11] Costa, A. F. (1997). X chart with variable sample size and sampling intervals. Journal of quality technology, 29(2), 197-204.[12] Costa, A. F. (1999). X charts with variable parameters. Journal of quality technology, 31(4), 408-416.[13] Deng, H., Runger, G., & Tuv, E. (2012). System monitoring with real-time contrasts. Journal of quality technology, 44(1), 9-27.[14] Graham, M. A., Chakraborti, S., & Human, S. W. (2011). A nonparametric EWMA sign chart for location based on individual measurements. Quality Engineering, 23(3), 227-241.[15] Graham, M. A., Mukherjee, A., & Chakraborti, S. (2012). Distribution-free exponentially weighted moving average control charts for monitoring unknown location. Computational Statistics & Data Analysis, 56(8), 2539-2561.[16] Guo, B., & Wang, B. X. (2016). The variable sampling interval S 2 chart with known or unknown in-control variance. International Journal of Production Research, 54(11), 3365-3379.[17] Hawkins, D. M., & Maboudou-Tchao, E. M. (2007). Self-starting multivariate exponentially weighted moving average control charting. Technometrics, 49(2), 199-209.[18] Henze, N., & Zirkler, B. (1990). A class of invariant consistent tests for multivariate normality. Communications in Statistics-Theory and Methods, 19(10), 3595-3617.[19] Holmes, D. S., & Mergen, A. E. (1993). Improving the performance of the T2 control chart. Quality Engineering, 5(4), 619-625.[20] Hotelling, H. (1947). Multivariate quality control. Techniques of statistical analysis.[21] Jackson, J. E. (1959). Quality control methods for several related variables. Technometrics, 1(4), 359-377.[22] Jackson, J. E., & Mudholkar, G. S. (1979). Control procedures for residuals associated with principal component analysis. Technometrics, 21(3), 341-349.[23] Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and psychological measurement, 20(1), 141-151.[24] Kazemzadeh, R. B., Karbasian, M., & Babakhani, M. A. (2013). An EWMA t chart with variable sampling intervals for monitoring the process mean. The International Journal of Advanced Manufacturing Technology, 66(1-4), 125-139.[25] Khan, N., Aslam, M., Aldosari, M. S., & Jun, C.-H. (2018). A Multivariate Control Chart for Monitoring Several Exponential Quality Characteristics Using EWMA. IEEE Access, 6, 70349-70358.[26] Lee, P.-H. (2011). Adaptive R charts with variable parameters. Computational Statistics & Data Analysis, 55(5), 2003-2010.[27] Li, Z., Zou, C., Wang, Z., & Huwang, L. (2013). A multivariate sign chart for monitoring process shape parameters. Journal of quality technology, 45(2), 149-165.[28] Liu, R. Y. (1995). Control charts for multivariate processes. Journal of the American Statistical Association, 90(432), 1380-1387.[29] Lowry, C. A., & Montgomery, D. C. (1995). A review of multivariate control charts. IIE transactions, 27(6), 800-810.[30] Lowry, C. A., Woodall, W. H., Champ, C. W., & Rigdon, S. E. (1992). A multivariate exponentially weighted moving average control chart. Technometrics, 34(1), 46-53.[31] Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519-530.[32] Muhammad, A. N. B., Yeong, W. C., Chong, Z. L., Lim, S. L., & Khoo, M. B. C. (2018). Monitoring the coefficient of variation using a variable sample size EWMA chart. Computers & Industrial Engineering, 126, 378-398.[33] Nijhuis, A., De Jong, S., & Vandeginste, B. (1997). Multivariate statistical process control in chromatography. Chemometrics and Intelligent Laboratory Systems, 38(1), 51-62.[34] Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41(1/2), 100-115.[35] Pearson, K. (1901). Principal components analysis. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 6(2), 559.[36] Phaladiganon, P., Kim, S. B., Chen, V. C., & Jiang, W. (2013). Principal component analysis-based control charts for multivariate nonnormal distributions. Expert systems with applications, 40(8), 3044-3054.[37] Prabhu, S., Runger, G., & Keats, J. (1993). X chart with adaptive sample sizes. The International Journal of Production Research, 31(12), 2895-2909.[38] Ranger, G. C., & Alt, F. B. (1996). Choosing principal components for multivariate statistical process control. Communications in Statistics-Theory and Methods, 25(5), 909-922.[39] Reynolds, M. R., Amin, R. W., Arnold, J. C., & Nachlas, J. A. (1988). Charts with variable sampling intervals. Technometrics, 30(2), 181-192.[40] Runger, G. C., Alt, F. B., & Montgomery, D. C. (1996). Contributors to a multivariate statistical process control chart signal. Communications in Statistics--Theory and Methods, 25(10), 2203-2213.[41] Saha, S., Khoo, M. B., Lee, M. H., & Haq, A. (2018). A variable sample size and sampling interval control chart for monitoring the process mean using auxiliary information. Quality Technology & Quantitative Management, 1-18.[42] 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.[44] Wang, H., Huwang, L., & Yu, J. H. (2015). Multivariate control charts based on the James–Stein estimator. European Journal of Operational Research, 246(1), 119-127.[45] White, R. W. (1959). Motivation reconsidered: The concept of competence. Psychological review, 66(5), 297.[46] Wu, T.-L. (2018). Distribution-free runs-based control charts. arXiv preprint arXiv:1801.06532.[47] Yang, S.-F. (2010). Variable control scheme in the cascade processes. Expert systems with applications, 37(1), 787-798.[48] Yang, S.-F. (2015). An improved distribution-free EWMA mean chart. Communications in Statistics-Simulation and Computation, 45(4), 1410-1427.[49] Yang, S.-F., & Arnold, B. C. (2014). A simple approach for monitoring business service time variation. The Scientific World Journal, 2014.[50] Yang, S.-F., & Chen, W.-Y. (2011). Monitoring and diagnosing dependent process steps using VSI control charts. Journal of Statistical Planning and Inference, 141(5), 1808-1816.[51] Yang, S.-F., Lin, J.-S., & Cheng, S. W. (2011). A new nonparametric EWMA sign control chart. Expert systems with applications, 38(5), 6239-6243.[52] Yang, S. F., Cheng, T. C., Hung, Y. C., & W. Cheng, S. (2012). A new chart for monitoring service process mean. Quality and Reliability Engineering International, 28(4), 377-386.[53] Yang, S. F., & Wu, S. H. (2017). A double sampling scheme for process variability monitoring. Quality and Reliability Engineering International, 33(8), 2193-2204.[54] Yeong, W. C., Lim, S. L., Khoo, M. B. C., & Castagliola, P. (2018). Monitoring the coefficient of variation using a variable parameters chart. Quality Engineering, 30(2), 212-235.[55] Yue, J., & Liu, L. (2017). Multivariate nonparametric control chart with variable sampling interval. Applied Mathematical Modelling, 52, 603-612.[56] Zhang, L., Chen, G., & Castagliola, P. (2009). On t and EWMA t charts for monitoring changes in the process mean. Quality and Reliability Engineering International, 25(8), 933-945.[57] Zhang, L., & Song, X. (2014). EWMA median control chart with variable sampling size. Information Technology Journal, 13(14), 2369-2373.[58] Zou, C., & Tsung, F. (2011). A multivariate sign EWMA control chart. Technometrics, 53(1), 84-97.[59] Zou, C., Wang, Z., & Tsung, F. (2012). A spatial rank‐based multivariate EWMA control chart. Naval Research Logistics (NRL), 59(2), 91-110. 描述 碩士
國立政治大學
統計學系
106354003資料來源 http://thesis.lib.nccu.edu.tw/record/#G0106354003 資料類型 thesis dc.contributor.advisor 楊素芬 zh_TW dc.contributor.author (Authors) 林健宏 zh_TW dc.contributor.author (Authors) Lin, Chian-Hung en_US dc.creator (作者) 林健宏 zh_TW dc.creator (作者) Lin, Chian-Hung en_US dc.date (日期) 2019 en_US dc.date.accessioned 7-Aug-2019 16:00:47 (UTC+8) - dc.date.available 7-Aug-2019 16:00:47 (UTC+8) - dc.date.issued (上傳時間) 7-Aug-2019 16:00:47 (UTC+8) - dc.identifier (Other Identifiers) G0106354003 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/124680 - 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) 106354003 zh_TW dc.description.abstract (摘要) 在監測產品或服務品質的方法中，管制圖是常使用的方法。傳統管制圖受限於常態分佈假設，因此許多學者投入研究非常態或是無母數管制圖的研究。另外，為了改善多變量製程之產品或服務品質，許多學者投入研究多變量管制圖。本文提出一個監控製程的管制圖。在母體分佈未知或非常態情況下，使用主成分分析方法結合符號平均值管制圖方法建立多元製程位置管制圖，EWMA-PM 管制圖，以監測未知多維度母體變數平均值向量。本文以平均連串長度 (ARL) 為指標評估此管制圖的偵測能力。本文以數值分析方法比較EWMA-PM 管制圖與其它文獻管制圖的偵測能力，結果顯示EWMA-PM 管制圖在樣本數大於5時、製程平均發生小幅度偏移時有較好的偵測效果。接著以半導體製程資料演示EWMA-PM管制圖的建立流程。此外，本文進一步建立變動樣本的標準多元製程位置管制圖，VSS EWMA-SM 管制圖，藉此提升偵測能力及降低抽樣成本。本文以抽樣的樣本期望值 (EN)、平均連串長度 (ARL) 和管制圖偵測出異常訊息所需平均抽樣的觀測值總數 (ANOS) 評估VSS EWMA-SM管制圖的偵測能力。 zh_TW dc.description.abstract (摘要) The control chart is a common tool to monitor industrial product process. Traditional Shewhart control charts are limited by the assumption of normal distribution. Furthermore, multivariate data are more common. For monitoring non-parametric multivariate quality variables, we propose a new phase II control chart. We propose multivariate exponentially weighted moving average (EWMA) location control chart, EWMA-PM control chart, that combines the methods of the principal component analysis method and sign control chart to efficiently detect an out-of-control process mean vector.We use the average run length (ARL) to measure the detection performance of the EWMA-PM chart. Comparing the EWMA-PM chart with other existing control charts, the EWMA-PM chart shows the superior detection performance for mean vectors in a small shift when sample size is larger than 5. Then, we use semiconductor process data to illustrate the application of the EWMA-PM chart.We also propose the EWMA-PM control chart with variables sample size (VSS) scheme, VSS EWMA-SM control chart, to monitor process mean vector, for enhancing the process detection ability and reduce the sampling cost. We use average expected number of samples (EN), ARL and average number of observations till the first signal (ANOS) to measure the detection performance of the VSS EWMA-SM chart. en_US dc.description.tableofcontents ContentChapter 1. Introduction 11.1 Literature review 11.2 Research motivation 61.3 Research method 7Chapter 2. The EWMA-PM Control Chart for Monitoring Process Mean Vector Under a Non-identity Correlation Coefficient Matrix 92.1 The construction of the two EWMA-PM charts 102.2 Determination of the coefficients for the proposed EWMA-PM chart 152.3 Detection performance of the proposed EWMA-PM chart 242.4 Detection performance comparison between the EWMA-PM chart and the existing control charts 422.5 An illustrative example 68Chapter 3. The Optimum VSS EWMA-SM Control Chart for Monitoring Process Mean Vector Under a Non-identity Correlation Matrix 813.1 The construction of the optimum VSS EWMA-SM chart 813.2 Determination of the control limits of the optimum VSS EWMA-SM chart 853.3 An illustrative example 121Chapter 4. Conclusions 128Reference 129 zh_TW dc.format.extent 2379227 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0106354003 en_US dc.subject (關鍵詞) 多維度管制圖 zh_TW dc.subject (關鍵詞) 主成分分析 zh_TW dc.subject (關鍵詞) 變動樣本 zh_TW dc.subject (關鍵詞) 平均連串長度 zh_TW dc.subject (關鍵詞) multivariate control chart en_US dc.subject (關鍵詞) principal component analysis en_US dc.subject (關鍵詞) variable sample size en_US dc.subject (關鍵詞) average run length en_US dc.title (題名) 以主成分分析方法建立多元製程位置管制圖之研究 zh_TW dc.title (題名) Design of Multivariate Location Control Chart Using Principal Component Analysis Method en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Abid, M., Nazir, H. Z., Riaz, M., & Lin, Z. (2017). An Efficient Nonparametric EWMA Wilcoxon Signed‐Rank Chart for Monitoring Location. Quality and Reliability Engineering International, 33(3), 669-685.[2] Amin, R. W., Reynolds Jr, M. R., & Saad, B. (1995). Nonparametric quality control charts based on the sign statistic. Communications in Statistics-Theory and Methods, 24(6), 1597-1623.[3] Amiri, A., Nedaie, A., & Alikhani, M. (2014). A new adaptive variable sample size approach in EWMA control chart. Communications in Statistics-Simulation and Computation, 43(4), 804-812.[4] Bakir, S. T. (2004). A distribution-free Shewhart quality control chart based on signed-ranks. Quality Engineering, 16(4), 613-623.[5] Bakir, S. T. (2006). Distribution-free quality control charts based on signed-rank-like statistics. Communications in Statistics-Theory and Methods, 35(4), 743-757.[6] Bakir, S. T., & Reynolds, M. R. (1979). A nonparametric procedure for process control based on within-group ranking. Technometrics, 21(2), 175-183.[7] Castagliola, P. (2005). A new S2‐EWMA control chart for monitoring the process variance. Quality and Reliability Engineering International, 21(8), 781-794.[8] Castagliola, P., Celano, G., Fichera, S., & Giuffrida, F. (2006). A variable sampling interval S2-EWMA control chart for monitoring the process variance. International Journal of Technology Management, 37(1-2), 125-146.[9] Chen, N., Zi, X., & Zou, C. (2016). A distribution-free multivariate control chart. Technometrics, 58(4), 448-459.[10] Costa, A. F. (1994). X charts with variable sample size. Journal of quality technology, 26(3), 155-163.[11] Costa, A. F. (1997). X chart with variable sample size and sampling intervals. Journal of quality technology, 29(2), 197-204.[12] Costa, A. F. (1999). X charts with variable parameters. Journal of quality technology, 31(4), 408-416.[13] Deng, H., Runger, G., & Tuv, E. (2012). System monitoring with real-time contrasts. Journal of quality technology, 44(1), 9-27.[14] Graham, M. A., Chakraborti, S., & Human, S. W. (2011). A nonparametric EWMA sign chart for location based on individual measurements. Quality Engineering, 23(3), 227-241.[15] Graham, M. A., Mukherjee, A., & Chakraborti, S. (2012). Distribution-free exponentially weighted moving average control charts for monitoring unknown location. Computational Statistics & Data Analysis, 56(8), 2539-2561.[16] Guo, B., & Wang, B. X. (2016). The variable sampling interval S 2 chart with known or unknown in-control variance. International Journal of Production Research, 54(11), 3365-3379.[17] Hawkins, D. M., & Maboudou-Tchao, E. M. (2007). Self-starting multivariate exponentially weighted moving average control charting. Technometrics, 49(2), 199-209.[18] Henze, N., & Zirkler, B. (1990). A class of invariant consistent tests for multivariate normality. Communications in Statistics-Theory and Methods, 19(10), 3595-3617.[19] Holmes, D. S., & Mergen, A. E. (1993). Improving the performance of the T2 control chart. Quality Engineering, 5(4), 619-625.[20] Hotelling, H. (1947). Multivariate quality control. Techniques of statistical analysis.[21] Jackson, J. E. (1959). Quality control methods for several related variables. Technometrics, 1(4), 359-377.[22] Jackson, J. E., & Mudholkar, G. S. (1979). Control procedures for residuals associated with principal component analysis. Technometrics, 21(3), 341-349.[23] Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and psychological measurement, 20(1), 141-151.[24] Kazemzadeh, R. B., Karbasian, M., & Babakhani, M. A. (2013). An EWMA t chart with variable sampling intervals for monitoring the process mean. The International Journal of Advanced Manufacturing Technology, 66(1-4), 125-139.[25] Khan, N., Aslam, M., Aldosari, M. S., & Jun, C.-H. (2018). A Multivariate Control Chart for Monitoring Several Exponential Quality Characteristics Using EWMA. IEEE Access, 6, 70349-70358.[26] Lee, P.-H. (2011). Adaptive R charts with variable parameters. Computational Statistics & Data Analysis, 55(5), 2003-2010.[27] Li, Z., Zou, C., Wang, Z., & Huwang, L. (2013). A multivariate sign chart for monitoring process shape parameters. Journal of quality technology, 45(2), 149-165.[28] Liu, R. Y. (1995). Control charts for multivariate processes. Journal of the American Statistical Association, 90(432), 1380-1387.[29] Lowry, C. A., & Montgomery, D. C. (1995). A review of multivariate control charts. IIE transactions, 27(6), 800-810.[30] Lowry, C. A., Woodall, W. H., Champ, C. W., & Rigdon, S. E. (1992). A multivariate exponentially weighted moving average control chart. Technometrics, 34(1), 46-53.[31] Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519-530.[32] Muhammad, A. N. B., Yeong, W. C., Chong, Z. L., Lim, S. L., & Khoo, M. B. C. (2018). Monitoring the coefficient of variation using a variable sample size EWMA chart. Computers & Industrial Engineering, 126, 378-398.[33] Nijhuis, A., De Jong, S., & Vandeginste, B. (1997). Multivariate statistical process control in chromatography. Chemometrics and Intelligent Laboratory Systems, 38(1), 51-62.[34] Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41(1/2), 100-115.[35] Pearson, K. (1901). Principal components analysis. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 6(2), 559.[36] Phaladiganon, P., Kim, S. B., Chen, V. C., & Jiang, W. (2013). Principal component analysis-based control charts for multivariate nonnormal distributions. Expert systems with applications, 40(8), 3044-3054.[37] Prabhu, S., Runger, G., & Keats, J. (1993). X chart with adaptive sample sizes. The International Journal of Production Research, 31(12), 2895-2909.[38] Ranger, G. C., & Alt, F. B. (1996). Choosing principal components for multivariate statistical process control. Communications in Statistics-Theory and Methods, 25(5), 909-922.[39] Reynolds, M. R., Amin, R. W., Arnold, J. C., & Nachlas, J. A. (1988). Charts with variable sampling intervals. Technometrics, 30(2), 181-192.[40] Runger, G. C., Alt, F. B., & Montgomery, D. C. (1996). Contributors to a multivariate statistical process control chart signal. Communications in Statistics--Theory and Methods, 25(10), 2203-2213.[41] Saha, S., Khoo, M. B., Lee, M. H., & Haq, A. (2018). A variable sample size and sampling interval control chart for monitoring the process mean using auxiliary information. Quality Technology & Quantitative Management, 1-18.[42] 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.[44] Wang, H., Huwang, L., & Yu, J. H. (2015). Multivariate control charts based on the James–Stein estimator. European Journal of Operational Research, 246(1), 119-127.[45] White, R. W. (1959). Motivation reconsidered: The concept of competence. Psychological review, 66(5), 297.[46] Wu, T.-L. (2018). Distribution-free runs-based control charts. arXiv preprint arXiv:1801.06532.[47] Yang, S.-F. (2010). Variable control scheme in the cascade processes. Expert systems with applications, 37(1), 787-798.[48] Yang, S.-F. (2015). An improved distribution-free EWMA mean chart. Communications in Statistics-Simulation and Computation, 45(4), 1410-1427.[49] Yang, S.-F., & Arnold, B. C. (2014). A simple approach for monitoring business service time variation. The Scientific World Journal, 2014.[50] Yang, S.-F., & Chen, W.-Y. (2011). Monitoring and diagnosing dependent process steps using VSI control charts. Journal of Statistical Planning and Inference, 141(5), 1808-1816.[51] Yang, S.-F., Lin, J.-S., & Cheng, S. W. (2011). A new nonparametric EWMA sign control chart. Expert systems with applications, 38(5), 6239-6243.[52] Yang, S. F., Cheng, T. C., Hung, Y. C., & W. Cheng, S. (2012). A new chart for monitoring service process mean. Quality and Reliability Engineering International, 28(4), 377-386.[53] Yang, S. F., & Wu, S. H. (2017). A double sampling scheme for process variability monitoring. Quality and Reliability Engineering International, 33(8), 2193-2204.[54] Yeong, W. C., Lim, S. L., Khoo, M. B. C., & Castagliola, P. (2018). Monitoring the coefficient of variation using a variable parameters chart. Quality Engineering, 30(2), 212-235.[55] Yue, J., & Liu, L. (2017). Multivariate nonparametric control chart with variable sampling interval. Applied Mathematical Modelling, 52, 603-612.[56] Zhang, L., Chen, G., & Castagliola, P. (2009). On t and EWMA t charts for monitoring changes in the process mean. Quality and Reliability Engineering International, 25(8), 933-945.[57] Zhang, L., & Song, X. (2014). EWMA median control chart with variable sampling size. Information Technology Journal, 13(14), 2369-2373.[58] Zou, C., & Tsung, F. (2011). A multivariate sign EWMA control chart. Technometrics, 53(1), 84-97.[59] Zou, C., Wang, Z., & Tsung, F. (2012). A spatial rank‐based multivariate EWMA control chart. Naval Research Logistics (NRL), 59(2), 91-110. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU201900411 en_US
