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題名 無母數多元製程位置管制圖之研究
The Study of Multivariate Process Location Control Chart作者 林奕志
Lin, Yi-Chih貢獻者 楊素芬
Yang, Su-Fen
林奕志
Lin, Yi-Chih關鍵詞 資料深度
符號管制圖
指數加權平均
變動抽樣時間
變動維度
偵測到異常所需的平均抽樣次數
偵測出異常所需的平均時間
Data depth
Sign chart
Exponentially weighted moving average
Variable sampling interval
Variable dimension
Average run length
Average time to signal日期 2019 上傳時間 7-Aug-2019 16:01:37 (UTC+8) 摘要 在工業產品製程中，管制圖為監控產品品質重要的工具。大多數的產品資料屬於多維度且不一定服從常態分配，因此無分配假設的多維度管制圖之研究更是相當重要。本文提出結合資料深度 (data depth) 與符號管制圖 (sign chart) 。建立一個新的指數加權移動平均 (EWMA) 的追蹤統計量來監控產品製程平均數向量是否有失控，並利用平均連串長度 (ARL) 來衡量所提出的新管制圖的表現。此外，我們加入變動抽樣區間時間 (VSI) 的監控技巧與考慮變動維度 (VD)的想法以降低偵測製程失控所需的時間及成本。我們利用管制圖偵測出異常訊息所需的平均時間 (ATS) 來衡量所提出之VSI管制圖。接下來與文獻上存在的管制圖做偵測力表現比較。經由許多不同平均數偏移情況的數值比較分析後，本文所提出的管制圖在製程平均數偏移幅度中等及大時，比其他管制圖有更好的偵測效果。因此，建議可以使用本文提出的新管制圖追蹤製程平均數向量。最後以礫石資料及半導體製程資料來示範本文所提出的管制圖之應用。
In industrial product process, control chart is an important tool for monitoring the process quality. Since many data are multivariate and do not follow normal distribution, this makes traditional Shewhart control charts cannot be applied. So the study of non-normal multivariate control chart is very important.This paper combines the methods of data depth and constructing sign chart to design a new exponentially weighted moving average (EWMA) chart for monitoring the multivariate process location. Performance measurement of the proposed control chart is the average run length (ARL). In addition, techniques for variable sampling interval (VSI) and variable dimension (VD) are added to reduce the detection time of an out-of-control process and sampling cost of detecting the out-of-control process. Performance measurement of the proposed VSI control chart is using the average time to signal (ATS) under an out-of-control process.We would compare the detection performance of the proposed control charts with existing control charts exist in the literatures. The proposed charts show superior detection performance compared the existing control charts when the mean shifts is medium and large under the out-of-control process. Therefore, it is recommended that the proposed control charts in this paper might be applied to detect the shifts in process location. Finally, we would demonstrate the proposed control charts via using gravel data and semiconductor process data.參考文獻 [1] Altukife, F. S. (2003). A new nonparametric control chart based on the observations exceeding the grand median. Pakistan journal of statistics-all series, 19(3), pp. 343-352.[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), pp. 1597-1623.[3] Amin, R. W., & Widmaier, O. (1999). Sign control charts with variable sampling intervals. Communications in Statistics-Theory and Methods, 28(8), pp. 1961-1985.[4] Aparisi, F. (1996). Hotelling`s T2 control chart with adaptive sample sizes. International Journal of Production Research, 34(10), pp. 2853-2862.[5] Aparisi F, Jabaloyes J, Carrion A. Statistical properties of the |S| multivariate control chart. Communications in Statistics—Theory and Methods 1999; 28:2671–2686.[6] Aparisi F, Jabaloyes J, Carrion A. Generalized variance chart design with adaptive sample sizes. The bivariate case.Communications in Statistics—Simulation and Computation 2001; 30:931–948.[7] Bakir, S. T. (2004). A distribution-free Shewhart quality control chart based on signed-ranks. Quality Engineering, 16(4), pp. 613-623.[8] Bakir, S. T. (2006). Distribution-free quality control charts based on signed-rank-like statistics. Communications in Statistics-Theory and Methods, 35(4), pp. 743-757.[9] 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), pp. 528-538.[10] Capizzi, G., & Masarotto, G. (2017). Phase I distribution-free analysis of multivariate data. Technometrics, 59(4), pp. 484-495.[11] Chakraborti, S., Van der Laan, P., & Bakir, S. T. (2001). Nonparametric control charts: an overview and some results. Journal of Quality Technology, 33(3), pp. 304-315.[12] Chen, N., Zi, X., & Zou, C. (2016). A distribution-free multivariate control chart. Technometrics, 58(4), pp. 448-459.[13] Chowdhury, S., Mukherjee, A., & Chakraborti, S. (2014). A new distribution‐free control chart for joint monitoring of unknown location and scale parameters of continuous distributions. Quality and Reliability Engineering International, 30(2), pp. 191-204.[14] Costa, A. F. (1997). X chart with variable sample size and sampling intervals. Journal of Quality Technology, 29(2), pp. 197-204.[15] Crosier, R. B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3), 291-303.[16] Epprecht, E. K., Aparisi, F., & Ruiz, O. (2018). Optimum variable-dimension EWMA chart for multivariate statistical process control. Quality Engineering, 30(2), pp. 268-282.[17] 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, pp. 1-24.[18] Ferrell, E. B. (1953). Control charts using midranges and medians. Industrial Quality Control, 9(5), pp. 30-34.[19] Grasso, M., Colosimo, B. M., Semeraro, Q., & Pacella, M. (2015). A comparison study of distribution‐free multivariate SPC methods for multimode data. Quality and Reliability Engineering International, 31(1), pp. 75-96.[20] Hawkins, D. M. (1991). Multivariate quality control based on regression-adiusted variables. Technometrics, 33(1), 61-75.[21] Hotelling, H. A. R. O. L. D. (1947). Multivariate quality control. Techniques of statistical analysis. McGraw-Hill, New York.[22] Li, Z., Zhang, J., & Wang, Z. (2010). Self-starting control chart for simultaneously monitoring process mean and variance. International Journal of Production Research, 48(15), pp. 4537-4553.[23] Li, J., Tsung, F., & Zou, C. (2014). Multivariate binomial/multinomial control chart. IIE Transactions, 46(5), pp. 526-542.[24] Li, C., Mukherjee, A., Su, Q., & Xie, M. (2016). Robust algorithms for economic designing of a nonparametric control chart for abrupt shift in location. Journal of Statistical Computation and Simulation, 86(2), pp. 306-323.[25] Liang, W., Xiang, D., & Pu, X. (2016). A robust multivariate EWMA control chart for detecting sparse mean shifts. Journal of Quality Technology, 48(3), pp. 265-283.[26] Liu, R. Y. (1995). Control charts for multivariate processes. Journal of the American Statistical Association, 90(432), pp. 1380-1387.[27] Liu, R. Y., & Tang, J. (1996). Control charts for dependent and independent measurements based on bootstrap methods. Journal of the American Statistical Association, 91(436), pp. 1694-1700.[28] Liu, R. Y., Singh, K., & Teng, J. H. (2004). DDMA-charts: nonparametric multivariate moving average control charts based on data depth. Allgemeines Statistisches Archiv, 88(2), pp. 235-258.[29] Liu, L., Zi, X., Zhang, J., & Wang, Z. (2013). A sequential rank-based nonparametric adaptive EWMA control chart. Communications in Statistics-Simulation and Computation, 42(4), pp. 841-859.[30] Liu, L., Tsung, F., & Zhang, J. (2014). Adaptive nonparametric CUSUM scheme for detecting unknown shifts in location. International Journal of Production Research, 52(6), pp. 1592-1606.[31] Liu, L., Chen, B., Zhang, J., & Zi, X. (2015). Adaptive phase II nonparametric EWMA control chart with variable sampling interval. Quality and Reliability Engineering International, 31(1), pp. 15-26.[32] 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.[33] Lowry, C. A., & Montgomery, D. C. (1995). A review of multivariate control charts. IIE transactions, 27(6), 800-810.[34] Lu, S. L. (2015). An extended nonparametric exponentially weighted moving average sign control chart. Quality and Reliability Engineering International, 31(1), pp. 3-13.[35] MacGregor, J. F., & Kourti, T. (1995). Statistical process control of multivariate processes. Control Engineering Practice, 3(3), 403-414.[36] Mahadik, S. B., & Shirke, D. T. (2011). A special variable sample size and sampling interval Hotelling’s T 2 chart. The International Journal of Advanced Manufacturing Technology, 53(1-4), pp. 379-384.[37] Messaoud, A., Weihs, C., & Hering, F. (2004). A nonparametric multivariate control chart based on data depth (No. 2004, 61). Technical Report/Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen.[38] 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).[39] Pignatiello Jr, J. J., & Runger, G. C. (1990). Comparisons of multivariate CUSUM charts. Journal of quality technology, 22(3), 173-186.[40] Qiu, P. (2008). Distribution-free multivariate process control based on log-linear modeling. IIE Transactions, 40(7), pp. 664-677.[41] Reynolds Jr, M. R. (1989). Optimal variable sampling interval control charts. Sequential Analysis, 8(4), pp. 361-379.[42] Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 1(3), pp. 239-250.[43] Sabahno, H., Amiri, A., & Castagliola, P. (2018). Optimal performance of the variable sample sizes Hotelling’s T 2 control chart in the presence of measurement errors. Quality Technology & Quantitative Management, pp. 1-25.[44] Shewhart, W. A. (1924). Some applications of statistical methods to the analysis of physical and engineering data. Bell System Technical Journal, 3(1), pp. 43-87.[45] Shokrizadeh, R., Saghaei, A., & Amirzadeh, V. (2018). Optimal design of the variable sampling size and sampling interval variable dimension T2 control chart for monitoring the mean vector of a multivariate normal process. Communications in Statistics-Simulation and Computation, 47(2), pp. 329-337.[46] Shu, L., & Fan, J. (2018). A distribution‐free control chart for monitoring high‐dimensional processes based on interpoint distances. Naval Research Logistics (NRL), 65(4), pp. 317-330.[47] Tagaras, G. (1998). A survey of recent developments in the design of adaptive control charts. Journal of quality technology, 30(3), pp. 212-231.[48] Tang, A., Castagliola, P., Hu, X., & Sun, J. (2019). The adaptive EWMA median chart for known and estimated parameters. Journal of Statistical Computation and Simulation, 89(5), pp. 844-863.[49] Tracy, N. D., Young, J. C., & Mason, R. L. (1992). Multivariate control charts for individual observations. Journal of quality technology, 24(2), 88-95.[50] Tran, P. H., Tran, K. P., Huong, T. T., Heuchenne, C., Nguyen, T. A. D., & Do, C. N. (2018, February). A Variable Sampling Interval EWMA Distribution-Free Control Chart for Monitoring Services Quality. In Proceedings of the 2018 International Conference on E-Business and Applications (pp. 1-5). ACM.[51] Wang, H., Huwang, L., & Yu, J. H. (2015). Multivariate control charts based on the James–Stein estimator. European Journal of Operational Research, 246(1), pp. 119-127.[52] Yang, S. F., Lin, J. S., & Cheng, S. W. (2011). A new nonparametric EWMA sign control chart. Expert systems with applications, 38(5), pp. 6239-6243.[53] 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), pp. 377-386.[54] Yang, S. F. (2016). An improved distribution-free EWMA mean chart. Communications in Statistics-Simulation and Computation, 45(4), pp. 1410-1427.[55] 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.[56] Yue, J., & Liu, L. (2017). Multivariate nonparametric control chart with variable sampling interval. Applied Mathematical Modelling, 52, pp. 603-612.[57] Zhang, J., Zou, C., & Wang, Z. (2010). A control chart based on likelihood ratio test for monitoring process mean and variability. Quality and Reliability Engineering International, 26(1), pp. 63-73.[58] Zou, C., & Qiu, P. (2009). Multivariate statistical process control using LASSO. Journal of the American Statistical Association, 104(488), 1586-1596.[59] Zou, C., & Tsung, F. (2011). A multivariate sign EWMA control chart. Technometrics, 53(1), pp. 84-97. 描述 碩士
國立政治大學
統計學系
106354013資料來源 http://thesis.lib.nccu.edu.tw/record/#G0106354013 資料類型 thesis dc.contributor.advisor 楊素芬 zh_TW dc.contributor.advisor Yang, Su-Fen en_US dc.contributor.author (Authors) 林奕志 zh_TW dc.contributor.author (Authors) Lin, Yi-Chih en_US dc.creator (作者) 林奕志 zh_TW dc.creator (作者) Lin, Yi-Chih en_US dc.date (日期) 2019 en_US dc.date.accessioned 7-Aug-2019 16:01:37 (UTC+8) - dc.date.available 7-Aug-2019 16:01:37 (UTC+8) - dc.date.issued (上傳時間) 7-Aug-2019 16:01:37 (UTC+8) - dc.identifier (Other Identifiers) G0106354013 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/124684 - 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) 106354013 zh_TW dc.description.abstract (摘要) 在工業產品製程中，管制圖為監控產品品質重要的工具。大多數的產品資料屬於多維度且不一定服從常態分配，因此無分配假設的多維度管制圖之研究更是相當重要。本文提出結合資料深度 (data depth) 與符號管制圖 (sign chart) 。建立一個新的指數加權移動平均 (EWMA) 的追蹤統計量來監控產品製程平均數向量是否有失控，並利用平均連串長度 (ARL) 來衡量所提出的新管制圖的表現。此外，我們加入變動抽樣區間時間 (VSI) 的監控技巧與考慮變動維度 (VD)的想法以降低偵測製程失控所需的時間及成本。我們利用管制圖偵測出異常訊息所需的平均時間 (ATS) 來衡量所提出之VSI管制圖。接下來與文獻上存在的管制圖做偵測力表現比較。經由許多不同平均數偏移情況的數值比較分析後，本文所提出的管制圖在製程平均數偏移幅度中等及大時，比其他管制圖有更好的偵測效果。因此，建議可以使用本文提出的新管制圖追蹤製程平均數向量。最後以礫石資料及半導體製程資料來示範本文所提出的管制圖之應用。 zh_TW dc.description.abstract (摘要) In industrial product process, control chart is an important tool for monitoring the process quality. Since many data are multivariate and do not follow normal distribution, this makes traditional Shewhart control charts cannot be applied. So the study of non-normal multivariate control chart is very important.This paper combines the methods of data depth and constructing sign chart to design a new exponentially weighted moving average (EWMA) chart for monitoring the multivariate process location. Performance measurement of the proposed control chart is the average run length (ARL). In addition, techniques for variable sampling interval (VSI) and variable dimension (VD) are added to reduce the detection time of an out-of-control process and sampling cost of detecting the out-of-control process. Performance measurement of the proposed VSI control chart is using the average time to signal (ATS) under an out-of-control process.We would compare the detection performance of the proposed control charts with existing control charts exist in the literatures. The proposed charts show superior detection performance compared the existing control charts when the mean shifts is medium and large under the out-of-control process. Therefore, it is recommended that the proposed control charts in this paper might be applied to detect the shifts in process location. Finally, we would demonstrate the proposed control charts via using gravel data and semiconductor process data. en_US dc.description.tableofcontents Chapter 1. Introduction 11.1 Literature Review 11.2 Study Motivation 41.3 Research Method 4Chapter 2. Using the EWMA-DM Chart to Monitor Multivariate Process Location 52.1 Design of the EWMA-DM Chart 52.2 Performance Measurement of the Proposed EWMA-DM Chart 112.3 Detection Performance Comparison between the EWMA-DM Chart and Existing Control charts 222.4 A Numerical Example of Using the EWMA-DM Chart 26Chapter 3. Using the Optimal Variable Sampling Interval (VSI) EWMA-DM Chart to Monitor Multivariate Process Location 323.1 Construction of the Optimal VSI EWMA-DM Chart 323.2 Performance Measurement of the Proposed Optimal VSI EWMA-DM Chart 383.3 Detection Performance Comparison between the Optimal VSI EWMA-DM Control Chart and Existing Control Charts 413.4 A Numerical Example of Using the Optimal VSI EWMA-DM Chart 49Chapter 4. Using the Variable Dimension (VD) EWMA-DM Chart to Monitor Multivariate Process Location 554.1 Design of the VD EWMA-DM Chart 554.2 Performance Measurement of the Proposed VD EWMA-DM Chart 624.3 Detection Performance Comparison between the VD EWMA-DM Chart and Existing Control Charts 714.4 A Numerical Example of Using the VD EWMA DM Chart 82Chapter 5. Using the Optimal Variable Sampling Interval Variable Dimension (VSI VD) EWMA-DM Chart to Monitor Multivariate Process Location 885.1 Construction of the Optimal VSI VD EWMA-DM Chart 885.2 Performance Measurement of the Optimal VSI VD EWMA-DM Chart 945.3 Detection Performance Comparison between the VSI VD EWMA-DM Chart and Existing Control Charts 1055.4 A Numerical Example of Using the optimal VSI VD EWMA-DM Chart 113Chapter 6. Summary and Future Study 116References 117 zh_TW dc.format.extent 3375734 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0106354013 en_US dc.subject (關鍵詞) 資料深度 zh_TW dc.subject (關鍵詞) 符號管制圖 zh_TW dc.subject (關鍵詞) 指數加權平均 zh_TW dc.subject (關鍵詞) 變動抽樣時間 zh_TW dc.subject (關鍵詞) 變動維度 zh_TW dc.subject (關鍵詞) 偵測到異常所需的平均抽樣次數 zh_TW dc.subject (關鍵詞) 偵測出異常所需的平均時間 zh_TW dc.subject (關鍵詞) Data depth en_US dc.subject (關鍵詞) Sign chart en_US dc.subject (關鍵詞) Exponentially weighted moving average en_US dc.subject (關鍵詞) Variable sampling interval en_US dc.subject (關鍵詞) Variable dimension en_US dc.subject (關鍵詞) Average run length en_US dc.subject (關鍵詞) Average time to signal en_US dc.title (題名) 無母數多元製程位置管制圖之研究 zh_TW dc.title (題名) The Study of Multivariate Process Location Control Chart en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Altukife, F. S. (2003). A new nonparametric control chart based on the observations exceeding the grand median. Pakistan journal of statistics-all series, 19(3), pp. 343-352.[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), pp. 1597-1623.[3] Amin, R. W., & Widmaier, O. (1999). Sign control charts with variable sampling intervals. Communications in Statistics-Theory and Methods, 28(8), pp. 1961-1985.[4] Aparisi, F. (1996). Hotelling`s T2 control chart with adaptive sample sizes. International Journal of Production Research, 34(10), pp. 2853-2862.[5] Aparisi F, Jabaloyes J, Carrion A. Statistical properties of the |S| multivariate control chart. Communications in Statistics—Theory and Methods 1999; 28:2671–2686.[6] Aparisi F, Jabaloyes J, Carrion A. Generalized variance chart design with adaptive sample sizes. The bivariate case.Communications in Statistics—Simulation and Computation 2001; 30:931–948.[7] Bakir, S. T. (2004). A distribution-free Shewhart quality control chart based on signed-ranks. Quality Engineering, 16(4), pp. 613-623.[8] Bakir, S. T. (2006). Distribution-free quality control charts based on signed-rank-like statistics. Communications in Statistics-Theory and Methods, 35(4), pp. 743-757.[9] 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), pp. 528-538.[10] Capizzi, G., & Masarotto, G. (2017). Phase I distribution-free analysis of multivariate data. Technometrics, 59(4), pp. 484-495.[11] Chakraborti, S., Van der Laan, P., & Bakir, S. T. (2001). Nonparametric control charts: an overview and some results. Journal of Quality Technology, 33(3), pp. 304-315.[12] Chen, N., Zi, X., & Zou, C. (2016). A distribution-free multivariate control chart. Technometrics, 58(4), pp. 448-459.[13] Chowdhury, S., Mukherjee, A., & Chakraborti, S. (2014). A new distribution‐free control chart for joint monitoring of unknown location and scale parameters of continuous distributions. Quality and Reliability Engineering International, 30(2), pp. 191-204.[14] Costa, A. F. (1997). X chart with variable sample size and sampling intervals. Journal of Quality Technology, 29(2), pp. 197-204.[15] Crosier, R. B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3), 291-303.[16] Epprecht, E. K., Aparisi, F., & Ruiz, O. (2018). Optimum variable-dimension EWMA chart for multivariate statistical process control. Quality Engineering, 30(2), pp. 268-282.[17] 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, pp. 1-24.[18] Ferrell, E. B. (1953). Control charts using midranges and medians. Industrial Quality Control, 9(5), pp. 30-34.[19] Grasso, M., Colosimo, B. M., Semeraro, Q., & Pacella, M. (2015). A comparison study of distribution‐free multivariate SPC methods for multimode data. Quality and Reliability Engineering International, 31(1), pp. 75-96.[20] Hawkins, D. M. (1991). Multivariate quality control based on regression-adiusted variables. Technometrics, 33(1), 61-75.[21] Hotelling, H. A. R. O. L. D. (1947). Multivariate quality control. Techniques of statistical analysis. McGraw-Hill, New York.[22] Li, Z., Zhang, J., & Wang, Z. (2010). Self-starting control chart for simultaneously monitoring process mean and variance. International Journal of Production Research, 48(15), pp. 4537-4553.[23] Li, J., Tsung, F., & Zou, C. (2014). Multivariate binomial/multinomial control chart. IIE Transactions, 46(5), pp. 526-542.[24] Li, C., Mukherjee, A., Su, Q., & Xie, M. (2016). Robust algorithms for economic designing of a nonparametric control chart for abrupt shift in location. Journal of Statistical Computation and Simulation, 86(2), pp. 306-323.[25] Liang, W., Xiang, D., & Pu, X. (2016). A robust multivariate EWMA control chart for detecting sparse mean shifts. Journal of Quality Technology, 48(3), pp. 265-283.[26] Liu, R. Y. (1995). Control charts for multivariate processes. Journal of the American Statistical Association, 90(432), pp. 1380-1387.[27] Liu, R. Y., & Tang, J. (1996). Control charts for dependent and independent measurements based on bootstrap methods. Journal of the American Statistical Association, 91(436), pp. 1694-1700.[28] Liu, R. Y., Singh, K., & Teng, J. H. (2004). DDMA-charts: nonparametric multivariate moving average control charts based on data depth. 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