學術產出-學位論文
文章檢視/開啟
書目匯出
-
題名 追蹤製程平均比的Phase II多元管制圖
Phase II Control Charts for Monitoring Multi-Dimensional Ratios of Process Means作者 周秋全
Chou, Chiu Chuan貢獻者 楊素芬<br>葉百堯
Yang, Su-Fen<br>Yeh, Arthur B
周秋全
Chou, Chiu Chuan關鍵詞 平均值比
不偏估計式
Phase II管制圖
多元分配
Multi-dimensional ratios of means
Multivariate distribution
Phase II control chart
Unbiased estimator日期 2022 上傳時間 2-九月-2022 14:46:41 (UTC+8) 摘要 近年來，用於監測平均值比管制圖有新的發展。然而，大多數現有的研究都集中在二元常態的平均值比管制圖上，且大多利用有偏差的平均值比估計式來發展管制圖。因此，本研究中，我們的動機是建立基於不偏估計式的Phase II管制圖，以監測來自多元常態和多元非常態製程的多維平均值比。本研究中，我們提供一個估計參數和管制界限的整體框架，適用於不同的多元分配。在不同的多元分配下，對所提出管制圖的表現進行衡量，並與文獻的管制圖進行比較。最後，介紹此管制圖的應用，以說明此管制圖如何用於監測成分數據的實務應用性，以及此管制圖如何用於監測成分數據。
In recent years, there has been a resurgence in the development of control charts for monitoring the ratio of process means. However, most of the existing research has focused on univariate ratio of means under the assumption that the process follows a normal distribution, and most of the existing research utilize biased estimators of the ratio of means to develop the control charts. We are thus motivated in this study to develop Phase II control charts based on unbiased estimators for monitoring multi-dimensional ratios of means derived from normal and non-normal multivariate processes.In this study, we provide a general framework for estimating parameters and control limits which is applicable to different multivariate distributions. The performances of the proposed charts are evaluated and compared with the existing charts under different multivariate distributions. Finally, applications of the proposed control charts are presented to monitor the compositional data of milk.參考文獻 Atchinson, J. A. (2005, October). Concise Guide to Compositional Data Analysis. In2do Compositional Data Analysis Workshop CoDaWork Oct, Vol. 5, pp. 17-21.Abubakar, S. S., Khoo, M. B., Saha, S., & Teoh, W. L. (2020). Run sum control chart for monitoring the ratio of population means of a bivariate normal distribution. Communications in Statistics-Theory and Methods, 1-30.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.Crosier, R. B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3), 291-303.Celano, G., Castagliola, P., Faraz, A., & Fichera, S. (2014). Statistical performance of a control chart for individual observations monitoring the ratio of two normal variables. Quality and Reliability Engineering International, 30(8), 1361-1377.Celano, G., & Castagliola, P. (2016a). Design of a phase II control chart for monitoring the ratio of two normal variables. Quality and Reliability Engineering International, 32(1), 291-308.Celano, G., & Castagliola, P. (2016b). A synthetic control chart for monitoring the ratio of two normal variables. Quality and Reliability Engineering International, 32(2), 681-696.Davis, R. B., & Woodall, W. H. (1991). Evaluation of control charts for ratios. In 22nd Annual Pittsburgh Conference on Modeling and Simulation, pp. 63-70.dos Santos Dias, C. T., Samaranayaka, A., & Manly, B. (2008). On the use of correlated beta random variables with animal population modelling. Ecological Modelling, 215(4), 293-300.Farokhnia, M., & Niaki, S. T. A. (2020). Principal component analysis-based control charts using support vector machines for multivariate non-normal distributions. Communications in Statistics-Simulation and Computation, 49(7), 1815-1838.Hotteling, H. (1947). Multivariate quality control, illustrated by the air testing of sample bombsights. Techniques of statistical analysis, 111-184.Hawkins, D. M. (1991). Multivariate quality control based on regression-adjusted variables. Technometrics, 33(1), 61-75.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.Liu, R. Y. (1995). Control charts for multivariate processes. Journal of the American Statistical Association, 90(432), 1380-1387.Lowry, C. A., & Montgomery, D. C. (1995). A review of multivariate control charts. IIE Transactions (Institute of Industrial Engineers), 27(6), 800-810.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.Montgomery, D. C., & Wadsworth, H. M. (1972, May). Some techniques for multivariate quality control applications. In ASQC Technical Conference Transactions, Vol. 26, pp. 427-435.Melo, M. S., Ho, L. L., & Medeiros, P. G. (2017). Max D: an attribute control chart to monitor a bivariate process mean. The International Journal of Advanced Manufacturing Technology, 90(1), 489-498.Montgomery, D. C. (2020). Introduction to statistical quality control. New Jersey, United States of America: John Wiley & Sons Inc.Nguyen, H. D., Tran, K. P., & Heuchenne, C. (2019). Monitoring the ratio of two normal variables using variable sampling interval exponentially weighted moving average control charts. Quality and Reliability Engineering International, 35(1), 439-460.ÖKSOY, D., Boulos, E., & DAVID PYE, L. (1993). Statistical process control by the quotient of two correlated normal variables. Quality Engineering, 6(2), 179-194.Pignatiello Jr, J. J., & Runger, G. C. (1990). Comparisons of multivariate CUSUM charts. Journal of Quality Technology, 22(3), 173-186.Roberts, S. W. (1959). Control Chart Tests Based on Geometric Moving Averages. Technometrics, 239-250.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.Spisak, A. W. (1990). A control chart for ratios. Journal of Quality Technology, 22(1), 34-37.Tran, K. P., Castagliola, P., & Celano, G. (2016a). Monitoring the ratio of two normal variables using run rules type control charts. International Journal of Production Research, 54(6), 1670-1688.Tran, K. P., Castagliola, P., & Celano, G. (2016b). Monitoring the ratio of two normal variables using EWMA type control charts. Quality and Reliability Engineering International, 32(5), 1853-1869.Tran, K. P., Castagliola, P., & Celano, G. (2016c). The performance of the Shewhart-RZ control chart in the presence of measurement error. International Journal of Production Research, 54(24), 7504-7522.Tran, K. P., Castagliola, P., & Celano, G. (2018). Monitoring the ratio of population means of a bivariate normal distribution using CUSUM type control charts. Statistical Papers, 59(1), 387-413.Tran, K. P., & Knoth, S. (2018). Steady‐state ARL analysis of ARL‐unbiased EWMA‐RZ control chart monitoring the ratio of two normal variables. Quality and Reliability Engineering International, 34(3), 377-390.Wang, S., & Reynolds Jr., 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.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, 37(6), 2384-2398. 描述 碩士
國立政治大學
統計學系
109354024資料來源 http://thesis.lib.nccu.edu.tw/record/#G0109354024 資料類型 thesis dc.contributor.advisor 楊素芬<br>葉百堯 zh_TW dc.contributor.advisor Yang, Su-Fen<br>Yeh, Arthur B en_US dc.contributor.author (作者) 周秋全 zh_TW dc.contributor.author (作者) Chou, Chiu Chuan en_US dc.creator (作者) 周秋全 zh_TW dc.creator (作者) Chou, Chiu Chuan en_US dc.date (日期) 2022 en_US dc.date.accessioned 2-九月-2022 14:46:41 (UTC+8) - dc.date.available 2-九月-2022 14:46:41 (UTC+8) - dc.date.issued (上傳時間) 2-九月-2022 14:46:41 (UTC+8) - dc.identifier (其他 識別碼) G0109354024 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/141551 - 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) 109354024 zh_TW dc.description.abstract (摘要) 近年來，用於監測平均值比管制圖有新的發展。然而，大多數現有的研究都集中在二元常態的平均值比管制圖上，且大多利用有偏差的平均值比估計式來發展管制圖。因此，本研究中，我們的動機是建立基於不偏估計式的Phase II管制圖，以監測來自多元常態和多元非常態製程的多維平均值比。本研究中，我們提供一個估計參數和管制界限的整體框架，適用於不同的多元分配。在不同的多元分配下，對所提出管制圖的表現進行衡量，並與文獻的管制圖進行比較。最後，介紹此管制圖的應用，以說明此管制圖如何用於監測成分數據的實務應用性，以及此管制圖如何用於監測成分數據。 zh_TW dc.description.abstract (摘要) In recent years, there has been a resurgence in the development of control charts for monitoring the ratio of process means. However, most of the existing research has focused on univariate ratio of means under the assumption that the process follows a normal distribution, and most of the existing research utilize biased estimators of the ratio of means to develop the control charts. We are thus motivated in this study to develop Phase II control charts based on unbiased estimators for monitoring multi-dimensional ratios of means derived from normal and non-normal multivariate processes.In this study, we provide a general framework for estimating parameters and control limits which is applicable to different multivariate distributions. The performances of the proposed charts are evaluated and compared with the existing charts under different multivariate distributions. Finally, applications of the proposed control charts are presented to monitor the compositional data of milk. en_US dc.description.tableofcontents 1. Introduction 111.1 Literature Review 111.2 Study Motivation 132. Methodologies 152.1 A General Framework 152.2 The Estimation under Multivariate Normal Processes 192.3 The Estimation under Multivariate Non-Normal Processes 202.3.1 Multivariate t_5 Distribution 202.3.2 Multivariate Uniform Distribution 202.3.3 Multivariate Gamma Distribution 222.4 An Example of a Two-Dimensional Ratios of Means 243. The Construction of the Proposed Control Charts 264. Empirical Investigation of the Distribution of Multi-dimensional Ratios of Means 305. Chart Performance Evaluations and Comparisons 325.1 The RM-T2 chart 325.2 The MEWMARM chart 336. Illustrative Examples 367. Conclusions and Future Study 38References 40 zh_TW dc.format.extent 5149837 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0109354024 en_US dc.subject (關鍵詞) 平均值比 zh_TW dc.subject (關鍵詞) 不偏估計式 zh_TW dc.subject (關鍵詞) Phase II管制圖 zh_TW dc.subject (關鍵詞) 多元分配 zh_TW dc.subject (關鍵詞) Multi-dimensional ratios of means en_US dc.subject (關鍵詞) Multivariate distribution en_US dc.subject (關鍵詞) Phase II control chart en_US dc.subject (關鍵詞) Unbiased estimator en_US dc.title (題名) 追蹤製程平均比的Phase II多元管制圖 zh_TW dc.title (題名) Phase II Control Charts for Monitoring Multi-Dimensional Ratios of Process Means en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Atchinson, J. A. (2005, October). Concise Guide to Compositional Data Analysis. In2do Compositional Data Analysis Workshop CoDaWork Oct, Vol. 5, pp. 17-21.Abubakar, S. S., Khoo, M. B., Saha, S., & Teoh, W. L. (2020). Run sum control chart for monitoring the ratio of population means of a bivariate normal distribution. Communications in Statistics-Theory and Methods, 1-30.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.Crosier, R. B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3), 291-303.Celano, G., Castagliola, P., Faraz, A., & Fichera, S. (2014). Statistical performance of a control chart for individual observations monitoring the ratio of two normal variables. Quality and Reliability Engineering International, 30(8), 1361-1377.Celano, G., & Castagliola, P. (2016a). Design of a phase II control chart for monitoring the ratio of two normal variables. Quality and Reliability Engineering International, 32(1), 291-308.Celano, G., & Castagliola, P. (2016b). A synthetic control chart for monitoring the ratio of two normal variables. Quality and Reliability Engineering International, 32(2), 681-696.Davis, R. B., & Woodall, W. H. (1991). Evaluation of control charts for ratios. In 22nd Annual Pittsburgh Conference on Modeling and Simulation, pp. 63-70.dos Santos Dias, C. T., Samaranayaka, A., & Manly, B. (2008). On the use of correlated beta random variables with animal population modelling. Ecological Modelling, 215(4), 293-300.Farokhnia, M., & Niaki, S. T. A. (2020). Principal component analysis-based control charts using support vector machines for multivariate non-normal distributions. Communications in Statistics-Simulation and Computation, 49(7), 1815-1838.Hotteling, H. (1947). Multivariate quality control, illustrated by the air testing of sample bombsights. Techniques of statistical analysis, 111-184.Hawkins, D. M. (1991). Multivariate quality control based on regression-adjusted variables. Technometrics, 33(1), 61-75.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.Liu, R. Y. (1995). Control charts for multivariate processes. Journal of the American Statistical Association, 90(432), 1380-1387.Lowry, C. A., & Montgomery, D. C. (1995). A review of multivariate control charts. IIE Transactions (Institute of Industrial Engineers), 27(6), 800-810.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.Montgomery, D. C., & Wadsworth, H. M. (1972, May). Some techniques for multivariate quality control applications. In ASQC Technical Conference Transactions, Vol. 26, pp. 427-435.Melo, M. S., Ho, L. L., & Medeiros, P. G. (2017). Max D: an attribute control chart to monitor a bivariate process mean. The International Journal of Advanced Manufacturing Technology, 90(1), 489-498.Montgomery, D. C. (2020). Introduction to statistical quality control. New Jersey, United States of America: John Wiley & Sons Inc.Nguyen, H. D., Tran, K. P., & Heuchenne, C. (2019). Monitoring the ratio of two normal variables using variable sampling interval exponentially weighted moving average control charts. Quality and Reliability Engineering International, 35(1), 439-460.ÖKSOY, D., Boulos, E., & DAVID PYE, L. (1993). Statistical process control by the quotient of two correlated normal variables. Quality Engineering, 6(2), 179-194.Pignatiello Jr, J. J., & Runger, G. C. (1990). Comparisons of multivariate CUSUM charts. Journal of Quality Technology, 22(3), 173-186.Roberts, S. W. (1959). Control Chart Tests Based on Geometric Moving Averages. Technometrics, 239-250.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.Spisak, A. W. (1990). A control chart for ratios. Journal of Quality Technology, 22(1), 34-37.Tran, K. P., Castagliola, P., & Celano, G. (2016a). Monitoring the ratio of two normal variables using run rules type control charts. International Journal of Production Research, 54(6), 1670-1688.Tran, K. P., Castagliola, P., & Celano, G. (2016b). Monitoring the ratio of two normal variables using EWMA type control charts. Quality and Reliability Engineering International, 32(5), 1853-1869.Tran, K. P., Castagliola, P., & Celano, G. (2016c). The performance of the Shewhart-RZ control chart in the presence of measurement error. International Journal of Production Research, 54(24), 7504-7522.Tran, K. P., Castagliola, P., & Celano, G. (2018). Monitoring the ratio of population means of a bivariate normal distribution using CUSUM type control charts. Statistical Papers, 59(1), 387-413.Tran, K. P., & Knoth, S. (2018). Steady‐state ARL analysis of ARL‐unbiased EWMA‐RZ control chart monitoring the ratio of two normal variables. Quality and Reliability Engineering International, 34(3), 377-390.Wang, S., & Reynolds Jr., 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.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, 37(6), 2384-2398. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202201225 en_US
