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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-Sep-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 Ben_US
dc.contributor.author (Authors) 周秋全zh_TW
dc.contributor.author (Authors) Chou, Chiu Chuanen_US
dc.creator (作者) 周秋全zh_TW
dc.creator (作者) Chou, Chiu Chuanen_US
dc.date (日期) 2022en_US
dc.date.accessioned 2-Sep-2022 14:46:41 (UTC+8)-
dc.date.available 2-Sep-2022 14:46:41 (UTC+8)-
dc.date.issued (上傳時間) 2-Sep-2022 14:46:41 (UTC+8)-
dc.identifier (Other Identifiers) G0109354024en_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) 109354024zh_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 11
1.1 Literature Review 11
1.2 Study Motivation 13
2. Methodologies 15
2.1 A General Framework 15
2.2 The Estimation under Multivariate Normal Processes 19
2.3 The Estimation under Multivariate Non-Normal Processes 20
2.3.1 Multivariate t_5 Distribution 20
2.3.2 Multivariate Uniform Distribution 20
2.3.3 Multivariate Gamma Distribution 22
2.4 An Example of a Two-Dimensional Ratios of Means 24
3. The Construction of the Proposed Control Charts 26
4. Empirical Investigation of the Distribution of Multi-dimensional Ratios of Means 30
5. Chart Performance Evaluations and Comparisons 32
5.1 The RM-T2 chart 32
5.2 The MEWMARM chart 33
6. Illustrative Examples 36
7. Conclusions and Future Study 38
References 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/#G0109354024en_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 meansen_US
dc.subject (關鍵詞) Multivariate distributionen_US
dc.subject (關鍵詞) Phase II control charten_US
dc.subject (關鍵詞) Unbiased estimatoren_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 Meansen_US
dc.type (資料類型) thesisen_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/NCCU202201225en_US