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題名 新多元變異係數定義與其對應之管制圖
A New Definition of Multivariate Coefficient of Variation and Its Corresponding Control Charts作者 潘維辰
Pan, Wei-Chen貢獻者 楊素芬<br>葉百堯<br>蕭又新
Yang, Su-Fen<br>Yeh, Bai-Yau<br>Shiau, Yuo-Hsien
潘維辰
Pan, Wei-Chen關鍵詞 向量化變異係數
多元指數加權移動平均
平均連串長度
多元變異係數
管制圖
Average run length
Control chart
Multivariate coefficient of variation
Multivariate exponentially moving average
Vectorized coefficient of variation日期 2022 上傳時間 2-九月-2022 14:46:53 (UTC+8) 摘要 傳統上，我們經常使用舒華特管制圖監控製程的平均數及變異數，即使在此之後有許多效果卓越的改良，但我們通常是將平均數即變異數分開監控，因此在某些臨床醫學或工業領域中，當我們希望監控的是製程變異係數(CV)時，傳統的平均數及變異數將不再適用，CV管制圖即是為了解決此問題而被提出。多元統計製程控制在近年日趨熱門，多元變異係數(MCV)管制圖也隨之誕生，然而，在現有的發展下，MCV管制圖中對於MCV統計量的定義對於單維度的CV偏移是不敏感的，因此我們嘗試使用向量化變異係數 (vectorized coefficient of variation, VCV)來建立管制圖並監控多元製程變量下的CV以得到更好的改善，我們也同時提出了多元指數加權移動平均(MEWMA)型VCV管制圖，並使用製程失控時的平均連串長度來進行偵測性能的測量，在本研究中已證實MEWMA型VCV管制圖可超越初始的舒華特型VCV管制圖，並且也優於現有在MCV定義下的管制圖。此外，本研究中展示了關於相關係數的偏移在VCV管制圖和MCV管制圖之間行為，最後使用兩不同分配之半導體數據說明VCV管制圖的實務應用。
In some clinical or industrial applications, it is critically important to monitor the process coefficient of variation (CV). Though there are many existing control charts for monitoring either process mean or variance, the conventional Shewhart X ̅-chart and R-chart (or S-chart) cannot deal with the setting of constant CV. Therefore, the CV control chart is proposed for dealing this problem.In recent years, there has been a resurgent interest in developing multivariate statistical process control (MSPC) charts. The multivariate coefficient of variation (MCV) control chart was soon proposed and has been further discussed. However, the existing MCV charts are not sensitive to CV changes which occur at individual variables. In this study, we propose a new definition of multivariate CV, the vectorized CV (VCV), to better capture more subtle changes in CV in individual variables. The multivariate exponential weighted moving average (MEWMA) type VCV control chart is also proposed and has been demonstrated to improve the Shewhart-type VCV chart in this study. The average run length (ARL) is used for the performance measurement. It is shown that the proposed VCV based control charts outperform the existing MCV charts, especially with regards to the MEWMA type VCV chart. Furthermore, the cases when only correlation changes are evaluated and compared between the VCV charts and the MCV charts. A multivariate normal process example and a multivariate non-normal process example are presented to show how the proposed charts can be applied in practice.參考文獻 Amdouni, A., Castagliola, P., Taleb, H., & Celano, G. (2016). One-sided run rules control charts for monitoring the coefficient of variation in short production runs. European Journal of Industrial Engineering, 10(5), 639-663.Calzada, M. E., & Scariano, S. M. (2013). A synthetic control chart for the coefficient of variation. Journal of Statistical Computation and Simulation, 83(5), 853-867.Castagliola, P., Amdouni, A., Taleb, H., & Celano, G. (2015). One-sided Shewhart-type charts for monitoring the coefficient of variation in short production runs. Quality Technology & Quantitative Management, 12(1), 53-67.Castagliola, P., Achouri, A., Taleb, H., Celano, G., & Psarakis, S. (2013). Monitoring the coefficient of variation using a variable sampling interval control chart. Quality and Reliability Engineering International, 29(8), 1135-1149.Castagliola, P., Achouri, A., Taleb, H., Celano, G., & Psarakis, S. (2015). Monitoring the coefficient of variation using a variable sample size control chart. The International Journal of Advanced Manufacturing Technology, 80(9), 1561-1576.Castagliola, P., Celano, G., & Psarakis, S. (2011). Monitoring the coefficient of variation using EWMA charts. Journal of Quality Technology, 43(3), 249-265.Castagliola, P., Achouri, A., Taleb, H., Celano, G., & Psarakis, S. (2013). Monitoring the coefficient of variation using control charts with run rules. Quality Technology & Quantitative Management, 10(1), 75-94.Chew, X., Khoo, M. B. C., Khaw, K. W., Yeong, W. C., & Chong, Z. L. (2019). A proposed variable parameter control chart for monitoring the multivariate coefficient of variation. Quality and Reliability Engineering International, 35(7), 2442-2461.Chew, X., & Khaw, K. W. (2020). One-sided downward control chart for monitoring the multivariate coefficient of variation with VSSI strategy. Journal of Mathematical Fundamental Sciences, 52(1), 112-130.Giner‐Bosch, V., Tran, K. P., Castagliola, P., & Khoo, M. B. C. (2019). An EWMA control chart for the multivariate coefficient of variation. Quality and Reliability Engineering International, 35(6), 1515-1541. Haq, A., & Khoo, M. B. (2019). New adaptive EWMA control charts for monitoring univariate and multivariate coefficient of variation. Computers & Industrial Engineering, 131, 28-40.Haq, A., Bibi, N., & Chong Khoo, M. B. (2020). Enhanced EWMA charts for monitoring the process coefficient of variation. Quality and Reliability Engineering International, 36(7), 2478-2494.Hong, E. P., Kang, C. W., Baek, J. W., & Kang, H. W. (2008). Development of CV control chart using EWMA technique. Journal of the Society of Korea Industrial and Systems Engineering, 31(4), 114-120.Iglewicz, B. (1967). Some Properties of the Sample Coefficient of Variation. Unpublished Ph.D. Dissertation, Virginia Polytechnic Institute and State University.Kang, C. W., Lee, M. S., Seong, Y. J., & Hawkins, D. M. (2007). A control chart for the coefficient of variation. Journal of Quality Technology, 39(2), 151-158.Khatun, M., Khoo, M. B., Lee, M. H., & Castagliola, P. (2019). One-sided control charts for monitoring the multivariate coefficient of variation in short production runs. Transactions of the Institute of Measurement and Control, 41(6), 1712-1728.Khaw, K. W., Khoo, M. B., Yeong, W. C., & Wu, Z. (2017). Monitoring the coefficient of variation using a variable sample size and sampling interval control chart. Communications in Statistics-Simulation and Computation, 46(7), 5772-5794.Khaw, K. W., Khoo, M. B., Castagliola, P., & Rahim, M. A. (2018). New adaptive control charts for monitoring the multivariate coefficient of variation. Computers & Industrial Engineering, 126, 595-610.Khaw, K. W., Chew, X., Yeong, W. C., & Lim, S. L. (2019). Optimal design of the synthetic control chart for monitoring the multivariate coefficient of variation. Chemometrics and Intelligent Laboratory Systems, 186, 33-40.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.Reed, G. F., Lynn, F., & Meade, B. D. (2002). Use of coefficient of variation in assessing variability of quantitative assays. Clinical and Vaccine Immunology, 9(6), 1235-1239.Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 42(1), 97-101.Teoh, W. L., Khoo, M. B., Castagliola, P., Yeong, W. C., & Teh, S. Y. (2017). Run-sum control charts for monitoring the coefficient of variation. European Journal of Operational Research, 257(1), 144-158.Voinov V. G., Nikulin M. S. (1996). Unbiased Estimators and Their Applications. Multivariate Case, Vol. 2. Kluwer: Dordrecht.Yeong, W. C., Lee, P. Y., Lim, S. L., Khaw, K. W., & Khoo, M. B. C. (2021). A side‐sensitive synthetic coefficient of variation chart. Quality and Reliability Engineering International, 37(5), 2014-2033.Yahaya, M., Lim, S. L., Ibrahim, A. I. N., Yeong, W. C., & Khoo, M. B. C. (2022). A variable sample size synthetic chart for the coefficient of variation. South African Journal of Industrial Engineering, 33(1), 1-15.Yeong, W. C., Tan, Y. Y., Lim, S. L., Khaw, K. W., & Khoo, M. B. C. (2022). A variable sample size run sum coefficient of variation chart. Quality and Reliability Engineering International, 38(4), 1869-1885.Yeong, W. C., Khoo, M. B. C., Teoh, W. L., & Castagliola, P. (2016). A control chart for the multivariate coefficient of variation. Quality and Reliability Engineering International, 32(3), 1213-1225.Yeong, W. C., Khoo, M. B., Lim, S. L., & Lee, M. H. (2017). A direct procedure for monitoring the coefficient of variation using a variable sample size scheme. Communications in Statistics-Simulation and Computation, 46(6), 4210-4225.You, H. W., Khoo, M. B., Castagliola, P., & Haq, A. (2016). Monitoring the coefficient of variation using the side sensitive group runs chart. Quality and Reliability Engineering International, 32(5), 1913-1927.Zhang, J., Li, Z., Chen, B., & Wang, Z. (2014). A new exponentially weighted moving average control chart for monitoring the coefficient of variation. Computers & Industrial Engineering, 78, 205-212. 描述 碩士
國立政治大學
統計學系
109354025資料來源 http://thesis.lib.nccu.edu.tw/record/#G0109354025 資料類型 thesis dc.contributor.advisor 楊素芬<br>葉百堯<br>蕭又新 zh_TW dc.contributor.advisor Yang, Su-Fen<br>Yeh, Bai-Yau<br>Shiau, Yuo-Hsien en_US dc.contributor.author (作者) 潘維辰 zh_TW dc.contributor.author (作者) Pan, Wei-Chen en_US dc.creator (作者) 潘維辰 zh_TW dc.creator (作者) Pan, Wei-Chen en_US dc.date (日期) 2022 en_US dc.date.accessioned 2-九月-2022 14:46:53 (UTC+8) - dc.date.available 2-九月-2022 14:46:53 (UTC+8) - dc.date.issued (上傳時間) 2-九月-2022 14:46:53 (UTC+8) - dc.identifier (其他 識別碼) G0109354025 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/141552 - 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) 109354025 zh_TW dc.description.abstract (摘要) 傳統上，我們經常使用舒華特管制圖監控製程的平均數及變異數，即使在此之後有許多效果卓越的改良，但我們通常是將平均數即變異數分開監控，因此在某些臨床醫學或工業領域中，當我們希望監控的是製程變異係數(CV)時，傳統的平均數及變異數將不再適用，CV管制圖即是為了解決此問題而被提出。多元統計製程控制在近年日趨熱門，多元變異係數(MCV)管制圖也隨之誕生，然而，在現有的發展下，MCV管制圖中對於MCV統計量的定義對於單維度的CV偏移是不敏感的，因此我們嘗試使用向量化變異係數 (vectorized coefficient of variation, VCV)來建立管制圖並監控多元製程變量下的CV以得到更好的改善，我們也同時提出了多元指數加權移動平均(MEWMA)型VCV管制圖，並使用製程失控時的平均連串長度來進行偵測性能的測量，在本研究中已證實MEWMA型VCV管制圖可超越初始的舒華特型VCV管制圖，並且也優於現有在MCV定義下的管制圖。此外，本研究中展示了關於相關係數的偏移在VCV管制圖和MCV管制圖之間行為，最後使用兩不同分配之半導體數據說明VCV管制圖的實務應用。 zh_TW dc.description.abstract (摘要) In some clinical or industrial applications, it is critically important to monitor the process coefficient of variation (CV). Though there are many existing control charts for monitoring either process mean or variance, the conventional Shewhart X ̅-chart and R-chart (or S-chart) cannot deal with the setting of constant CV. Therefore, the CV control chart is proposed for dealing this problem.In recent years, there has been a resurgent interest in developing multivariate statistical process control (MSPC) charts. The multivariate coefficient of variation (MCV) control chart was soon proposed and has been further discussed. However, the existing MCV charts are not sensitive to CV changes which occur at individual variables. In this study, we propose a new definition of multivariate CV, the vectorized CV (VCV), to better capture more subtle changes in CV in individual variables. The multivariate exponential weighted moving average (MEWMA) type VCV control chart is also proposed and has been demonstrated to improve the Shewhart-type VCV chart in this study. The average run length (ARL) is used for the performance measurement. It is shown that the proposed VCV based control charts outperform the existing MCV charts, especially with regards to the MEWMA type VCV chart. Furthermore, the cases when only correlation changes are evaluated and compared between the VCV charts and the MCV charts. A multivariate normal process example and a multivariate non-normal process example are presented to show how the proposed charts can be applied in practice. en_US dc.description.tableofcontents Contents1. Introduction 92. The Existing MCV and the VCV Control Chart 112.1 A Brief Review of Shewhart-type MCV Chart and EWMA MCV2 Chart 112.2 The proposed VCV control chart 143. The Chart Performance Evaluations and Comparisons 163.1 The Performance of the T_VCV^2-chart 163.2 Comparisons with the MCV Chart 194. The Multivariate EWMA (MEWMA) VCV Control Chart 204.1 The Methodologies 204.2 Chart Performance Evaluations and Comparisons 234.3 Chart Performance When only Correlations Change 245. Real Examples 255.1 A Bivariate Normal Example 255.2 A Bivariate Non-Normal Example 296. Conclusions and Future Study 31References 33 zh_TW dc.format.extent 3590312 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0109354025 en_US dc.subject (關鍵詞) 向量化變異係數 zh_TW dc.subject (關鍵詞) 多元指數加權移動平均 zh_TW dc.subject (關鍵詞) 平均連串長度 zh_TW dc.subject (關鍵詞) 多元變異係數 zh_TW dc.subject (關鍵詞) 管制圖 zh_TW dc.subject (關鍵詞) Average run length en_US dc.subject (關鍵詞) Control chart en_US dc.subject (關鍵詞) Multivariate coefficient of variation en_US dc.subject (關鍵詞) Multivariate exponentially moving average en_US dc.subject (關鍵詞) Vectorized coefficient of variation en_US dc.title (題名) 新多元變異係數定義與其對應之管制圖 zh_TW dc.title (題名) A New Definition of Multivariate Coefficient of Variation and Its Corresponding Control Charts en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Amdouni, A., Castagliola, P., Taleb, H., & Celano, G. (2016). One-sided run rules control charts for monitoring the coefficient of variation in short production runs. European Journal of Industrial Engineering, 10(5), 639-663.Calzada, M. E., & Scariano, S. M. (2013). A synthetic control chart for the coefficient of variation. Journal of Statistical Computation and Simulation, 83(5), 853-867.Castagliola, P., Amdouni, A., Taleb, H., & Celano, G. (2015). One-sided Shewhart-type charts for monitoring the coefficient of variation in short production runs. Quality Technology & Quantitative Management, 12(1), 53-67.Castagliola, P., Achouri, A., Taleb, H., Celano, G., & Psarakis, S. (2013). Monitoring the coefficient of variation using a variable sampling interval control chart. Quality and Reliability Engineering International, 29(8), 1135-1149.Castagliola, P., Achouri, A., Taleb, H., Celano, G., & Psarakis, S. (2015). Monitoring the coefficient of variation using a variable sample size control chart. The International Journal of Advanced Manufacturing Technology, 80(9), 1561-1576.Castagliola, P., Celano, G., & Psarakis, S. (2011). Monitoring the coefficient of variation using EWMA charts. Journal of Quality Technology, 43(3), 249-265.Castagliola, P., Achouri, A., Taleb, H., Celano, G., & Psarakis, S. (2013). Monitoring the coefficient of variation using control charts with run rules. Quality Technology & Quantitative Management, 10(1), 75-94.Chew, X., Khoo, M. B. C., Khaw, K. W., Yeong, W. C., & Chong, Z. L. (2019). A proposed variable parameter control chart for monitoring the multivariate coefficient of variation. Quality and Reliability Engineering International, 35(7), 2442-2461.Chew, X., & Khaw, K. W. (2020). One-sided downward control chart for monitoring the multivariate coefficient of variation with VSSI strategy. Journal of Mathematical Fundamental Sciences, 52(1), 112-130.Giner‐Bosch, V., Tran, K. P., Castagliola, P., & Khoo, M. B. C. (2019). An EWMA control chart for the multivariate coefficient of variation. Quality and Reliability Engineering International, 35(6), 1515-1541. Haq, A., & Khoo, M. B. (2019). New adaptive EWMA control charts for monitoring univariate and multivariate coefficient of variation. Computers & Industrial Engineering, 131, 28-40.Haq, A., Bibi, N., & Chong Khoo, M. B. (2020). Enhanced EWMA charts for monitoring the process coefficient of variation. Quality and Reliability Engineering International, 36(7), 2478-2494.Hong, E. P., Kang, C. W., Baek, J. W., & Kang, H. W. (2008). Development of CV control chart using EWMA technique. Journal of the Society of Korea Industrial and Systems Engineering, 31(4), 114-120.Iglewicz, B. (1967). Some Properties of the Sample Coefficient of Variation. Unpublished Ph.D. Dissertation, Virginia Polytechnic Institute and State University.Kang, C. W., Lee, M. S., Seong, Y. J., & Hawkins, D. M. (2007). A control chart for the coefficient of variation. Journal of Quality Technology, 39(2), 151-158.Khatun, M., Khoo, M. B., Lee, M. H., & Castagliola, P. (2019). One-sided control charts for monitoring the multivariate coefficient of variation in short production runs. Transactions of the Institute of Measurement and Control, 41(6), 1712-1728.Khaw, K. W., Khoo, M. B., Yeong, W. C., & Wu, Z. (2017). Monitoring the coefficient of variation using a variable sample size and sampling interval control chart. Communications in Statistics-Simulation and Computation, 46(7), 5772-5794.Khaw, K. W., Khoo, M. B., Castagliola, P., & Rahim, M. A. (2018). New adaptive control charts for monitoring the multivariate coefficient of variation. Computers & Industrial Engineering, 126, 595-610.Khaw, K. W., Chew, X., Yeong, W. C., & Lim, S. L. (2019). Optimal design of the synthetic control chart for monitoring the multivariate coefficient of variation. Chemometrics and Intelligent Laboratory Systems, 186, 33-40.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.Reed, G. F., Lynn, F., & Meade, B. D. (2002). Use of coefficient of variation in assessing variability of quantitative assays. Clinical and Vaccine Immunology, 9(6), 1235-1239.Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 42(1), 97-101.Teoh, W. L., Khoo, M. B., Castagliola, P., Yeong, W. C., & Teh, S. Y. (2017). Run-sum control charts for monitoring the coefficient of variation. European Journal of Operational Research, 257(1), 144-158.Voinov V. G., Nikulin M. S. (1996). Unbiased Estimators and Their Applications. Multivariate Case, Vol. 2. Kluwer: Dordrecht.Yeong, W. C., Lee, P. Y., Lim, S. L., Khaw, K. W., & Khoo, M. B. C. (2021). A side‐sensitive synthetic coefficient of variation chart. Quality and Reliability Engineering International, 37(5), 2014-2033.Yahaya, M., Lim, S. L., Ibrahim, A. I. N., Yeong, W. C., & Khoo, M. B. C. (2022). A variable sample size synthetic chart for the coefficient of variation. South African Journal of Industrial Engineering, 33(1), 1-15.Yeong, W. C., Tan, Y. Y., Lim, S. L., Khaw, K. W., & Khoo, M. B. C. (2022). A variable sample size run sum coefficient of variation chart. Quality and Reliability Engineering International, 38(4), 1869-1885.Yeong, W. C., Khoo, M. B. C., Teoh, W. L., & Castagliola, P. (2016). A control chart for the multivariate coefficient of variation. Quality and Reliability Engineering International, 32(3), 1213-1225.Yeong, W. C., Khoo, M. B., Lim, S. L., & Lee, M. H. (2017). A direct procedure for monitoring the coefficient of variation using a variable sample size scheme. Communications in Statistics-Simulation and Computation, 46(6), 4210-4225.You, H. W., Khoo, M. B., Castagliola, P., & Haq, A. (2016). Monitoring the coefficient of variation using the side sensitive group runs chart. Quality and Reliability Engineering International, 32(5), 1913-1927.Zhang, J., Li, Z., Chen, B., & Wang, Z. (2014). A new exponentially weighted moving average control chart for monitoring the coefficient of variation. Computers & Industrial Engineering, 78, 205-212. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202201231 en_US
