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題名 雙次抽樣平均數和變異數管制圖設計之研究
Study on design of double sampling mean and variance control charts
作者 吳信宏
Wu, Sin Hong
貢獻者 楊素芬
Yang, Su Fen
吳信宏
Wu, Sin Hong
關鍵詞 二次抽樣
平均串連長度
二項分配
Double sampling
Average run length
Binomial distribution
日期 2016
上傳時間 2-Aug-2016 15:53:29 (UTC+8)
摘要 雙次抽樣平均數和變異數管制圖設計之研究
Control charts are effective tools for detecting manufacturing processes and service processes. Nowadays, much of the data in manufacturing or service industries comes from processes having non-normal or unknown distributions. The commonly used Shewhart control charts, which depend heavily on the normality assumption, are not appropriately used for this situation. In this paper, we propose a standardized dynamic double sampling asymmetric EWMA mean control chart (SDDS EWMA-AM chart), a standardized dynamic double sampling asymmetric EWMA variance control chart (SDDS EWMA-AV chart), and their combined charts (joint SDDS EWMA-AM and SDDS EWMA-AV charts) to monitor process mean, variance and both shifts, respectively. The charts based on the double sampling procedure and two simple distribution-free transformed statistics are used for non-normal distribution of a quality variable. The performance of the proposed charts and that of some existing distribution-free mean and variance charts are compared. Further, a non-normal service times example from the service system of a bank branch is used to illustrate the applications of the proposed charts and to compare detection performance with the existing distribution-free mean and variance control charts. The charts we proposed show superior detection performance compared to the existing distribution-free mean and variance charts. Thus they are recommended.
參考文獻 Carot, V., Jabaloyes, J. and Carot, T. (2002). "Combined double sampling and variable sampling interval X-bar chart." International Journal of Production Research 40(9): 2175-2186.
Chowdhury, S., Mukherjee, A. and 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): 191-204.
Daudin, J.J. (1992). "Double sampling X-bar charts." Quality control and applied statistics 37(11): 583-586.
Deng, Q. (2009). "Combined charts for mean and variance information." Journal of Quality Technology 41(4): 415-425.
Ghute, V. (2014). "Nonparametric Control Charts for Variability Using Runs Rules." The Experiment 24(4): 1683.
He, D. and Grigoryan, A. (2006). "Joint statistical design of double sampling X-bar and S charts." European Journal of Operational Research 168(1): 122-142.
Khoo, M. B. and Lim, E. (2005). "An improved R (range) control chart for monitoring the process variance." Quality and Reliability Engineering International 21(1): 43-50.
Lee, P.H., Chang, Y.C. and Torng, C.C. (2012). "A design of S control charts with a combined double sampling and variable sampling interval scheme." Communications in Statistics-Theory and Methods 41(1): 153-165.
Mukherjee, A. and Chakraborti, S. (2012). "A Distribution‐free Control Chart for the Joint Monitoring of Location and Scale." Quality and Reliability Engineering International 28(3): 335-352.
Torng, C.C. and Lee, P.H. (2009). "The Performance of Double Sampling X-bar Control Charts Under Non Normality." Communications in Statistics: Simulation and Computation 38(3): 541-557.
Yang, S.F. and Arnold, B. C. (2014). "A simple approach for monitoring business service time variation." The Scientific World Journal 2014. online publishing.
Yang, S.F. and Arnold, B. C. (2015). "A new approach for monitoring process variance." Journal of Statistical Computation and Simulation: 1-17. online publishing.
Zhang, C., Xie, M., Liu, J. and Goh, T. (2007). "A control chart for the Gamma distribution as a model of time between events." International Journal of Production Research 45(23): 5649-5666.
Zhang, G. (2014). "Improved R and S control charts for monitoring the process variance." Journal of Applied Statistics 41(6): 1260-1273.
Zhang, J., Zou, C. and Wang, Z. (2010). "A control chart based on likelihood ratio test for monitoring process mean and variability." Quality and Reliability Engineering International 26(1): 63-73.
Zou, C. and Tsung, F. (2010). "Likelihood ratio-based distribution-free EWMA control charts." Journal of Quality Technology 42(2): 174.
描述 碩士
國立政治大學
統計學系
103354016
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0103354016
資料類型 thesis
dc.contributor.advisor 楊素芬zh_TW
dc.contributor.advisor Yang, Su Fenen_US
dc.contributor.author (Authors) 吳信宏zh_TW
dc.contributor.author (Authors) Wu, Sin Hongen_US
dc.creator (作者) 吳信宏zh_TW
dc.creator (作者) Wu, Sin Hongen_US
dc.date (日期) 2016en_US
dc.date.accessioned 2-Aug-2016 15:53:29 (UTC+8)-
dc.date.available 2-Aug-2016 15:53:29 (UTC+8)-
dc.date.issued (上傳時間) 2-Aug-2016 15:53:29 (UTC+8)-
dc.identifier (Other Identifiers) G0103354016en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/99531-
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) 103354016zh_TW
dc.description.abstract (摘要) 雙次抽樣平均數和變異數管制圖設計之研究zh_TW
dc.description.abstract (摘要) Control charts are effective tools for detecting manufacturing processes and service processes. Nowadays, much of the data in manufacturing or service industries comes from processes having non-normal or unknown distributions. The commonly used Shewhart control charts, which depend heavily on the normality assumption, are not appropriately used for this situation. In this paper, we propose a standardized dynamic double sampling asymmetric EWMA mean control chart (SDDS EWMA-AM chart), a standardized dynamic double sampling asymmetric EWMA variance control chart (SDDS EWMA-AV chart), and their combined charts (joint SDDS EWMA-AM and SDDS EWMA-AV charts) to monitor process mean, variance and both shifts, respectively. The charts based on the double sampling procedure and two simple distribution-free transformed statistics are used for non-normal distribution of a quality variable. The performance of the proposed charts and that of some existing distribution-free mean and variance charts are compared. Further, a non-normal service times example from the service system of a bank branch is used to illustrate the applications of the proposed charts and to compare detection performance with the existing distribution-free mean and variance control charts. The charts we proposed show superior detection performance compared to the existing distribution-free mean and variance charts. Thus they are recommended.en_US
dc.description.tableofcontents 1. Introduction 1
2. The SDDS EWMA-AM Chart 3
2.1. Construction of the SDDS EWMA-AM Chart 3
2.2. Detection Performance of the SDDS EWMA-AM Chart 7
2.3. Performance Comparison with Existing Control Charts 14
2.4. Example 32
3. The SDDS EWMA-AV Chart 39
3.1. Construction of the SDDS EWMA-AV Chart 39
3.2. Detection Performance of the SDDS EWMA-AV Chart 43
3.3. Performance Comparison with Existing Control Charts 49
3.4. Example 63
4. The Joint SDDS EWMA-AM and SDDS EWMA-AV Charts 72
4.1. Construction of the Joint SDDS EWMA-AM and SDDS EWMA-AV Charts 72
4.2. Detection Performance of the Joint SDDS EWMA-AM and SDDS EWMA-AV Charts 76
4.3. Detection Performance of the Joint EWMA-AM and EWMA-AV Charts 94
4.4. Performance Comparison with Existing Control Charts 104
4.5. Example 129
5. Conclusions 140
References 141		zh_TW
dc.format.extent 4668697 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0103354016en_US
dc.subject (關鍵詞) 二次抽樣zh_TW
dc.subject (關鍵詞) 平均串連長度zh_TW
dc.subject (關鍵詞) 二項分配zh_TW
dc.subject (關鍵詞) Double samplingen_US
dc.subject (關鍵詞) Average run lengthen_US
dc.subject (關鍵詞) Binomial distributionen_US
dc.title (題名) 雙次抽樣平均數和變異數管制圖設計之研究zh_TW
dc.title (題名) Study on design of double sampling mean and variance control chartsen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Carot, V., Jabaloyes, J. and Carot, T. (2002). "Combined double sampling and variable sampling interval X-bar chart." International Journal of Production Research 40(9): 2175-2186.
Chowdhury, S., Mukherjee, A. and 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): 191-204.
Daudin, J.J. (1992). "Double sampling X-bar charts." Quality control and applied statistics 37(11): 583-586.
Deng, Q. (2009). "Combined charts for mean and variance information." Journal of Quality Technology 41(4): 415-425.
Ghute, V. (2014). "Nonparametric Control Charts for Variability Using Runs Rules." The Experiment 24(4): 1683.
He, D. and Grigoryan, A. (2006). "Joint statistical design of double sampling X-bar and S charts." European Journal of Operational Research 168(1): 122-142.
Khoo, M. B. and Lim, E. (2005). "An improved R (range) control chart for monitoring the process variance." Quality and Reliability Engineering International 21(1): 43-50.
Lee, P.H., Chang, Y.C. and Torng, C.C. (2012). "A design of S control charts with a combined double sampling and variable sampling interval scheme." Communications in Statistics-Theory and Methods 41(1): 153-165.
Mukherjee, A. and Chakraborti, S. (2012). "A Distribution‐free Control Chart for the Joint Monitoring of Location and Scale." Quality and Reliability Engineering International 28(3): 335-352.
Torng, C.C. and Lee, P.H. (2009). "The Performance of Double Sampling X-bar Control Charts Under Non Normality." Communications in Statistics: Simulation and Computation 38(3): 541-557.
Yang, S.F. and Arnold, B. C. (2014). "A simple approach for monitoring business service time variation." The Scientific World Journal 2014. online publishing.
Yang, S.F. and Arnold, B. C. (2015). "A new approach for monitoring process variance." Journal of Statistical Computation and Simulation: 1-17. online publishing.
Zhang, C., Xie, M., Liu, J. and Goh, T. (2007). "A control chart for the Gamma distribution as a model of time between events." International Journal of Production Research 45(23): 5649-5666.
Zhang, G. (2014). "Improved R and S control charts for monitoring the process variance." Journal of Applied Statistics 41(6): 1260-1273.
Zhang, J., Zou, C. and Wang, Z. (2010). "A control chart based on likelihood ratio test for monitoring process mean and variability." Quality and Reliability Engineering International 26(1): 63-73.
Zou, C. and Tsung, F. (2010). "Likelihood ratio-based distribution-free EWMA control charts." Journal of Quality Technology 42(2): 174.		zh_TW