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題名 無母數模糊相關權重指數加權移動平均管制圖設計
An nonparametric Fuzzy Relative Weight Exponentially Weighted Moving Average control chart design
作者 游善涵
You, Shan Han
貢獻者 鄭宇庭<br>郭訓志
Cheng, Yu Ting<br>Ku, Hsun Chih
游善涵
You, Shan Han
關鍵詞 無母數管制圖
移動加權平均
模糊相關權重
日期 2018
上傳時間 1-六月-2018 17:34:09 (UTC+8)
摘要 隨著品質管制技術的開發，越來越多產業將品質管制的理念應用在產業資料中，而品質管制的方法非常多樣，其中統計製程管制(SPC)為品質管制中重要的技術，其主要是以統計理論背景做支持對產品製程進行監控，本文也將針對SPC中理論背景較完整的管制圖方法做進一步的研究，然而品管在實務應用上，母體資料通常為非特定分配或者未知分配，諸多文獻中已證實，若使用特定假設分配的有母數管制圖用於製程狀態為非假設分布時，會導致管制狀態下的平均連串長度不穩健的情形，若使用無母數管制圖做監控，其管制狀態平均連串長度具有穩健性，因此無母數管制圖實用性能高出許多，近年來對無母數管制圖的研究越來越進步，然而現存的無母數管制圖大多是針對產品製程中平均數、變異數的變動，或者是使用符號函數(sign function)、排序(rank)等方式對觀測值和目標值的差距做監控，又或者觀察資料的分佈狀況監控其分配或目標值是否有偏移的情形等，較少有針對觀測值前後之間變動的差距來偵測資料出現偏移的狀況，因此本文提出一個新的無母數管制圖，想利用模糊相關權重統計量的性質來呈現觀測值之間變動的情形，以此統計量為基礎，建構無母數模糊相關權重指數加權平均(FRWEWMA)管制圖，對製程資料中的平均數(位置參數)和標準差(尺度參數)進行監控，並透過平均連串長度來比較FRWEWMA 管制圖和其他管制圖偵測效能的差異與優勢為何。
參考文獻 一、中文文獻
1. 黃榮臣、張耕銘，2012，利用無母數EWMA 管制圖監控製程平均數/位置參
數與變異數/尺度參數。
2. 黃子銘、鄭舜壕，2010，無母數指數加權移動平管制圖伴隨變動管制界線。
二、英文文獻
1. Amin, R.W. and A. J. Searcy. 1991. A nonparametric exponentially weighted
moving average control scheme. Communications in Statistics - Simulation and
Computation, Vol. 20, No. 4, pp.1049-1072.
2. Balakrishnan, N. and H. K.T. Ng. 2006. Precedence-type tests and applications.
3. Borror, C. M. and D. C. Montgomery. 1999. Robustness of the EWMA control
chart to non-normality. Journal of Quality Technology, Vol. 31, No. 3, pp.309-
316.
4. Chahraborti, S. 2011. Distribution-Free quality control charts.
5. Chakraborti, S., P. Van Der Laan, and S. T. Bakir. 2001. Nonparametric control
charts: An overview and some results. Journal of Quality Technology, Vol. 33,
No3, pp.304-315.
6. Chakraborti, S., S. W. Human, and M. A. Graham. 2008. Phase I statistic process
control charts: an overview and some results. Quality Engineering, Vol. 21, No.
1, pp.52-62
7. Champ, C. W. and S. E. Rigdon. 2007. A comparison of the markov chain and
the integral equation approaches for evaluating the run length distribution of
quality control charts. Communications in Statistics - Simulation and
Computation, Vol. 20, No. 1, pp.191-204.
8. Yang, C. C. 2017. An Evaluation of the FRWMA Chart for Dependent Interval‧
valued Data. Cluster Computing, Vol. 17, No. 6, pp.1-8.
9. Gemai, C., W. C. Smiley, and X. Hansheng. 2001. Monitoring process mean and
variability with one EWMA chart. Journal of Quality Technology, Vol. 33, No.
2, pp.223-233.
10. Gibbons, J. D. and S. Chakraborti. 2003. Nonparametric statistic inference.
pp.508
11. Gramham, M. A., A. Mukherjee and S. Chahraborti. 2012. Distribution-free
exponentially weighted moving average control charts for monitoring unknown
location. Computational Statistics & Data Analysis, Vol. 56, No. 8, pp.2539-
2561.
12. Gramham, M. A., S. Chahraborti and S. W. Human. 2011. A nonparametric
exponentially weighted moving average signed-rank chart for monitoring
location. Computational Statistics & Data Analysis, Vol. 55, No. 8, pp.2490-
2503.
13. Hackl, P. and J. Leodolter. 1999. A control chart based on ranks. Journal of
Quality Technology, Vol. 23, No. 2, pp.117-124.
14. Longcheen, H., C. J. Huang and Y. H. T. Wang. 2010. New EWMA control
charts for monitoring process dispersion. Computational Statistics & Data
Analysis, Vol. 54, No. 10, pp.2328-2342.
15. Lucas, M. J. and S. M. Saccucci. 1990. Exponentially weighted moving average
control schemes: properties and enhancements. Technometrics, Vol. 32, No. 1,
pp.1-12.
16. Montgomery, D. C., G. C. Runger and N. F. Hubele. 2009. Statistical quality
control. pp. 386-411.
17. Roberts, S. W. 1959. Control chart test based on geometric moving averages.
Technometrics, Vol. 1, No. 3, pp.239-250.
18. Robinson, P. B. and T. Y. Ho. 1978. Average run lengths of geometric moving
average charts by numerical methods. Technometrics, Vol. 20, No. 1, pp.85-93
19. Stoumbos, Z. G. and J. H. Sullivan. 2002. Robustness to non-normarlity of
multivariate EWMA control chart. Journal of Quality Technology, Vol. 34, No.
3, pp.260-276.
20. Li, S. U., T. L. Ching and S. H. Ng. 2010. Nonparametric CUSUM and EWMA
control charts for detecting mean shifts. Journal of Quality Technology, Vol. 42,
No. 2, pp.209-226.
21. Woodall, W. H. and D. C. Montgomery. 1999. Research issues and ideas in
statistical process control. Journal of Quality Technology, Vol. 49, No. 4,
pp.376-386
描述 碩士
國立政治大學
統計學系
105354012
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0105354012
資料類型 thesis
dc.contributor.advisor 鄭宇庭<br>郭訓志zh_TW
dc.contributor.advisor Cheng, Yu Ting<br>Ku, Hsun Chihen_US
dc.contributor.author (作者) 游善涵zh_TW
dc.contributor.author (作者) You, Shan Hanen_US
dc.creator (作者) 游善涵zh_TW
dc.creator (作者) You, Shan Hanen_US
dc.date (日期) 2018en_US
dc.date.accessioned 1-六月-2018 17:34:09 (UTC+8)-
dc.date.available 1-六月-2018 17:34:09 (UTC+8)-
dc.date.issued (上傳時間) 1-六月-2018 17:34:09 (UTC+8)-
dc.identifier (其他 識別碼) G0105354012en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/117441-
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) 105354012zh_TW
dc.description.abstract (摘要) 隨著品質管制技術的開發，越來越多產業將品質管制的理念應用在產業資料中，而品質管制的方法非常多樣，其中統計製程管制(SPC)為品質管制中重要的技術，其主要是以統計理論背景做支持對產品製程進行監控，本文也將針對SPC中理論背景較完整的管制圖方法做進一步的研究，然而品管在實務應用上，母體資料通常為非特定分配或者未知分配，諸多文獻中已證實，若使用特定假設分配的有母數管制圖用於製程狀態為非假設分布時，會導致管制狀態下的平均連串長度不穩健的情形，若使用無母數管制圖做監控，其管制狀態平均連串長度具有穩健性，因此無母數管制圖實用性能高出許多，近年來對無母數管制圖的研究越來越進步，然而現存的無母數管制圖大多是針對產品製程中平均數、變異數的變動，或者是使用符號函數(sign function)、排序(rank)等方式對觀測值和目標值的差距做監控，又或者觀察資料的分佈狀況監控其分配或目標值是否有偏移的情形等，較少有針對觀測值前後之間變動的差距來偵測資料出現偏移的狀況，因此本文提出一個新的無母數管制圖，想利用模糊相關權重統計量的性質來呈現觀測值之間變動的情形，以此統計量為基礎，建構無母數模糊相關權重指數加權平均(FRWEWMA)管制圖，對製程資料中的平均數(位置參數)和標準差(尺度參數)進行監控，並透過平均連串長度來比較FRWEWMA 管制圖和其他管制圖偵測效能的差異與優勢為何。zh_TW
dc.description.tableofcontents 目 錄 I
表目錄 II
圖目錄 III
第壹章 緒論 1
第一節 研究背景 1
第二節 研究動機與目的 2
第三節 研究流程 3
第貳章 EWMA管制圖 4
第一節 EWMA管制理論 4
第二節 管制圖效能評估準則-平均連串長度 10
第參章 模糊相關權重 13
第一節 模糊相關權重的介紹 13
第二節 模糊相關權重的應用 14
第肆章 模糊相關權重指數加權移動平均管制圖 22
第一節 模糊相關權重指數加權移動平均(FRW Exponentially Weighted Moving Average, FRWEWMA)管制圖設計 22
第二節 模擬分析 26
第三節 實證分析 46
第伍章 結論與建議 49
第一節 結論 49
第二節 建議 50
參考文獻 52		zh_TW
dc.format.extent 1431851 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0105354012en_US
dc.subject (關鍵詞) 無母數管制圖zh_TW
dc.subject (關鍵詞) 移動加權平均zh_TW
dc.subject (關鍵詞) 模糊相關權重zh_TW
dc.title (題名) 無母數模糊相關權重指數加權移動平均管制圖設計zh_TW
dc.title (題名) An nonparametric Fuzzy Relative Weight Exponentially Weighted Moving Average control chart designen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) 一、中文文獻
1. 黃榮臣、張耕銘，2012，利用無母數EWMA 管制圖監控製程平均數/位置參
數與變異數/尺度參數。
2. 黃子銘、鄭舜壕，2010，無母數指數加權移動平管制圖伴隨變動管制界線。
二、英文文獻
1. Amin, R.W. and A. J. Searcy. 1991. A nonparametric exponentially weighted
moving average control scheme. Communications in Statistics - Simulation and
Computation, Vol. 20, No. 4, pp.1049-1072.
2. Balakrishnan, N. and H. K.T. Ng. 2006. Precedence-type tests and applications.
3. Borror, C. M. and D. C. Montgomery. 1999. Robustness of the EWMA control
chart to non-normality. Journal of Quality Technology, Vol. 31, No. 3, pp.309-
316.
4. Chahraborti, S. 2011. Distribution-Free quality control charts.
5. Chakraborti, S., P. Van Der Laan, and S. T. Bakir. 2001. Nonparametric control
charts: An overview and some results. Journal of Quality Technology, Vol. 33,
No3, pp.304-315.
6. Chakraborti, S., S. W. Human, and M. A. Graham. 2008. Phase I statistic process
control charts: an overview and some results. Quality Engineering, Vol. 21, No.
1, pp.52-62
7. Champ, C. W. and S. E. Rigdon. 2007. A comparison of the markov chain and
the integral equation approaches for evaluating the run length distribution of
quality control charts. Communications in Statistics - Simulation and
Computation, Vol. 20, No. 1, pp.191-204.
8. Yang, C. C. 2017. An Evaluation of the FRWMA Chart for Dependent Interval‧
valued Data. Cluster Computing, Vol. 17, No. 6, pp.1-8.
9. Gemai, C., W. C. Smiley, and X. Hansheng. 2001. Monitoring process mean and
variability with one EWMA chart. Journal of Quality Technology, Vol. 33, No.
2, pp.223-233.
10. Gibbons, J. D. and S. Chakraborti. 2003. Nonparametric statistic inference.
pp.508
11. Gramham, M. A., A. Mukherjee and S. Chahraborti. 2012. Distribution-free
exponentially weighted moving average control charts for monitoring unknown
location. Computational Statistics & Data Analysis, Vol. 56, No. 8, pp.2539-
2561.
12. Gramham, M. A., S. Chahraborti and S. W. Human. 2011. A nonparametric
exponentially weighted moving average signed-rank chart for monitoring
location. Computational Statistics & Data Analysis, Vol. 55, No. 8, pp.2490-
2503.
13. Hackl, P. and J. Leodolter. 1999. A control chart based on ranks. Journal of
Quality Technology, Vol. 23, No. 2, pp.117-124.
14. Longcheen, H., C. J. Huang and Y. H. T. Wang. 2010. New EWMA control
charts for monitoring process dispersion. Computational Statistics & Data
Analysis, Vol. 54, No. 10, pp.2328-2342.
15. Lucas, M. J. and S. M. Saccucci. 1990. Exponentially weighted moving average
control schemes: properties and enhancements. Technometrics, Vol. 32, No. 1,
pp.1-12.
16. Montgomery, D. C., G. C. Runger and N. F. Hubele. 2009. Statistical quality
control. pp. 386-411.
17. Roberts, S. W. 1959. Control chart test based on geometric moving averages.
Technometrics, Vol. 1, No. 3, pp.239-250.
18. Robinson, P. B. and T. Y. Ho. 1978. Average run lengths of geometric moving
average charts by numerical methods. Technometrics, Vol. 20, No. 1, pp.85-93
19. Stoumbos, Z. G. and J. H. Sullivan. 2002. Robustness to non-normarlity of
multivariate EWMA control chart. Journal of Quality Technology, Vol. 34, No.
3, pp.260-276.
20. Li, S. U., T. L. Ching and S. H. Ng. 2010. Nonparametric CUSUM and EWMA
control charts for detecting mean shifts. Journal of Quality Technology, Vol. 42,
No. 2, pp.209-226.
21. Woodall, W. H. and D. C. Montgomery. 1999. Research issues and ideas in
statistical process control. Journal of Quality Technology, Vol. 49, No. 4,
pp.376-386		zh_TW