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題名 變動樣本大小的無母數平均值管制圖之研究
Study of nonparametric mean control chart with variable sample sizes
作者 周遊宇
Zhou, Youyu
貢獻者 楊素芬
周遊宇
Zhou, Youyu
關鍵詞 無母數管制圖
變動樣本
抽樣的樣本數期望值
平均連串長度
平均觀測值總數
Non-parametric
Variable sampling sizes
Expected value of the sample size
Average run length
The average number of observations to signal
日期 2017
上傳時間 24-Jul-2017 11:59:25 (UTC+8)
摘要 自舒華特發明以管制圖監測製程以來，管制圖在工程的應用日趨重要。在特殊工程中，一個高效的管制圖方法尤為重要。基於此項事實，在文獻中各式各樣的管制圖層出不窮且技術日益完善。但傳統管制圖往往受制于常態分佈，因此在無母數管制圖研究方向仍有大量工作值得探討。於是本文在母體分佈未知情況下，推廣Yang (2015)的無母數平均值管制圖方法建立變動樣本指数加权移动平均管制圖，VSS EWMA-np control chart。新的管制圖將變動樣本大小（VSS）和指數加權移動平均（EWMA）方法結合建立一種新的管制圖方法，並用這種新型管制圖監測未知分佈母體的平均值是否發生變動。而為了監測平均數是否發生變化，也為了減少抽樣損失，本文評估管制圖監測效力的指標為管制圖偵測出異常訊息所需抽樣的樣本數期望值（EN）、平均連串長度（ARL）和平均觀測值總數（ANOS）。從本文的比較結果看出新的變動樣本指數加權移動平均管制圖擁有更好的失控偵測力。
Since Shewhart invention control chart monitor the process, control charts are increasingly important in engineering applications. In special projects, an efficient control chart is especially important. Based on this fact, the various kinds of control charts in the literature are not poor and the technology is improving. However, traditional control charts are often subject to normal distribution, so there is still a lot of work to be discussed in the direction of the study of non-parametric control charts. So in this paper under unknown distribution in the matrix, Yang (2015) established on the basis of the theory of a non-parametric method of control chart - Exponentially Weighted Moving Average Control Chart with Variable Sampling Sizes (VSS EWMA - np control chart). New control chart will change the sample size (VSS) and exponential weighted moving average (EWMA) method to establish a new control chart, and use new control chart for monitoring the mean of unknown distribution matrix is changed. And whether to monitor the average changes in order to reduce the loss of sampling, this paper mainly evaluate control chart for monitoring the effectiveness of the statistics for the expected value of the sample size (EN), the average run length (ARL) and the average number of observations to signal (ANOS). From the comparison shown in this paper, the new control chart has better detection.
參考文獻 [1] Amin, R. M. R. Reynolds, Jr. and Bakir, S. T. (1995). “Nonparametric quality control charts based on the sign statistic.” Commun. Statist. -Theory Method, vol. 24, no. 6, pp. 1597-1624.
     [2] Altukif, P. F. (2003). “A new nonparametric control charts based on the observations exceeding the grand median.” Pakistan J. Statist., vol. 19, no. 3, pp. 343-351.
     [3] Altukife, F. (2003). “Nonparametric control charts based on sum of ranks.” Pakistan J. Statist., vol. 19, no. 3, pp. 291-300.
     [4] Bakir, S. T. and Reynolds, M. R. (1979), Jr. “A nonparametric procedure for process control based on within-group ranking.” Technometrics, vol. 21, no. 2, pp. 175-183.
     [5] Bakir, S. T. (2004). “A distribution-free Shewhart quality control chart based on signed-ranks.” Quality Eng., vol. 16, no. 4, pp. 613-623.
     [6] Bakir, S. T. (2006). “Distribution-free quality control charts based on signed-rank-like statistics.” Commun. Statist., Theory Methods, vol. 35, no. 4, pp. 743-757.
     [7] Chakraborti, S. and Eryilmaz, S. (2007). “A non-parametric Shewhart type sign rank control chart based on runs.” Commun. Statist., Simul. Comput., vol. 36, no. 2, pp. 335-356.
     [8] Chakraborti, S. and Graham, M. (2007). “Nonparametric Control Charts.” Ency clopedia of Quality and Reliability. New York, NY, USA: Wiley.
     [9] Chakraborti, S. P. van der Lann. and Bakir, S. T. (2001). “Nonparametric control charts: An overview and some results.” J. Quality Technol., vol. 33, no. 3, pp. 304-315.
     [10] Costa, A.F.B. (1994), “X-bar charts with variable sample size.” J. Qual. Technol., vol. 26, pp. 155-163.
     [11] Ferrell, E. B. (1953). “Control charts using midranges and medians.” Ind. Quality Control, vol. 9, pp. 30-34.
     [12] Graham, M. A. Chakraborti, S. and Human, S. W. (2011). “A nonparametric EWMA sign chart for location based on individual measurements.” Quality Eng., vol. 23, no. 3, pp. 227-241.
     [13] Graham, Chakraborti, M. A. S. and S. W. Human. (2011), “A nonparametric exponentially weighted moving average signed-rank chart for monitoring location.” Comput. Statist. Data Anal., vol. 55, no. 8, pp. 2490-2503.
     [14] Graham, M. A. Mukherjee, A. and Chakraborti, S. (2012). “Distribution-free exponentially weighted moving average control charts for monitoring unknown location.” Comput. Statist. Data Anal., vol. 56, no. 8, pp. 2539-2561.
     [15] Li. S. Tang, L. and Ng, S. (2010). “Nonparametric CUSUM and EWMA control charts for detecting mean shifts.” J. Quality Technol., vol. 42, no. 2, pp. 209-226.
     [16] Li. Z. and Song, X.D. (2014). “EWMA Median Control Chart with Variable Sampling Size.” Information Technology Journal., vol. 13, pp. 2369-2373.
     [17] Prabhu, S.S. Ruger, G.C. and Keats, J.B. (1993). “An adaptive sample size X-bar chart.” Int. J. Prod. Res., vol. 31, pp. 2895-2909.
     [18] Reynolds, Jr. M.R. and Arnold, J.C. (2001). “EWMA control charts with variable sample size and variable sample intervals.” IIE Trans., vol. 33, pp. 511-530.
     [19] Reynolds, Jr. M.R. (1996), “Variable-sampling-interval control charts with sampling at fixed times.” IIE Trans., vol. 28, pp. 497-510.
     [20] Saccucci, M.S. and Lucas, J.M. (1990). “Average run lengths for exponentially weighted moving average control schemes using the Markov chain approach.” J. Qual. Technol., vol. 22, pp. 154-162.
     [21] Yang, SF. and Chen, W. (2011), “Monitoring and Diagnosing Dependent Process Steps Using VSI Control Charts.” Journal of Statistical Planning and Inference, vol. 141, no. 5, pp. 1808-1816.
     [22] Yang, SF. and Cheng, S. (2011), “A New Nonparametric CUSUM Mean Chart.” Quality and reliability engineering international, vol. 27, no. 7, pp. 864-875.
     [23] Yang, SF., Cheng, T. Hung, Y. and Cheng, S. (2012), “A New Chart for Monitoring Service Process Mean, Quality and Reliability Engineering International.” vol. 28, no. 4, pp. 377-386.
     [24] Yang, SF. (2015), “An Improved Distribution-Free EWMA Mean Chart.” Communications in Statistics—Simulation and Computation, vol. 44, pp. 1-18.
     [25] Yang, SF. and Arnold, B. (2014), “A simple approach for monitoring business service time variation.” Scientic World Journal, pp. 16.
     [26] Yang, SF. and Arnold, B. (2016), “Signal Detection for Process with Unknown Distribution.” Advanced Materials Research, vol. 504, pp. 1472-1475.
     [27] Yang, SF. and Wu, SH. (2017), “A Double Sampling Scheme for Process Mean Monitoring.” IEE Access., vol.5, pp. 6668-6677.
     [28] Zou, C. and Tsung, F. (2010), “Likelihood ratio-based distribution-free EWMA control charts.” J. Quality Technol., vol. 42, no. 2, pp. 174-196.
描述 碩士
國立政治大學
統計學系
104354034
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0104354034
資料類型 thesis
dc.contributor.advisor 楊素芬zh_TW
dc.contributor.author (Authors) 周遊宇zh_TW
dc.contributor.author (Authors) Zhou, Youyuen_US
dc.creator (作者) 周遊宇zh_TW
dc.creator (作者) Zhou, Youyuen_US
dc.date (日期) 2017en_US
dc.date.accessioned 24-Jul-2017 11:59:25 (UTC+8)-
dc.date.available 24-Jul-2017 11:59:25 (UTC+8)-
dc.date.issued (上傳時間) 24-Jul-2017 11:59:25 (UTC+8)-
dc.identifier (Other Identifiers) G0104354034en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/111306-
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) 104354034zh_TW
dc.description.abstract (摘要) 自舒華特發明以管制圖監測製程以來，管制圖在工程的應用日趨重要。在特殊工程中，一個高效的管制圖方法尤為重要。基於此項事實，在文獻中各式各樣的管制圖層出不窮且技術日益完善。但傳統管制圖往往受制于常態分佈，因此在無母數管制圖研究方向仍有大量工作值得探討。於是本文在母體分佈未知情況下，推廣Yang (2015)的無母數平均值管制圖方法建立變動樣本指数加权移动平均管制圖，VSS EWMA-np control chart。新的管制圖將變動樣本大小（VSS）和指數加權移動平均（EWMA）方法結合建立一種新的管制圖方法，並用這種新型管制圖監測未知分佈母體的平均值是否發生變動。而為了監測平均數是否發生變化，也為了減少抽樣損失，本文評估管制圖監測效力的指標為管制圖偵測出異常訊息所需抽樣的樣本數期望值（EN）、平均連串長度（ARL）和平均觀測值總數（ANOS）。從本文的比較結果看出新的變動樣本指數加權移動平均管制圖擁有更好的失控偵測力。zh_TW
dc.description.abstract (摘要) Since Shewhart invention control chart monitor the process, control charts are increasingly important in engineering applications. In special projects, an efficient control chart is especially important. Based on this fact, the various kinds of control charts in the literature are not poor and the technology is improving. However, traditional control charts are often subject to normal distribution, so there is still a lot of work to be discussed in the direction of the study of non-parametric control charts. So in this paper under unknown distribution in the matrix, Yang (2015) established on the basis of the theory of a non-parametric method of control chart - Exponentially Weighted Moving Average Control Chart with Variable Sampling Sizes (VSS EWMA - np control chart). New control chart will change the sample size (VSS) and exponential weighted moving average (EWMA) method to establish a new control chart, and use new control chart for monitoring the mean of unknown distribution matrix is changed. And whether to monitor the average changes in order to reduce the loss of sampling, this paper mainly evaluate control chart for monitoring the effectiveness of the statistics for the expected value of the sample size (EN), the average run length (ARL) and the average number of observations to signal (ANOS). From the comparison shown in this paper, the new control chart has better detection.en_US
dc.description.tableofcontents 1.文獻綜述 1
     2.VSS EWMA-np control chart之建立 4
      2.1.VSS EWMA-np control chart的建立方法 4
      2.2.VSS EWMA-np control chart的管制界限決定 8
      2.3.VSS EWMA-np control chart之失控偵測力 17
     3.和文獻上無母數平均值管制圖的失控偵測力比較 20
      3.1.品質變數X_(j,t)為未知分佈時失控偵測力的比較 21
      3.2.品質變數X_(j,t)為已知分佈時失控偵測力的比較 31
     4.實際案例 59
     5.結論 67
     參考文獻 68
     附錄 71
      附錄一.馬爾科夫鏈詳細過程 71
      附錄二.不同樣本組合下VSS EWMA-np control chart在不同b值下 的完整結果 74		zh_TW
dc.format.extent 2985409 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0104354034en_US
dc.subject (關鍵詞) 無母數管制圖zh_TW
dc.subject (關鍵詞) 變動樣本zh_TW
dc.subject (關鍵詞) 抽樣的樣本數期望值zh_TW
dc.subject (關鍵詞) 平均連串長度zh_TW
dc.subject (關鍵詞) 平均觀測值總數zh_TW
dc.subject (關鍵詞) Non-parametricen_US
dc.subject (關鍵詞) Variable sampling sizesen_US
dc.subject (關鍵詞) Expected value of the sample sizeen_US
dc.subject (關鍵詞) Average run lengthen_US
dc.subject (關鍵詞) The average number of observations to signalen_US
dc.title (題名) 變動樣本大小的無母數平均值管制圖之研究zh_TW
dc.title (題名) Study of nonparametric mean control chart with variable sample sizesen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] Amin, R. M. R. Reynolds, Jr. and Bakir, S. T. (1995). “Nonparametric quality control charts based on the sign statistic.” Commun. Statist. -Theory Method, vol. 24, no. 6, pp. 1597-1624.
     [2] Altukif, P. F. (2003). “A new nonparametric control charts based on the observations exceeding the grand median.” Pakistan J. Statist., vol. 19, no. 3, pp. 343-351.
     [3] Altukife, F. (2003). “Nonparametric control charts based on sum of ranks.” Pakistan J. Statist., vol. 19, no. 3, pp. 291-300.
     [4] Bakir, S. T. and Reynolds, M. R. (1979), Jr. “A nonparametric procedure for process control based on within-group ranking.” Technometrics, vol. 21, no. 2, pp. 175-183.
     [5] Bakir, S. T. (2004). “A distribution-free Shewhart quality control chart based on signed-ranks.” Quality Eng., vol. 16, no. 4, pp. 613-623.
     [6] Bakir, S. T. (2006). “Distribution-free quality control charts based on signed-rank-like statistics.” Commun. Statist., Theory Methods, vol. 35, no. 4, pp. 743-757.
     [7] Chakraborti, S. and Eryilmaz, S. (2007). “A non-parametric Shewhart type sign rank control chart based on runs.” Commun. Statist., Simul. Comput., vol. 36, no. 2, pp. 335-356.
     [8] Chakraborti, S. and Graham, M. (2007). “Nonparametric Control Charts.” Ency clopedia of Quality and Reliability. New York, NY, USA: Wiley.
     [9] Chakraborti, S. P. van der Lann. and Bakir, S. T. (2001). “Nonparametric control charts: An overview and some results.” J. Quality Technol., vol. 33, no. 3, pp. 304-315.
     [10] Costa, A.F.B. (1994), “X-bar charts with variable sample size.” J. Qual. Technol., vol. 26, pp. 155-163.
     [11] Ferrell, E. B. (1953). “Control charts using midranges and medians.” Ind. Quality Control, vol. 9, pp. 30-34.
     [12] Graham, M. A. Chakraborti, S. and Human, S. W. (2011). “A nonparametric EWMA sign chart for location based on individual measurements.” Quality Eng., vol. 23, no. 3, pp. 227-241.
     [13] Graham, Chakraborti, M. A. S. and S. W. Human. (2011), “A nonparametric exponentially weighted moving average signed-rank chart for monitoring location.” Comput. Statist. Data Anal., vol. 55, no. 8, pp. 2490-2503.
     [14] Graham, M. A. Mukherjee, A. and Chakraborti, S. (2012). “Distribution-free exponentially weighted moving average control charts for monitoring unknown location.” Comput. Statist. Data Anal., vol. 56, no. 8, pp. 2539-2561.
     [15] Li. S. Tang, L. and Ng, S. (2010). “Nonparametric CUSUM and EWMA control charts for detecting mean shifts.” J. Quality Technol., vol. 42, no. 2, pp. 209-226.
     [16] Li. Z. and Song, X.D. (2014). “EWMA Median Control Chart with Variable Sampling Size.” Information Technology Journal., vol. 13, pp. 2369-2373.
     [17] Prabhu, S.S. Ruger, G.C. and Keats, J.B. (1993). “An adaptive sample size X-bar chart.” Int. J. Prod. Res., vol. 31, pp. 2895-2909.
     [18] Reynolds, Jr. M.R. and Arnold, J.C. (2001). “EWMA control charts with variable sample size and variable sample intervals.” IIE Trans., vol. 33, pp. 511-530.
     [19] Reynolds, Jr. M.R. (1996), “Variable-sampling-interval control charts with sampling at fixed times.” IIE Trans., vol. 28, pp. 497-510.
     [20] Saccucci, M.S. and Lucas, J.M. (1990). “Average run lengths for exponentially weighted moving average control schemes using the Markov chain approach.” J. Qual. Technol., vol. 22, pp. 154-162.
     [21] Yang, SF. and Chen, W. (2011), “Monitoring and Diagnosing Dependent Process Steps Using VSI Control Charts.” Journal of Statistical Planning and Inference, vol. 141, no. 5, pp. 1808-1816.
     [22] Yang, SF. and Cheng, S. (2011), “A New Nonparametric CUSUM Mean Chart.” Quality and reliability engineering international, vol. 27, no. 7, pp. 864-875.
     [23] Yang, SF., Cheng, T. Hung, Y. and Cheng, S. (2012), “A New Chart for Monitoring Service Process Mean, Quality and Reliability Engineering International.” vol. 28, no. 4, pp. 377-386.
     [24] Yang, SF. (2015), “An Improved Distribution-Free EWMA Mean Chart.” Communications in Statistics—Simulation and Computation, vol. 44, pp. 1-18.
     [25] Yang, SF. and Arnold, B. (2014), “A simple approach for monitoring business service time variation.” Scientic World Journal, pp. 16.
     [26] Yang, SF. and Arnold, B. (2016), “Signal Detection for Process with Unknown Distribution.” Advanced Materials Research, vol. 504, pp. 1472-1475.
     [27] Yang, SF. and Wu, SH. (2017), “A Double Sampling Scheme for Process Mean Monitoring.” IEE Access., vol.5, pp. 6668-6677.
     [28] Zou, C. and Tsung, F. (2010), “Likelihood ratio-based distribution-free EWMA control charts.” J. Quality Technol., vol. 42, no. 2, pp. 174-196.		zh_TW