English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  Items with full text/Total items : 113303/144284 (79%)
Visitors : 50807658      Online Users : 880
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
  • Adv. Search
    HomeLoginUploadHelpAboutAdminister Goto mobile version
    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/99315
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/99315


    Title: 中位數和四分位距管制圖設計之研究
    Study on Design of Median and IQR Control Charts for Monitoring Location and Dispersion
    Authors: 姜亭安
    Contributors: 楊素芬
    姜亭安
    Keywords: 平均連串長度
    不受分配限制
    統計製程管制
    雙次抽樣
    Average run length
    Distribution-free
    Statistical process control
    Double sampling
    Date: 2016
    Issue Date: 2016-07-20 16:53:05 (UTC+8)
    Abstract: 不論在製造流程或是其他產業上,管制圖是一個能夠監督流程失控的非常有效工具。不受分配限制的管制圖的發展對於非常態或分配未知的品質變數是非常重要的。根據無母數方法所建立的不受分配限制的管制圖對使用者來說是不容易的,因為他們並不是統計學家。本文提出了一種簡單的指數加權移動平均(EWMA)中位數和四分位距管制圖,採用單次抽樣方法和雙次抽樣方法以分別監控製程的位置與離散程度。此外,本文亦提出了一種核密度估計方法的管制區以同時監控製程的位置與離散程度。這裡以平均連串長度(ARL)來衡量所提出的管制圖的偵測效果。我們比較所提出的管制圖以及現有的一些不受分配限制的管制圖的偵測效果。以服務時間的示例來說明所提出的指數加權移動平均中位數管制圖、指數加權移動平均四分位距管制圖和核密度估計方法的管制區的應用。與其他現有的不受分配限制的管制圖相比,所提出的管制圖在製程的位置與離散有小幅度的偏移時有較好的偵測效果。因此,我們建議可以使用所提出的管制圖。
    Control charts are effective tools for monitoring the process parameters in manufacturing processes and other industries. The development of distribution-free charts is important for non-normal or unknown distributed quality variable in statistical process control. The distribution-free control charts based on nonparametric statistics are not easy for practitioners to apply because they are not statisticians and do not know the scheme. This paper proposes a simple EWMA median chart and IQR char with single sampling scheme and double sampling scheme to monitor the location and dispersion, respectively. Furthermore, a kernel control region is proposed for monitoring the location and dispersion simultaneously. The average run lengths (ARL) is used to measure the detection performance of the proposed control chart(s). We compare the location and dispersion detection performance of the proposed charts and those of some existing distribution-free charts. An example of service times is used to illustrate the application of the proposed EWMA median and EWMA IQR charts and kernel control region. The proposed charts show superior detection performance compared to the existing distribution-free location and dispersion charts when the shifts in process location and/or dispersion are small. The SS EWMA-Md and DS EWMA-D charts and SS kernel control region are thus recommended.
    Reference: Bakir, S., & Reynolds, M. (1979). A Nonparametric Procedure for Process Control Based on Within-Group Ranking. Technometrics, 21, 175-183.
    [2] Chacón, J. E., & Duong, T. (2010). Multivariate plug-in bandwidth selection with unconstrained pilot bandwidth matrices. Test, 19(2), 375-398.
    [3] Chowdhury, S., Mukherjee, A., & 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.
    [4] Das, N. (2008). Non-parametric control chart for controlling variability based on rank test. Economic Quality Control, 23(2), 227-242.
    [5] Daudin, J. J. (1992). Double sampling X̄ charts. Journal of Quality Technology, 24(2), 78-87.
    [6] Downton, F. (1966). Linear estimates with polynomial coefficients. Biometrika, 53(1/2), 129-141.
    [7] Ghute, V. (2014). Nonparametric control chart for variability using runs rules. The Experiment, 24(4), 1683-1691.
    [8] Hawkins, D.M., and Olwell, D.H. (1998), Cumulative Sum Charts and Charting for Quality Improvement, New York: Springer-Verlag.
    [9] Hawkins, D.M., Qiu, P., and Chang Wook Kang (2003), The changepoint model for statistical process control. Journal of Quality Technology, 35, 355–366.
    [10] He, D., & Grigoryan, A. (2002). Construction of double sampling s‐control charts for agile manufacturing. Quality and Reliability Engineering International, 18(4), 343-355.
    [11] He, D., & Grigoryan, A. (2003). An improved double sampling s chart. International Journal of Production Research, 41(12), 2663-2679.
    [12] Hu, F.-S. (2015). Design of a Control Region for Monitoring Joint Location and Dispersion.
    [13] Jensen, W. A., Jones-Farmer, L. A., Champ, C. W., & Woodall, W. H. (2006). Effects of parameter estimation on control chart properties: a literature review. Journal of Quality Technology, 38(4), 349.
    [14] Jones, M. A., & Steiner, S. H. (2012). Assessing the effect of estimation error on risk-adjusted CUSUM chart performance. International Journal for Quality in Health Care, 24(2), 176-181.
    [15] Khoo, M. B. (2005). A control chart based on sample median for the detection of a permanent shift in the process mean. Quality engineering, 17(2), 243-257.
    [16] Lepage, Y. (1971). A combination of Wilcoxon`s and Ansari-Bradley`s statistics. Biometrika, 58(1), 213-217.
    [17] Liu, L., Tsung, F., & Zhang, J. (2014). Adaptive nonparametric CUSUM scheme for detecting unknown shifts in location. International Journal of Production Research, 52(6), 1592-1606.
    [18] Liu, R. Y., & Tang, J. (1996). Control charts for dependent and independent measurements based on bootstrap methods. Journal of the American Statistical Association, 91(436), 1694-1700.
    [19] Lucas, J. M., & Saccucci, M. S. (1990). Exponentially weighted moving average control schemes: properties and enhancements. Technometrics, 32(1), 1-12.
    [20] McCracken, A., & Chakraborti, S. (2013). Control charts for joint monitoring of mean and variance: an overview. Quality Technology & Quantitative Management, 10(1), 17-36.
    [21] Montgomery, D. C. (2009). Statistical quality control (Vol. 7): Wiley New York.
    [22] Mood AM. (1954). On the asymptotic efficiency of certain nonparametric two-sample tests. Annals of Mathematical Statistics 1954; 25: 514-522.
    [23] Mukherjee, A., & 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.
    [24] Nelson, L. S. (1963). Tables for a precedence life test. Technometrics, 5(4), 491-499..
    [25] Nelson, L. S. (1993) Tests on early failures: the precedence life test. Journal of quality technology, 25(2), 140-143.
    [26] Page, E. (1954). Continuous inspection schemes. Biometrika, 41(1/2), 100-115.
    [27] Parzen, E. (1962). On estimation of a probability density function and mode. Annals of Mathematical Statistics 33: 1065–1076.
    [28] Rosenblatt, M. (1956). Remarks on some nonparametric estimates of a density function. Annals of Mathematical Statistics 27: 832–837
    [29] Shewhart, W. A. (1931). Economic control of quality of manufactured product: ASQ Quality Press.
    [30] Siegel, S., & Tukey, J. W. (1960). A nonparametric sum of ranks procedure for relative spread in unpaired samples. Journal of the American Statistical Association, 55(291), 429-445.
    [31] Stromberg, A., Griffith, W., & Smith, M. (2003). Control Charts for the Median and Interquartile Range. In R. Dutter, Filzmoser, P., Gather, U., Rousseeuw, P. (Ed.), International Conference on Robust Statistics 2001-Developments in Robust Statistics (pp. 368-376). Heidelberg GmbH: Springer-Verlag Berlin.
    [32] Sukhatme, B. V. (1957). On certain two-sample nonparametric tests for variances. The Annals of Mathematical Statistics, 28(1), 188-194.
    [33] Wu, C. F. (1990). On the asymptotic properties of the jackknife histogram. The Annals of Statistics, 1438-1452.
    [34] Yang, L., Pai, S., & Wang, Y. R. (2010). A novel CUSUM median control chart. Paper presented at the Proceedings of International Multiconference of Engineers and Computer Scientists.
    [35] Yang, S. F. (2013). Using a new VSI EWMA average loss control chart to monitor changes in the difference between the process mean and target and/or the process variability. Applied Mathematical Modelling, 37(16), 7973-7982.
    [36] Yang, S. F., & Arnold, B. C. (2014). A Simple Approach for Monitoring Business Service Time Variation. The Scientific World Journal, 2014, 238719. doi:10.1155/2014/238719
    [37] Yang, S. F., & Cheng, S. W. (2011). A new non‐parametric CUSUM mean chart. Quality and Reliability Engineering International, 27(7), 867-875.
    [38] Yang, S. F., Cheng, T. C., Hung, Y. C., & W Cheng, S. (2012). A new chart for monitoring service process mean. Quality and Reliability Engineering International, 28(4), 377-386.
    [39] Zhang, G. (2014). Improved R and s control charts for monitoring the process variance. Journal of Applied Statistics, 41(6), 1260-1273. doi:10.1080/02664763.2013.864264
    [40] Zou, C., & Tsung, F. (2010). Likelihood ratio-based distribution-free EWMA control charts. Journal of Quality Technology, 42(2), 174.
    Description: 碩士
    國立政治大學
    統計學系
    103354005
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G1033540051
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

    Files in This Item:

    File SizeFormat
    005101.pdf2961KbAdobe PDF253View/Open


    All items in 政大典藏 are protected by copyright, with all rights reserved.


    社群 sharing

    著作權政策宣告 Copyright Announcement
    1.本網站之數位內容為國立政治大學所收錄之機構典藏,無償提供學術研究與公眾教育等公益性使用,惟仍請適度,合理使用本網站之內容,以尊重著作權人之權益。商業上之利用,則請先取得著作權人之授權。
    The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

    2.本網站之製作,已盡力防止侵害著作權人之權益,如仍發現本網站之數位內容有侵害著作權人權益情事者,請權利人通知本網站維護人員(nccur@nccu.edu.tw),維護人員將立即採取移除該數位著作等補救措施。
    NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - Feedback