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題名 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
作者 姜亭安
貢獻者 楊素芬
姜亭安
關鍵詞 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
日期 2016
上傳時間 20-Jul-2016 16:53:05 (UTC+8)
摘要 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.
參考文獻 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.
描述 碩士
國立政治大學
統計學系
103354005
資料來源 http://thesis.lib.nccu.edu.tw/record/#G1033540051
資料類型 thesis
dc.contributor.advisor 楊素芬zh_TW
dc.contributor.author (Authors) 姜亭安zh_TW
dc.creator (作者) 姜亭安zh_TW
dc.date (日期) 2016en_US
dc.date.accessioned 20-Jul-2016 16:53:05 (UTC+8)-
dc.date.available 20-Jul-2016 16:53:05 (UTC+8)-
dc.date.issued (上傳時間) 20-Jul-2016 16:53:05 (UTC+8)-
dc.identifier (Other Identifiers) G1033540051en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/99315-
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) 103354005zh_TW
dc.description.abstract (摘要) 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。zh_TW
dc.description.abstract (摘要) 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.en_US
dc.description.tableofcontents 1. Introduction 1
2. The EWMA-Md Chart 5
2.1. Construction of the EWMA-Md chart 5
2.1.1. Determination of the control limits of the EWMA-Md chart 7
2.2. Detection performance of the EWMA-Md chart 7
2.3. Performance comparison with existing location control charts 9
3. The DS EWMA-Md chart 15
3.1. Construction of the DS EWMA-Md chart 15
3.1.1. Use simulation to calculate ARL and EN of the DS EWMA-Md chart 17
3.1.2. Determination of the control limits of the DS EWMA-Md chart 18
3.2. Detection performance of the DS EWMA-Md chart 19
3.3. Performance comparison of the proposed single sampling (SS) and DS EWMA-Md charts 21
4. The EWMA-D Chart 22
4.1. Construction of the EWMA-D chart 22
4.1.1. Determination of the control limits of the EWMA-D control chart 24
4.2. Detection performance of the EWMA-D chart 24
5. The DS EWMA-D Chart 25
5.1. Construction of the DS EWMA-D chart 25
5.1.1. Use simulation to calculate ARL and EN of the DS EWMA-D chart 27
5.1.2. Determination of the control limits of the DS EWMA-D chart 28
5.2. Detection performance of the DS EWMA-D chart 29
5.3. Performance comparison of the proposed SS and DS EWMA-D charts 32
5.4. Performance comparison with existing dispersion control charts 33
6. Monitoring Location and Dispersion Simultaneously 36
6.1. Design of the kernel control region 36
6.1.1. Kernel density estimation 37
6.1.2. Determination of the control region based on joint statistics of the EWMA-Md and EWMA-D 38
6.1.3. Detection performance of the proposed kernel control region 40
6.1.4. Design of the proposed kernel control chart 40
6.1.5. Misusing both the EWMA-Md and EWMA-D charts to monitor the process location and/or dispersion. 42
6.2. DS kernel control region 42
6.2.1. Design of the DS control region constructed by joint statistics of EWMA-Md and EWMA-D 42
6.2.2. Detection performance of the DS kernel control region 45
6.3. Performance comparison with existing control charts 48
7. Real Example 60
7.1. Example for single sampling scheme 60
7.2. Example for double sampling scheme 66
8. Contamination 74
8.1. The SS and DS EWMA-Md charts with contamination 74
8.2. The SS and DS EWMA-D charts with contamination 75
9. Summary 79
10. Reference 80		zh_TW
dc.format.extent 3032704 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G1033540051en_US
dc.subject (關鍵詞) 平均連串長度zh_TW
dc.subject (關鍵詞) 不受分配限制zh_TW
dc.subject (關鍵詞) 統計製程管制zh_TW
dc.subject (關鍵詞) 雙次抽樣zh_TW
dc.subject (關鍵詞) Average run lengthen_US
dc.subject (關鍵詞) Distribution-freeen_US
dc.subject (關鍵詞) Statistical process controlen_US
dc.subject (關鍵詞) Double samplingen_US
dc.title (題名) 中位數和四分位距管制圖設計之研究zh_TW
dc.title (題名) Study on Design of Median and IQR Control Charts for Monitoring Location and Dispersionen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) 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.		zh_TW