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題名 建立管制區域來同時監控製程的位置與離散
Design of a Control Region for Monitoring Joint Location and Dispersion
作者 胡逢升
貢獻者 楊素芬
Yang, Su Fen
胡逢升
關鍵詞 控制區域
不受分配限制
核密度估計方法
同時監控製程
日期 2015
上傳時間 27-Jul-2015 11:21:28 (UTC+8)
摘要 不論在製造流程或是在服務流程上，管制圖是一個能夠監督流程失控的非常有效工具。現今社會中，在製造流程與服務流程上，資料大多來自非常態分佈或是未知的分佈，以至於最為人所常用且建立在常態分配假設下的舒華特管制圖不適用於此。此文章中，我們提出了一個使用核密度估計方法(kernel density estimation approach)來建構出一個不受分配限制的中位數與四分位差控制區域，以同時監控製程的位置與離散程度。平均連串長度(ARL)是用以測量管制圖的失控偵測能力。在此文章中，比較了我們所提出來的控制區域與文獻上其他無母數管制圖的偵測製程失控能力。數值分析顯示我們所提出的中位數與四分位數的控制區域在同時監測位置與離散的能力較好。文章中亦提出運用此控制區域的例子，最後則為本文章的總結。
Control charts are effective tools for monitoring quality of manufacturing processes and service processes. Nowadays, much of the data in service or manufacturing industries comes from processes having non-normal distributions or unknown distributions. The commonly used Shewhart mean and variable control charts, which depend heavily on the normality assumption, are not appropriately used here. In this article, we propose a distribution-free control region of the median and IQR using the kernel density estimation methods to simultaneously monitor the location and dispersion of an unknown underlying continuous distribution. Furthermore, the average run lengths (ARL) of the proposed control region is used to measure the out-of-control detection performance. The performance of the proposed control region and some other non-parametric charts for detecting out-of-control location and scale are compared. The proposed control region of the median and IQR shows as well or better detection performance compared to existing non-parametric control charts that can simultaneously monitor the location and scale. Numerical examples illustrate the application of the proposed control region. Summary and conclusions are offered.
參考文獻 [1] Abbasi, S.A. and Miller, A., (2011). “ MDEWMA chart: An efficient and robust
alternative to monitor process dispersion, ’’ Journal of Statistical Computation
and Simulation, 83(2), 247-268.
[2] Abbasi, S.A., Miller, A. and Riaz, M., (2013). “ Nonparameteric Progressive Control Chart for Monitoring Process Target, ” Quality and Reliability Engineering
International, 29, 1069-1080.
[3] Altukife, P. F., (2003). “ A new nonparametric control charts based on the
observations exceeding the grand median, ” Pakistan Journal of Statistics, 19(3), 343–351.
[4] Alwan, L. C., (1981). Statistical Process Analysis, McGraw-Hill: New York.
[5] Amin, R., Reynolds, M.R., and Baker, S., (1995). “ Nonparametric quality control
charts based on the sign statistic, ” Communications in Statistics—Theory and
Methods, 24, 1597–1624.
[6] Arnold, B.C., Balakrishnan, N., and Nagaraja, H.N., (1992). A First Course in
Order Statistics, John Wiley & Sons, Inc: New York.
[7] Azzalini, A., (1981). “ A note on the estimation of a distribution function and quantiles by a kernel method, ” Biometrika, 68(1), 326—328.
[8] Bowman, A.W. and Azzalini, A., (1997). Applied Smoothing Techniques for Data Analysis--The Kernel Approach with S-Plus Illustrations, Oxford Science Publication.
[9] Braun, W.J. and Park, D., (2008). “ Estimation of for individuals charts, ” Journal of Quality Technology, 40(3), 332–344.
[10] Casella, G. and Berger, R.L., (2002). Statistical Inference, second Edition, Duxbury (2002).
[11] Chacon, J.E. and Duong, T., (2010). “ Multivariate plug-in bandwidth selection with unconstrained pilot matrices, ” Test, 19, 375-398.
[12] Chakraborti, S. and Graham, M., (2007). Nonparametric Control Charts, Encyclopedia of Quality and Reliability, John Wiley & Sons, Inc: New York.
[13] Chakraborti, S., Lann, P. and Van der Wiel, M.A., (2001). “ Nonparametric control charts: an overview and some results, ” Journal of Quality Technology, 33(3), 304–315.
[14] Chao, M. T. and Cheng, S. W., (2008). “ On 2-D control charts, ” Quality Technology and Quantitative Management, 5(3), 243-261.
[15] 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.
[16] Das, N. and Bhattacharya, A., (2008). “ A new non-parametric control chart for controlling variability, ” Quality Technology and Quantitative Management, 5(4), 351–361.
[17] Duong, T. and Hazelton, M.L., (2003). “ Plug-in bandwidth matrices for bivariate kernel density estimation, ” Journal of Nonparametric Statistics, 15, 17-30.
[18] Gan, F.F., (1995). “ Joint Monitoring of Process Mean and Variance Using Exponentially Weighted Moving Average Control Charts, ” Technometrics, 37, 446-453.
[19] Jones, M.C., (1990). “ The performance of kernel density functions in kernel distribution estimation, ” Statistics and Probability Letters, 9, 129—132.
[20] Maravelakis, P., Panaretos, J., and Psararkis, S., (2005). “ An examination of the robustness to nonnormality of the EWMA control chart for the dispersion ”, Communications in Statistics: Simulation and Computation, 34 (4), 1069-1079.
[21] McCracken, A. K. and Chakraborti, S., (2013). “ Control charts for joint monitoring of the mean and variance: an overview, ” Quality Technology & Quantitative Management, 10(1), 17-36.
[22] Mukherjee, A. and Chakraborti, S., (2012). “ A nonparametric phase II control chart for simultaneous monitoring of location and scale, ” Quality and Reliability Engineering International, 28(3), 335-352.
[23] Park, B. U. and Marron, J. S., (1990). “ Comparison of data-driven bandwidth selectors, ” H. Am. Statist, 85, 66-72.
[24] Sheather, S. J. and Jones, M. C., (1991). “ A reliable data-based bandwidth selection method for kernel density estimation, ” Journal of the Royal Statistical Society, Series B, 53, 683–690.
[25] Silverman, BW., (1996). Density Estimation, Chapman & Hall: London.
[26] Sturges, H.A., (1926). “ The choice of a class interval, ” Journal of the American Statistical Association, 21, 65-66.
[27] Wand, M.P. and Jones, M.C., (1994). “ Multivariate plug in bandwidth selection, ” Computational Statistics, 9, 97-116.
[28] Yang, S.F. and Arnold, B.C., (2014). “ A Simple Approach for Monitoring Business Service Time Variation, ” The scientific World Journal, 2014, 1-16.
[29] Yang, S.F., Lin, J. and Cheng, S., (2011). “ A New Nonparametric EWMA Sign
Chart, ” Expert Systems with Applications, 38(5), 6239-6243.
[30] 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.
[31] Zhou, M., Geng W. and Wang Z., (2014). “ Likelihood Ratio-Based Distribution-Free Sequential Change-Point Detection, ” Journal of Statitical Computation and Simulation ,84(12), 2748-2758.
[32] Zou, C. and Tsung, F., (2010). “ Likelihood ratio-based distribution-free EWMA control Charts, ” Journal of Quality Technology, 42(2), 174-196.
描述 碩士
國立政治大學
統計研究所
102354007
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0102354007
資料類型 thesis
dc.contributor.advisor 楊素芬zh_TW
dc.contributor.advisor Yang, Su Fenen_US
dc.contributor.author (Authors) 胡逢升zh_TW
dc.creator (作者) 胡逢升zh_TW
dc.date (日期) 2015en_US
dc.date.accessioned 27-Jul-2015 11:21:28 (UTC+8)-
dc.date.available 27-Jul-2015 11:21:28 (UTC+8)-
dc.date.issued (上傳時間) 27-Jul-2015 11:21:28 (UTC+8)-
dc.identifier (Other Identifiers) G0102354007en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/76858-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計研究所zh_TW
dc.description (描述) 102354007zh_TW
dc.description.abstract (摘要) 不論在製造流程或是在服務流程上，管制圖是一個能夠監督流程失控的非常有效工具。現今社會中，在製造流程與服務流程上，資料大多來自非常態分佈或是未知的分佈，以至於最為人所常用且建立在常態分配假設下的舒華特管制圖不適用於此。此文章中，我們提出了一個使用核密度估計方法(kernel density estimation approach)來建構出一個不受分配限制的中位數與四分位差控制區域，以同時監控製程的位置與離散程度。平均連串長度(ARL)是用以測量管制圖的失控偵測能力。在此文章中，比較了我們所提出來的控制區域與文獻上其他無母數管制圖的偵測製程失控能力。數值分析顯示我們所提出的中位數與四分位數的控制區域在同時監測位置與離散的能力較好。文章中亦提出運用此控制區域的例子，最後則為本文章的總結。zh_TW
dc.description.abstract (摘要) Control charts are effective tools for monitoring quality of manufacturing processes and service processes. Nowadays, much of the data in service or manufacturing industries comes from processes having non-normal distributions or unknown distributions. The commonly used Shewhart mean and variable control charts, which depend heavily on the normality assumption, are not appropriately used here. In this article, we propose a distribution-free control region of the median and IQR using the kernel density estimation methods to simultaneously monitor the location and dispersion of an unknown underlying continuous distribution. Furthermore, the average run lengths (ARL) of the proposed control region is used to measure the out-of-control detection performance. The performance of the proposed control region and some other non-parametric charts for detecting out-of-control location and scale are compared. The proposed control region of the median and IQR shows as well or better detection performance compared to existing non-parametric control charts that can simultaneously monitor the location and scale. Numerical examples illustrate the application of the proposed control region. Summary and conclusions are offered.en_US
dc.description.tableofcontents 1. Introduction 1
2. Determination of the True Control Region of the Median and IQR for the Quality Variable with a Specified Distribution 3
2.1 Design of a median control chart 3
2.2 Design of an IQR control chart 4
2.3 Design of the control region of the median and IQR 5
2.3.1 Determination of the control region of the median and IQR using the joint CDF of the median and IQR 6
2.3.2 Determination of the control region of the median and IQR using joint pdf of the median and IQR 7
2.4 Performance measurement of the control region of the median and IQR 11
3. Determination of the Control Region of the Median and IQR for the Quality Variable with Unknown Distribution – the Kernel Density Estimation Method 15
3.1 Using the kernel density estimation method to estimate the pdf of the distribution-free process data 15
3.2 Determination of the approximated control region using the kernel density estimation method 17
3.2.1 Determining the control region using the one-dimensional kernel density estimation method 17
3.2.2 Determining the control region using the two-dimensional kernel density estimation method 19
3.3 Performance measurement of the control region of the median and IQR 19
4. Design the K Control Chart for Monitoring Joint Location and Dispersion 29
4.1 Design the K control chart using the one-dimensional kernel density estimation method 29
4.2 Design the K control chart using the two-dimensional kernel density estimation method 30
5. Performance Comparison 30
6. Real Examples 38
6.1 TSMC Company’s stock price data 38
6.1.1 Control region of the median and IQR of TSMC company’s stock price using the kernel density estimation method 41
6.1.2 The K control chart 44
6.2 Service Times Data 49
6.2.1 Control region of the median and IQR of service times data using the kernel density estimation method 49
6.2.2 The K control chart 53
6.2.3 Performance comparison of the proposed control charts 55
7. Summary and Concluding Remarks 57
Reference 58		zh_TW
dc.format.extent 1473913 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0102354007en_US
dc.subject (關鍵詞) 控制區域zh_TW
dc.subject (關鍵詞) 不受分配限制zh_TW
dc.subject (關鍵詞) 核密度估計方法zh_TW
dc.subject (關鍵詞) 同時監控製程zh_TW
dc.title (題名) 建立管制區域來同時監控製程的位置與離散zh_TW
dc.title (題名) Design of a Control Region for Monitoring Joint Location and Dispersionen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] Abbasi, S.A. and Miller, A., (2011). “ MDEWMA chart: An efficient and robust
alternative to monitor process dispersion, ’’ Journal of Statistical Computation
and Simulation, 83(2), 247-268.
[2] Abbasi, S.A., Miller, A. and Riaz, M., (2013). “ Nonparameteric Progressive Control Chart for Monitoring Process Target, ” Quality and Reliability Engineering
International, 29, 1069-1080.
[3] Altukife, P. F., (2003). “ A new nonparametric control charts based on the
observations exceeding the grand median, ” Pakistan Journal of Statistics, 19(3), 343–351.
[4] Alwan, L. C., (1981). Statistical Process Analysis, McGraw-Hill: New York.
[5] Amin, R., Reynolds, M.R., and Baker, S., (1995). “ Nonparametric quality control
charts based on the sign statistic, ” Communications in Statistics—Theory and
Methods, 24, 1597–1624.
[6] Arnold, B.C., Balakrishnan, N., and Nagaraja, H.N., (1992). A First Course in
Order Statistics, John Wiley & Sons, Inc: New York.
[7] Azzalini, A., (1981). “ A note on the estimation of a distribution function and quantiles by a kernel method, ” Biometrika, 68(1), 326—328.
[8] Bowman, A.W. and Azzalini, A., (1997). Applied Smoothing Techniques for Data Analysis--The Kernel Approach with S-Plus Illustrations, Oxford Science Publication.
[9] Braun, W.J. and Park, D., (2008). “ Estimation of for individuals charts, ” Journal of Quality Technology, 40(3), 332–344.
[10] Casella, G. and Berger, R.L., (2002). Statistical Inference, second Edition, Duxbury (2002).
[11] Chacon, J.E. and Duong, T., (2010). “ Multivariate plug-in bandwidth selection with unconstrained pilot matrices, ” Test, 19, 375-398.
[12] Chakraborti, S. and Graham, M., (2007). Nonparametric Control Charts, Encyclopedia of Quality and Reliability, John Wiley & Sons, Inc: New York.
[13] Chakraborti, S., Lann, P. and Van der Wiel, M.A., (2001). “ Nonparametric control charts: an overview and some results, ” Journal of Quality Technology, 33(3), 304–315.
[14] Chao, M. T. and Cheng, S. W., (2008). “ On 2-D control charts, ” Quality Technology and Quantitative Management, 5(3), 243-261.
[15] 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.
[16] Das, N. and Bhattacharya, A., (2008). “ A new non-parametric control chart for controlling variability, ” Quality Technology and Quantitative Management, 5(4), 351–361.
[17] Duong, T. and Hazelton, M.L., (2003). “ Plug-in bandwidth matrices for bivariate kernel density estimation, ” Journal of Nonparametric Statistics, 15, 17-30.
[18] Gan, F.F., (1995). “ Joint Monitoring of Process Mean and Variance Using Exponentially Weighted Moving Average Control Charts, ” Technometrics, 37, 446-453.
[19] Jones, M.C., (1990). “ The performance of kernel density functions in kernel distribution estimation, ” Statistics and Probability Letters, 9, 129—132.
[20] Maravelakis, P., Panaretos, J., and Psararkis, S., (2005). “ An examination of the robustness to nonnormality of the EWMA control chart for the dispersion ”, Communications in Statistics: Simulation and Computation, 34 (4), 1069-1079.
[21] McCracken, A. K. and Chakraborti, S., (2013). “ Control charts for joint monitoring of the mean and variance: an overview, ” Quality Technology & Quantitative Management, 10(1), 17-36.
[22] Mukherjee, A. and Chakraborti, S., (2012). “ A nonparametric phase II control chart for simultaneous monitoring of location and scale, ” Quality and Reliability Engineering International, 28(3), 335-352.
[23] Park, B. U. and Marron, J. S., (1990). “ Comparison of data-driven bandwidth selectors, ” H. Am. Statist, 85, 66-72.
[24] Sheather, S. J. and Jones, M. C., (1991). “ A reliable data-based bandwidth selection method for kernel density estimation, ” Journal of the Royal Statistical Society, Series B, 53, 683–690.
[25] Silverman, BW., (1996). Density Estimation, Chapman & Hall: London.
[26] Sturges, H.A., (1926). “ The choice of a class interval, ” Journal of the American Statistical Association, 21, 65-66.
[27] Wand, M.P. and Jones, M.C., (1994). “ Multivariate plug in bandwidth selection, ” Computational Statistics, 9, 97-116.
[28] Yang, S.F. and Arnold, B.C., (2014). “ A Simple Approach for Monitoring Business Service Time Variation, ” The scientific World Journal, 2014, 1-16.
[29] Yang, S.F., Lin, J. and Cheng, S., (2011). “ A New Nonparametric EWMA Sign
Chart, ” Expert Systems with Applications, 38(5), 6239-6243.
[30] 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.
[31] Zhou, M., Geng W. and Wang Z., (2014). “ Likelihood Ratio-Based Distribution-Free Sequential Change-Point Detection, ” Journal of Statitical Computation and Simulation ,84(12), 2748-2758.
[32] Zou, C. and Tsung, F., (2010). “ Likelihood ratio-based distribution-free EWMA control Charts, ” Journal of Quality Technology, 42(2), 174-196.		zh_TW