進階搜尋


   電子論文尚未授權公開,紙本請查館藏目錄
(※如查詢不到或館藏狀況顯示「閉架不公開」,表示該本論文不在書庫,無法取用。)
系統識別號 U0026-0407201300562300
論文名稱(中文) 各種指數加權移動平均多變量管制圖偵測能力之比較研究
論文名稱(英文) A Comparative Study on the Detecting Performance for Various EWMA-type Multivariate Control Charts
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 101
學期 2
出版年 102
研究生(中文) 錢柏維
研究生(英文) Bo-Wei Chien
學號 R26001100
學位類別 碩士
語文別 英文
論文頁數 47頁
口試委員 指導教授-潘浙楠
口試委員-鄭春生
口試委員-溫敏杰
口試委員-鄭順林
中文關鍵字 同時監控平均與變異指數加權移動平均多變量管制圖  指數加權移動平均  平均連串長度 
英文關鍵字 EWMA-type multivariate control chart for simultaneously monitoring mean and variability  Multivariate exponentially weighted moving average (MEWMA)  Average run length (ARL) 
學科別分類
中文摘要 在實際使用管制圖監控製程時,通常呈管制狀態下的製程參數為未知,因此在試用第一階段欲取得穩定狀態下之資料以估計製程參數,並以此估計量做為製程參數。由於多變量管制圖在監控製程之第二階段會受到第一階段樣本數大小的影響,故已有多位學者探討第一階段下多變量管制圖樣本數大小之決定與管制界線之制定。然而前大多數文獻中只著重於偵測平均數研究,尚未有學者針對各種同時監控平均與變異之指數加權移動平均(EWMA)之多變量管制圖進行比較研究。由於大多數同時監控平均與變異之指數加權移動平均多變量管制圖均建立在製程參數已知下。因此,本研究乃針對Chen et al. (2005)所提出的Max-MEWMA管制圖之缺點進行修正,並提出參數未知時,以統計估計量修正Max-MEWMA管制圖的RMax-MEWMA管制圖,再與其他學者所提出之指數加權移動平均多變量管制圖進行比較與分析。藉由模擬結果證實,當第一階段樣本的組數(m)較小時,本研究所提出之修正後的多變量(RMax-MEWMA)管制圖其平均連串長度在穩定與失控狀態下在大多數情況均優於現有的管制圖。
英文摘要 When implementing a multivariate control chart, in-control parameters of the process are usually unknown in practice. Thus, we need to estimate in-control parameters using in-control data set from Phase I analysis and replace these parameters with their estimates. Moreover, the detecting performance of multivariate control charts in Phase II is affected by number of samples in Phase I. Several authors have dealt with this problem for process mean, but most previous studies did not compare the effect of parameter estimates on the detecting performance of various EWMA-type multivariate control charts in Phase II for simultaneously monitoring mean and variability, and the test statistics of these EWMA-type multivariate control charts are established when parameters are known. In this paper, we propose a RMax-MEWMA control chart in which the unknown in-control parameters are replaced by their estimates based on Chen’s Max-MEWMA control chart. Then, the detecting performances of our RMax-MEWMA and other EWMA-type multivariate control charts are compared. The simulation results show that RMax-MEWMA chart outperforms the other EWMA-type multivariate control charts in terms of in-control and out-of-control ARLs when number of samples is small.
論文目次 Contents
1. Introduction: Motivation and Research Objectives 1
2. Mathematical notations and definitions 3
3. Review of the pertinent multivariate control charts 5
3.1. Combined EWMA M-chart and EWMA V-chart 6
3.2. Max-EWMA chart 8
3.3. Combined chart and chart 11
3.4. ELR control chart 13
4. Development of RMax-MEWMA Charts 16
5. Comparison of the detecting performance for RMax-MEWMA and Other
Multivariate Control Charts 20
5.1. Simulation procedure 20
5.2. In-control performance 23
5.3. Determining the minimum number of samples 31
5.4. Out-of-control performance 36
6. Conclusions and Future works 43
References 45

List of Tables
Table 1. A summary of the characteristics for various multivariate EWMA control charts 15
Table 2. The upper control limit value that produces an overall in-control ARL of 200 for various control charts under different p = 2, n=5 and λ=0.1, 0.2 when number of samples approaches infinity. 21
Table 3. The upper control limit value that produces an overall in-control ARL of 200 for various control charts under different p (p = 3, 4), n=5 and λ=0.1, 0.2 when number of samples approaches infinity. 22
Table 4. The simulation results of in-control ARL and SDRL for the various multivariate control charts with p=2, n=5, λ=0.1. 25
Table 5. The simulation results of in-control ARL and SDRL for the various multivariate control charts with p=3, n=5, λ=0.1. 26
Table 6. The simulation results of in-control ARL and SDRL for the various multivariate control charts with p=4, n=5, λ=0.1. 27
Table 7. The simulation results of in-control ARL and SDRL for the various multivariate control charts with p=2, n=5, λ=0.2. 28
Table 8. The simulation results of in-control ARL and SDRL for the various multivariate control charts with p=3, n=5, λ=0.2. 29
Table 9. The simulation results of in-control ARL and SDRL for the various multivariate control charts with p=4, n=5, λ=0.2. 30
Table 10. Minimum numbers of samples required for various multivariate control charts under p=2 35
Table 11. Minimum numbers of samples required for various multivariate control charts under p=3, 4 35
Table 12. The simulation results of out-of-control ARL for the various multivariate control charts under m=300, p=2, n=5,λ=0.1 given the in-control ARL=200 when number of samples approaches infinity 37
Table 13. The simulation results of out-of-control ARL for the various multivariate control charts under m=300, p=2, n=5,λ=0.2 given the in-control ARL=200 when number of samples approaches infinity 38
Table 14. The simulation results of out-of-control ARL for the various multivariate control charts under m=300, p=3, n=5,λ=0.1 given the in-control ARL=200 when number of samples approaches infinity 40
Table 15. The simulation results of out-of-control ARL for the various multivariate control charts under m=300, p=3, n=5,λ=0.2 given the in-control ARL=200 when number of samples approaches infinity 41



List of Figures
Figure 1. The relationship between in-control ARLs and different numbers of samples (m) for various multivariate control charts under p=2, n=5, . 31
Figure 2. The relationship between in-control ARLs and different numbers of samples (m) for various multivariate control charts under p=3, n=5, . 32
Figure 3. The relationship between in-control ARLs and different numbers of samples (m) for various multivariate control charts based on p=4, n=5, . 32
Figure 4. The relationship between in-control ARLs and different numbers of samples (m) for various multivariate control charts under p=2, n=5, . 33
Figure 5. The relationship between in-control ARLs and different numbers of samples (m) for various multivariate control charts under p=3, n=5, . 33
Figure 6. The relationship between in-control ARLs and different numbers of samples (m) for various multivariate control charts under p=4, n=5, . 34


參考文獻 Anderson, T. W. (1984), An introduction to multivariate statistical analysis. 2nd ed. New York: Wiley.

Alt, F. B. (1985), “Multivariate quality control,” Encyclopedia Stat. Sci., 6, pp.110–122.

Alt, F. B. and Bedewi, G. E. (1986), “SPC for dispersion for multivariate data,” ASQC. Qual. Congress Trans, pp.248–254.

Cho, G. Y. (1991), “Multivariate control charts for the mean vector and variance-covariance matrix with variable sampling intervals,” Ph.D. Dissertation, Department of Statistics, Virginia Tech.

Crosier, R. B. (1988), “Multivariate generalizations of cumulative quality control schemes,” Technometrics, 30, pp.291–303.

Chan, L. K. and Zhang, J. (2001), “Cumulative sum control chart for the covariance matrix,” Statist. Sinica, 11, pp.767–790.

Chen, G., Cheng, S. W. and Xie, H. (2005), “A new multivariate control chart for monitoring both location and dispersion,” Communications in Statistics - Simulation and Computation, 34, pp.203–217.

Champ, C. W., Jones-Farmer, L. A. and Rigdon, S. E. (2005), “Properties of the T2 Control chart when parameters are estimated,” Technometrics, 47, pp.437–445.

Champ, C. W. and Jones-Farmer, L. A. (2007), “Properties of multivariate control chart with estimated parameters,” Sequential Analysis, 26, pp.153–169.

Chen, S. C. and Pan, J. N. (2011), “Determining optimal number of samples for constructing multivariate control charts,” Communications in Statistics-Simulation and Computation, 40(2), pp.228–240.

Hotelling, H. H. (1947), Multivariate Quality Control - Illustrated by the Air Testing of Sample Bombsights, in Techniques of Statistical Analysis, Eisenhart C., Hastay M.W., and Wallis W.A., (eds) McGraw-Hill, New York, pp. 111–184.

Healy, J. D. (1987), “A note on multivariate CUSUM procedures,” Technometrics, 29, pp.409–412.

Hawkins, D. M. (1991), “Multivariate quality control based on regression variables,” Technometrics, 33, pp.61–75.

Hawkins, D. M. (1993), “Regression adjustment for variables in multivariate quality control,” Journal of Quality Technology, 25, pp.170–182.

Hawkins, D. M. and Maboudou-Tchao, E. M. (2008), “Multivariate exponentially weighted moving covariance matrix,” Technometrics, 50, pp.155–166.

Huwang, L., Yeh, A. B. and Wu, C. W. (2007), “Monitoring multivariate process variability for individual observations,” J. Qual. Technol., 39 (3), pp.258–278.

Jensen, W. A., Jones-Farmer, L. A., Champ, C. W. and Woodall, W. H. (2006), “Effects of parameter estimation on control chart properties: a literature review.” Journal of Quality Technology, 38, pp349–364.

Khoo, B. C. (2005), “A new bivariate control chart to monitor the multivariate process mean and variance simultaneously,” Quality Engineering, 17, pp.109–118.

Lowry, C. A., Woodall, W. H., Champ, C. W. and Rigdon, S. E. (1992), “A multivariate EWMA control chart,” Technometrics, 34, pp.46–53.

Liu, R.Y. (1995), “Control charts for multivariate process,” J. Amer. Statist. Assoc., 90, pp.1380–1387.

Linderman, K. and Love, T. E. (2000), “Economic and economic statistical designs for MA control charts,” Journal of Quality Technology, 32, pp.410–417.

Mathai, A. M. and Provost. S. B. (1992), Quadratic Forms in Random Variables: Theory and Applications, M. Dekker, New York.

Muirhead, R. J. (1982), Aspects of Multivariate Statistical Theory, New York, Wiley.

Montgomery D. C. (2009), “Introduction to Statistical Quality Control, 6th Ed., J. Wiley, New York.

Mahmoud, M. A. and Maravelakis, P. E. (2010), “The performance of the MEWMA control chart when parameters are estimated,” Communication in Statistics-Simulation and Computation, 39, pp.1803–1817.

Nedumaran, G. and Pignatiello, J. J. Jr. (1999), “On constructing T2 control charts for on-line process monitoring,” IIE Transactions, 31, pp.529–536.

Pignatiello, J. J. and Runger, G. C. (1990), Comparisons of multivariate CUSUM charts,” Journal of Quality Technology, 22, pp.173–186.

Runger, M. R. and Prabhu, S. S. (1996), “A markov chain model for the multivariate exponentially weighted moving averages control chart,” J. Amer. Statist. Assoc., 91, pp.1701–1706.

Reynolds, M. R. and Cho, G. Y. (2006), “Multivariate control charts for monitoring the mean vector and covariance matrix,” Journal of Quality Technology, 38(3), pp.230–253.

Tang, P. F. and Barnett, N. S. (1996), “Dispersion control for multivariate processes–some comparisons,” Aust. N. Z. J. Stat, 38, pp.253–273.
Woodall, W. H. and Ncube, M. M. (1985), “Multivariate CUSUM quality control procedures,” Technometrics, 27, pp.285–292.

Yeh, A. B. and Lin, D. K. (2002), “A new variables control chart for simultaneously monitoring multivariate process mean and variability,” International Journal of Reliability, Quality and Safety Engineering, 9(1), pp.41–59.

Yeh, A. B., Lin, K. J., Zhou, H. H. and Venkataramani, C. (2003), “ A multivariate exponentially weighted moving average control chart for monitoring process variability,” Journal of Applied Statistics, 30(5), pp.507–536.

Yeh, A. B., Lin, D. K.-J. and McGrath, R. N. (2006), “Multivariate control charts for monitoring covariance matrix: a review,” Quality Technology and Quantitative Management, 3(4), pp.415–436.

Yeh, A. B., Li, B. and Wang, K. (2012), “Monitoring multivariate process variability with individual observations via penalized likelihood estimation,” International Journal of Production Research, 50(22), pp. 6624-6638.

Zhang, J., Li, Z. and Wang, Z. (2010), “A multivariate control chart for simultaneously monitoring process mean and variability,” Computational Statistics and Data Analysis, 54(10), pp.2244–2252.
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2016-07-12起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw