系統識別號 | U0002-0107201017361100 |
---|---|
DOI | 10.6846/TKU.2010.00019 |
論文名稱(中文) | 利用單一觀測值建立監控製程變異之適應性多變量指數加權移動 平均管制圖 |
論文名稱(英文) | Multivariate Adaptive Exponentially Weighted Moving Average Control Charts for Monitoring Multivariate Process Variability with Individual Observations |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 統計學系碩士班 |
系所名稱(英文) | Department of Statistics |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 98 |
學期 | 2 |
出版年 | 99 |
研究生(中文) | 陳怡婷 |
研究生(英文) | Yi-Ting Chen |
學號 | 697650041 |
學位類別 | 碩士 |
語言別 | 英文 |
第二語言別 | |
口試日期 | 2010-06-04 |
論文頁數 | 48頁 |
口試委員 |
指導教授
-
蔡宗儒
委員 - 劉玉龍 委員 - 廖敏治 |
關鍵字(中) |
共變異矩陣 指數加權移動平均 單一觀測值 平均連串長度 |
關鍵字(英) |
Covariance Matrix Exponentially Weighted Moving Average Individual Observation Average Run Length |
第三語言關鍵字 | |
學科別分類 | |
中文摘要 |
本論文對單一觀測值建立監控製程變異之適應性多變量指數加權移動平均管制圖。 此一管制圖有助於針對製程變異提早發出警訊。並在模擬研究下, 我們利用數值分析法 找出不同條件下之最佳管制圖參數。相較於目前文獻中的方法, 數值分析的結果顯示, 本論文建議的管制圖可以有較佳的錯誤預警效果。 |
英文摘要 |
Based on an adaptive adjustment, this thesis provides a multivariate expo- nentially weighted moving average control chart with individual observations. This chart is used for monitoring shifts on process variances or correlation. A computation procedure is give to determine the chart parameters. More- over, some of these parameters are tabulated. Numerical results show that the proposed variances or correlation with shorter average run lengths to alarm out-of-control signals. |
第三語言摘要 | |
論文目次 |
Contents 1 Introduction 1 2 Literature Review 6 3 The Adaptive MEWMA Control Chart 10 4 Numerical Study 16 5 Conclusions 42 List of Tables 4.1 The values of L for different combinations of r and v when p=2 and ARL0=200. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.2 The values of L for different combinations of r and v when p=2 and ARL0=370. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 The values of L for different combinations of r and v when p=2 and ARL0=500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.4 The values of L for different combinations of r and v when p=3 and ARL0=200. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.5 The values of L for different combinations of r and v when p=3 and ARL0=370. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.6 The values of L for different combinations of r and v when p=3 and ARL0=500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.7 The values of L for different combinations of r and v when p=5 and ARL0=370. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.8 The values of L for different combinations of r and v when p=5 and ARL0=500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.9 The values of L for different combinations of r and v when p=10 and ARL0=370. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.10 The values of L for different combinations of r and v when p=10 and ARL0=500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.11 Out-of-control ARLs of AMEWMA for p = 2 and ARL0=370. . . . . . . . 29 4.12 Out-of-control ARLs of AMEWMA for p = 2 and ARL0=370. . . . . . . . 30 4.13 Out-of-control ARLs of AMEWMA for p = 2 and ARL0=370. . . . . . . . 31 4.14 Out-of-control ARLs of AMEWMA for p = 2 and ARL0=370. . . . . . . . 32 4.15 Out-of-control ARLs of AMEWMA for p = 2 and ARL0=370. . . . . . . . 33 4.16 Out-of-control ARLs of AMEWMA for p = 3 and ARL0=370. . . . . . . . 34 4.17 Out-of-control ARLs of AMEWMA for p = 3 and ARL0=370. . . . . . . . 35 4.18 Out-of-control ARLs of AMEWMA for p = 3 and ARL0=370. . . . . . . . 36 4.19 Out-of-control ARLs of AMEWMA for p = 3 and ARL0=370. . . . . . . . 37 4.20 Out-of-control ARLs of AMEWMA for p = 3 and ARL0=370. . . . . . . . 38 4.21 Out-of-control ARLs of AMEWMA for p = 3 and ARL0=370. . . . . . . . 39 4.22 Performance comparison for various multivariate control charts with p = 2. 40 4.23 Performance comparison for various multivariate control charts with p = 2 and only q shifts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 |
參考文獻 |
[1] Yeh, A. B., Huwang, L. and Wu C.-W. (2005). A multivariate EWMA control chart for monitoring process variability with individual observations. IIE Transactions, 37: 1023-1035. [2] Lowry, C. A., Woodall, W. H., Champ, C. W. and Rigdon, S. E. (1992). A multi- variate exponentially weighted moving average control chart.Technometrics, 34(1): 46-53. [3] Hawkins, D. M. (1981). A cuaum for a scale parameter, Journal of Quality Technology , 13: 228-231. [4] Hawkins, D. M. (1991). Multivariate quality control based on regression-adjusted variables, Technometrics, 33(1): 61-75. [5] Hawkins, D. M. (1993). Regression adjustment for variables in multivariate quality control, Journal of Quality Technology, 25: 170-182. [6] Huber, P. J. (1981). Robust Statistics. John Wiley and Sons. New York. [7] Shu, L. (2008). An adaptive exponentially weighted moving average control chart for monitoring process variances. Journal of Statistical Computation and Simulation, 78(4): 367-384 [8] Huwang, L, Yeh, A. B. and Wu C.-W. (2007). Monitoring multivariate process vari- ability for individual observations. Journal of Quality Technology, 39(3): 258-278. [9] Reynolds, M. R. Jr. and Stoumbos, Z. G. (2005). Should exponentially weighted mov- ing average and cumulative sum charts be used with shewhart limits? Technometrics, 47(4): 409-424. [10] Reynolds, M. R. Jr. and Kim, K. (2007). Multivariate control charts for monitoring the process mean and variability using sequential sampling. Sequential Analysis, 26: 283-315. [11] Montgomery, D. C., (2005). Statistical Quality Control, A Modern Introduction (6th ed., Wiley, New York.). [12] Yashchin, E., (1995). Estimating the current mean of a process subject to abrupt changes. Technometrics, 37: 311-323. |
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