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研究生: 張智翔
Chang, Chih Hsiang
論文名稱: 利用無母數方法來監控一般線性輪廓的EWMA管制圖
Exponentially weighted moving average control chart for monitoring general linear profiles based on nonparametric method
指導教授: 黃榮臣
Huwang, Longcheen
口試委員: 楊淑芬
王藝華
學位類別: 碩士
Master
系所名稱: 理學院 - 統計學研究所
Institute of Statistics
論文出版年: 2015
畢業學年度: 103
語文別: 中文
論文頁數: 41
中文關鍵詞: 管制圖線性輪廓EWMA無母數重抽法
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  • 在許多工業製程中,產品或製程的品質特徵可以用一個反應變數以及一個或多個解釋變數的函數關係來界定,這種函數關係被稱為輪廓製程。本文主要是利用無母數的重複抽樣方法來建構監控線性輪廓製程的管制圖。我們用統計模擬來評估新管制圖的監控效果並說明傳統上假設隨機誤差項為常態分佈所構造的管制圖為何不具有良好的監控效果。最後我們利用一個例子來說明實務上如何操作與使用我們所提出的管制圖。


    In many industrial processes, the quality of a product or a process can be represented by the relationship of a function between a response variable and one or more explanatory variables. This function is called a profile. This article uses a nonparametric resampling method to develop a control chart to monitor the linear profile process. We evaluate the effectiveness of the new and the traditional control charts by simulation studies. The traditional control charts assuming normal random error term is shown not having good performance. Finally, we use an example to illustrate how to complement our proposed control chart.

    第一章 緒論 1 1.1 前言 1 1.2 輪廓製程的監控 2 1.3 研究動機與目的 4 第二章 監控線性輪廓的方法 6 2.1 模型假設 6 2.2 有母數的線性輪廓監控方法 6 2.3 無母數的線性輪廓監控方法 8 2.3.1 ZTW的無母數監控方法 9 2.3.2 CH的無母數監控方法 10 第三章 平均連串長度的比較 12 3.1 真實的平均連串長度比較 12 3.2 非管制狀態下的平均連串長度比較 17 第四章 例子 22 第五章 結論與後續研究 25 參考文獻: 27 附表: 29 附圖: 40

    [1] Crowder, S. V., and Hamilton, M. D. (1992). “An EWMA for Monitoring a Process Standard Deviation”. Journal of Quality Technology 24, pp. 12-21.
    [2] Eyvazian, M., Noorossana, R., Saghaei, A., and Amiri, A. (2011). “Phase II Monitoring of Multivariate Multiple Linear Regression Profiles”. Quality and Reliability Engineering International 27, pp. 281-296.
    [3] Huwang, L., Wang, Y., and Shen, C. (2014). “Monitoring General Linear Profiles When Random Errors Have Contaminated Normal Distributions”. Quality and Reliablility Engineering International 30, 1131-1144.
    [4] Kang, L., and Albin, S. L. (2000). “On-Line Monitoring When the Process Yields a Linear Profile”. Journal of Quality Technology 32, pp. 418-426.
    [5] Kim, K., Mahmoud, M. A., and Woodall, W. H. (2003). “On the Monitoring of Linear Profiles”. Journal of Quality Technology 35, pp. 317-328.
    [6] Mestek, O., Pavlik, J., and Suchanek, M. (1944). “Multivariate Control Charts: Control Charts for Calibration Curves”. Journal of Analytical Chemistry 350, pp. 344-351.
    [7] Montgomery, D. C. (2012). Statistical Quality Control: A Modern Introduction
    . 7th ed., John Wiley & Sons, Canada.
    [8] Page, E. S. (1954). “Continuous Inspection Schemes”. Biometrics 41, pp. 100-114.
    [9] Roberts, S. W. (1959). “Control Chart Tests Based on Geometric Moving Average”. Technometrics 1, pp. 239-250.
    [10] Shewhart, W. A. (1924). “Some Application of Statistical Methods to the Analysis of Physical and Engineering Data”. Bell System Technical Journal 3, pp. 43-87.

    [11] Shi, J. (2007). Stream of Variation Modeling and Analysis for Multistage Manufacturing Processes. 1st ed., CRC Press, Florida.
    [12] Zi X, Zou C, and Tsung F. (2012). “A distribution-free robust method for monitoring linear profiles using rank-based regression”. IIE Transactions 2012 44, pp. 949-963.
    [13] Zou, C., Tsung, F., and Wang, Z. (2007). “Monitoring General Linear Profiles Using Multivariate Exponentially Weighted Moving Average Schemes”. Technometrics 49, pp. 395-408.

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