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系統識別號 U0026-2607201812400600
論文名稱(中文) 加權一般概似比管制圖對非常態分配穩健性研究
論文名稱(英文) A Study about Robustness of Weighted GLR Control Chart to Non-Normal Process
校院名稱 成功大學
系所名稱(中) 工業與資訊管理學系
系所名稱(英) Department of Industrial and Information Management
學年度 106
學期 2
出版年 107
研究生(中文) 賴冠儒
研究生(英文) Guan-Ru, Lai
學號 R36051173
學位類別 碩士
語文別 中文
論文頁數 60頁
口試委員 指導教授-胡政宏
口試委員-張裕清
口試委員-劉任修
中文關鍵字 指數加權移動平均管制圖  一般概似比管制圖  累積和管制圖  平均監控時間 
英文關鍵字 generalized likelihood ratio control chart  exponentially weighted moving average control chart  cumulative sum control chart  average time to signal 
學科別分類
中文摘要 統計製程管制(Statistical Process Control,SPC)常被用於做為製程改善的工具,其透過持續監控製程之手法,若製程發生變異,管制圖會在最短時間內發出警訊,使用者須採取必要行動,找出變異並使製程儘快回到穩定狀態。常見管制圖包含蕭華特、累積和以及指數加權移動平均管制圖等,而一般概似比(Generalized Likelihood Ratio,GLR)管制圖也在近年開始受到學者們的關注。
Reynolds and Lou (2010)提出一般概似比管制圖在常態分配時,使用者可選擇作者提供之管制界限達到特定的管制圖績效表現,且作者證明其能有效監控製程廣泛的偏移。過往一般概似比管制圖研究中大多假設製程參數已知且服從常態分配,即使製程不為常態,只要增加樣本數最終製程也會趨近於常態分配,但在現實中增加樣本數同時也增加使用者的成本,若在小樣本抽樣且製程與常態假設不符的情況時,將會使得管制圖發出警訊的頻率與預期的不符,增加在後續使用上的困難度。指數加權移動平均(Exponentially Weighted Moving Average,EWMA)管制圖被認為有著對非常態資料的穩健性(Non-Normality Robustness),其被認定可有效改善管制圖在製程不為常態分配的績效表現,本研究將應用指數加權移動平均中的加權方法,透過對管制圖統計量做加權的方式,改善管制圖在製程資料與常態不符的情形,並以平均監控時間(Average Time to Signal,ATS)為績效指標,和過去學者所提出之指數加權移動平均以及累積和管制圖比較在製程資料改變時管制圖的績效表現。
英文摘要 Normal distribution has been widely assumed while using control chart. GLR (Generalized Likelihood Ratio, GLR) control chart is considered that can be very sensitive to different shift occurred in process. Prior researches have showed that the underlying data disobey the normal assumption that partitioners assumed, the performance of control chart would deteriorate.
EWMA (Exponentially Weighted Moving Average, EWMA) control chart can be robust to non-normal by weighting statistics of samples. Owing to the deteriorated effect caused by non-normal data, statistics of GLR control chart will be weighted to achieve robust to improve the change of underlying data. By doing so, GLR control chart can perform more effective than EWMA and CUSUM control chart when normal assumption is disobeyed.
論文目次 摘要 I
誌謝 X
目錄 XI
表目錄 XIII
圖目錄 XIV
第一章 緒論 1
1.1 研究背景 1
1.2 研究動機 2
1.3 文獻探討 3
1.4 研究目的 12
1.5 研究流程 13
1.6 論文架構 13
第二章 管制圖建構方法 15
2.1 符號定義 15
2.2 研究假設 16
2.3 管制圖建構 17
2.4 問題描述 20
2.5 小結 21
第三章 管制圖在管制內績效表現 22
3.1 績效指標 22
3.2 模擬步驟 23
3.3 數值實例 24
3.4 管制圖之管制界限 30
3.5 小結 35
第四章 管制圖在管制外績效表現 36
4.1 績效指標 36
4.2 模擬步驟 37
4.3 數值實例 38
4.4 小結 48
第五章 數值分析與比較 49
5.1 累積和管制圖 49
5.2 指數加權移動平均管制圖 50
5.3 數值實例 51
5.4 小結 55
第六章 結論與未來發展 56
6.1 研究結論 56
6.2 未來研究方向 57
參考文獻 58

參考文獻 中文文獻:
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英文文獻:
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