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研究生:陳偉政
研究生(外文):Chen Wei Cheng
論文名稱:相關性製程下EWMAST管制圖的使用與評估
論文名稱(外文):The Use and Evaluation of EWMAST Control Chart for Autocorrelation Processes
指導教授:鄭盛樹鄭盛樹引用關係
指導教授(外文):Cheng Sheng Su
學位類別:碩士
校院名稱:育達商業技術學院
系所名稱:企業管理所
學門:商業及管理學門
學類:企業管理學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:84
中文關鍵詞:指數加權移動平均相關性製程製程平均值偏移平均連串長度
外文關鍵詞:exponentially weighted moving averagecorrelated processprocess mean shiftaverage run length
相關次數:
  • 被引用被引用:0
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  • 下載下載:36
  • 收藏至我的研究室書目清單書目收藏:2
當製程之品質特性數據具有相關性時,EWMAST管制法由EWMA管制統計量所構成,並且利用修正管制界限的方式直接監控製程資料。換句話說,EWMAST管制法在相關性製程之下,改寫傳統EWMA管制法進而直接應用於自我相關製程資料的監控上以降低錯誤警報的發生。使用EWMAST管制法最大的優勢在於,操作上不需時間序列模型配適製程資料之假設。不同於以殘差為基礎的傳統管制法,當自我相關並不是非常強烈時,EWMAST管制法可以在偵測製程發生微量和中度平均值偏移之下,得到比大部份的殘差管制圖更高的偵測效益。一般而言,在實務上操作管制圖時必需先選擇合宜的參數值。但是合宜的管制參數卻與平均值之偏移量、管制內平均連串長度之需求和自我相關的強度有關。然而,實際之製程平均值偏移量通常都是未知的。因此要去尋找出最佳化的參數設定值進而提升EWMAST管制法之偵測效益是非常困難的。為了要去處理這些問題,本文首先將探討最佳的參數設定值以提升單一EWMAST管制法之偵測能力。再者為了擴大EWMAST管制法之有效偵測範圍,本文將發展聯合使用兩組不同管制參數設定值之雙重EWMAST管制法。在基於自我迴歸(AR(1))模式下所得到之模擬結果,我們發現在較佳的參數選擇之下可以提升EWMAST管制法在特定製程平均值偏移量的偵測效益,而在製程之平均值偏移量大小是未知的情況之下,雙重EWMAST管制法可以進一步的提升整體的偵測能力。最後,藉由本文所提供之參數組合列表,可以幫助操作者在實務上使用單一EWMAST管制法或雙重EWMAST管制法時之參考。
When the process data are correlated, an EWMAST(exponentially weighted moving average for stationary process)control chart that consist of an EWMA statistics and a modified control limits can be used to monitor the process data directly. In other word, the chart is a version of the traditional EWMA chart which applies directly to the autocorrelated process data and reduces the false alarms caused by the autocorrelation process. The best advantage in using an EWMAST chart is that the chart can be operated without a time-series model effort. Unlike to the traditional control charts that based on the residuals, the EWMAST chart can detect the small and medium process mean shifts more efficiently than most of residual-based charts when the autocorrelation is not very strong. In general, the operator is needed to select a suitable parameter for operating the control chart. But the suitable control parameter is relative to those of the magnitude of mean shifts, the required in-control average run length and the strength of autocorrelation. However, the truly magnitude of process mean shifts are usually unknown. Therefore, it is a hard task to find the optimal parameter to enhance the performance of EWMAST chart. In order to tackle these problems, the first of our research is to find a better parameter to enhance the detecting ability of single-EWMAST chart. Secondly, in order to extend the detecting ability of EWMAST chart a double-EWMAST chart with jointly of two different sets of control parameter is developed. Based on the results from our extensive simulations of the autoregressive(AR(1))processes dynamic, we find that the selected parameters improve the performance of the EWMAST chart with the specified mean shifts and the double-EWMAST chart also improves the entire detecting ability when the magnitude of mean shift size is unknown. Finally, the tabulate of parameters setting are provided to help the operators for the practical use of single-EWMAST chart or double-EWMAST chart.
目 錄
頁次
書名頁 ………………………………………………………………………… i
論文口試委員審定書 ………………………………………………………… ii
博碩士論文電子檔案上網授權書 …………………………………………… iii
中文摘要 ……………………………………………………………………… iv
英文摘要 ……………………………………………………………………… v
誌謝 …………………………………………………………………………… vii
目錄 …………………………………………………………………………… viii
表目錄 ………………………………………………………………………… x
圖目錄 ………………………………………………………………………… xi
第一章 緒論 ………………………………………………………………… 1
第一節 研究背景與動機 ………………………………………… 1
第二節 研究目的 ………………………………………………… 3
第三節 研究範圍 ………………………………………………… 4
第四節 研究流程 ………………………………………………… 4
第二章 文獻回顧與探討 …………………………………………………… 7
第一節 統計製程管制 …………………………………………… 7
第二節 自我相關 ………………………………………………… 8
第三節 平均連串長度 …………………………………………… 10
第四節 殘差管製圖 ……………………………………………… 10
一、SCC管制圖 ………………………………………… 11
二、CUSUM殘差管制圖 ……………………………… 12
第五節 原始資料管制圖 ………………………………………… 15
一、EWMAST管制圖 ………………………………… 15
二、ARMA管制圖 ……………………………………… 23
第三章 研究方法 …………………………………………………………… 28
第一節 製程模式與單一EWMAST管制圖之管制方法 ……… 28
一、製程模式 …………………………………………… 28
二、單一EWMAST管制圖之管制方法………………… 28
第二節 管制圖偵測效果之衡量標準 …………………………… 29
一、平均連串長度 ……………………………………… 29
二、最佳化平滑參數值 之定義 ……………………… 30
第三節 EWMAST管制圖之最佳化參數選擇過程 …………… 30
一、單一EWMAST管制圖最佳化平滑參數選擇過程 … 30
二、雙重EWMAST管制圖最佳化平滑參數選擇過程 … 30
第四節 管制效益之比較 ………………………………………… 34
第四章 研究結果之衡量與評估 …………………………………………… 35
第一節 單一EWMAST管制圖之最佳化平滑參數……………… 35
第二節 雙重EWMAST管制圖之最佳化平滑參數 …………… 46
第三節 最佳化雙重EWMAST管制圖與單一EWMAST管制圖
之整體管制效益比較 …………………………………… 56
第五章 結論與展望 ………………………………………………………… 66
第一節 結論 …………………………………………………………… 66
第二節 研究之貢獻 …………………………………………………… 67
第三節 展望 …………………………………………………………… 69
參考文獻 ……………………………………………………………………… 70
自傳 …………………………………………………………………………… 72
參考文獻
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