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研究生:許玉潔
論文名稱:一個新自相關性製程監控方法之研究
論文名稱(外文):A new monitoring scheme for autocorrelated processes
指導教授:洪志真洪志真引用關係
學位類別:碩士
校院名稱:國立交通大學
系所名稱:統計所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
中文關鍵詞:自相關跳階偏移緩慢偏移
相關次數:
  • 被引用被引用:3
  • 點閱點閱:148
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:1
傳統管制圖的建構,常假設製程觀察值是具獨立性,然而實務上卻有許多情形違背此假設。此類不具獨立性的自相關性製程資料文獻中,對於製程平均值發生跳階偏移(step shift)的研究遠多於製程平均值發生緩慢偏移(trend shift)。本研究的目的即是針對自相關性製程之純噪音(white noise)平均值發生跳階偏移導致製程緩慢移動至新水準的問題上,提出一個不監控預測誤差(forecast error)的新方法,而是直接使用管制圖來監控原始資料。經由統計模擬,可證實所提出的方法,對某些常發生的自相關性製程之純噪音平均值發生跳階偏移導致製程緩慢移動至新水準有不錯的偵測力。
目 錄:
第一章 緒論…………………………………………………………1
1.1 研究背景………………………………………………………………1
1.2 研究動機與目的………………………………………………………2
1.3 論文架構………………………………………………………………3
第二章 文獻回顧……………………………………………………5
2.1 平均連串長度………………………………………………………....5
2.2 傳統管制圖…………………………………………………………....6
2.2.1 Shewhart管制圖………………………………………………………………7
2.2.2 個別值X管制圖………………………………………………………………9
2.2.3 移動全距管制圖…………………………………………………………..….11
2.2.4 EWMA管制圖……………………………………………………………….11
2.3 時間序列模式簡介…………………………………………………..13
2.3.1 ARIMA 模型……………………………………………………………...…13
2.3.2 以預測為基準的監控方法…………………………………………………...15
2.3.3 共同原因管制圖與特殊原因管制圖………...………………………………18
第三章 製程之偏移………………………………………………..19
3.1 跳階偏移………………………………………………………….….19
3.1.1 AR模型……………………………………………………………………….19
3.1.2 IMA模型…………………………………………………………………..…20
3.2 緩慢偏移………………………………………………………..……21
3.2.1 AR模型……………………………………………………….…………..…..22
3.2.2 MA模型………………………………………………………………………25
3.2.3 ARMA模型與預測誤差……………………………………………………..27
第四章 平均連串長度的表現…………………………………..…32
4.1 管制界限的選擇與ARL 、SE 的求法……………………………32
4.2 平均連串長度之比較………………………………………..………34
4.2.1 個別值X管制圖和EWMA管制圖監控預測誤差之比較…………………34
4.2.2 個別值X管制圖和EWMA管制圖監控AR(1)原始資料與預測誤差之比較
……………………………………………………………………..………....35
4.2.3 個別值X管制圖和EWMA管制圖監控MA(1)原始資料與預測誤差之比較
………………………………………………………………………………..36
4.2.4 個別值X管制圖和EWMA管制圖監控ARMA(1, 1)原始資料與預測誤差之比較………………………………………………………………………37
第五章 實例………………………………………………………..43
第六章 結論………………………………………………………..46
參考文獻……………………………………………………………..…47
附錄 A………………………………………………………………….50
附錄 B………………………………………………………………….52
圖表……………………………………………………………………..53
參考文獻
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