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研究生:顏家鈴
研究生(外文):Chia-Ling Yen
論文名稱:監控多變量製程變異性增加之管制圖
論文名稱(外文):A control chart ffor detecting increases in multivariate process variability
指導教授:洪志真洪志真引用關係
指導教授(外文):Jyh-Jen Horng Shiau
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:多變量製程製程變異增加管制圖多變量單邊檢定管制界限平均連串長度
外文關鍵詞:multivariate processvariability increasescontrol chartmultivariate one-sided testcontrol limitaverage run length
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本文主要利用多變量單邊檢定發展偵測多變量製程變異增加的方法,也就是檢定H0:Σ=Σ0 versus H1:Σ≧Σ0 且 Σ≠Σ0,其中Σ為所監控品質特性的共變異數矩陣及Σ0為在控制狀態下的製程變異,並且分成為Σ0已知或未知兩種情形來討論製程如何監控變異增加的問題。我們導出概似比檢定統計量,並用靴環法得出管制限界。針對此控制圖之績效問題,我們經統計模擬對幾種Σ的變化比較平均連串長度,並以一個實例和模擬例子,證實所提出的單邊檢定方法對多變量製程變異增加的問題在偵測能力上有相當不錯的效率,且與對允許多變量製程變異性可增加或減少之雙邊檢定方法作比較,也有較佳的偵測效率。

In this paper, a method for detecting increases in multivariate process variability has been proposed. It is based on the one-sided likelihood ratio test of H0:Σ=Σ0 versus H1:Σ≧Σ0 and Σ≠Σ0, where Σ is the covariance matrix associated with the monitored quality characteristic and Σ0 is the in-control process variability. We derive the likelihood ratio test statistic for the cases that Σ0 is known and not known, respectively. We further obtain the control limit of the control chart by the bootstrap method. The applicability of the proposed Control chart in detecting increases in multivariate process variability is demonstrated through a real example. The simulation studies further show that the proposed method outperforms the method based on the two-sided
likelihood ratio test in most cases.

中文摘要 ………………………………………………………… i
英文摘要 ………………………………………………………… ii
誌謝 ………………………………………………………… iii
目錄 ………………………………………………………… iv
附圖目錄 ………………………………………………………… v
附表目錄 ………………………………………………………… vi
第一章 緒論………………………………………………… 1
第二章 製程變異性增加之管制……………………………… 2
2.1 文獻探討……………………………………………… 2
2.2 兩個獨立母體的共變異數矩陣的單邊檢定………… 6
2.2.1 當 為已知時之檢定統計量………………………………6
2.2.2 當 為未知時之檢定統計量…………………………… 13
2.3 利用概似比統計量來建構單邊檢定管制圖………………23
2.3.1 已知時之單邊檢定管制圖………………………… 24
2.3.2 未知時之單邊檢定管制圖…………………………… 25
第三章 管制界限的選擇…………………………………… 28
3.1 管制界限與樣本分位數…………………………………28
3.2 樣本分位數的特性……………………………………28
3.3 控制變異的管制界限……………………………… 29
3.3.1 當Σ0為已知時之管制界限…………………………… 29
3.3.2 當Σ0為未知時之管制界限…………………………… 31
3.4 管制界限程式之使用………………………………… 33
第四章 比較平均連串長度…………………………………… 34
4.1 兩個獨立母體共變異數矩陣的雙邊檢定…………… 34
4.1.1 當Σ0為已知時之雙邊檢定統計量…………………… 34
4.1.2 當Σ0為未知時之雙邊檢定統計量…………………… 35
4.2 比較平均連串長度………………………………………36
4.2.1 當Σ0為已知時之檢定力……………………………… 36
4.2.2 當Σ0為未知時之檢定力…………………………………38
4.3 單邊檢定之平均連串長度………………………………………38
4.4 比較單邊與雙邊檢定的表現…………………… 40
4.4.1 當Σ0為已知時之模擬結果…………………………… 41
4.4.2 當Σ0為未知時之模擬結果…………………………… 41
第五章 實例與模擬例子……………………………………… 43
5.1 實例………………………………………………… 43
5.2 模擬例子……………………………………………… 44
第六章 結論與未來展望…………………………………… 47
附錄 ………………………………………………………… 49
參考文獻 ……………………………………………………… 52
附圖與附表 …………………………………………… 55

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