臺灣博碩士論文加值系統

在許多工業製程上，基於產品特性，技術上或是成本上的考量，使得可以用來做為製程管制的樣本數都很小，在樣本數很小的情況下，若要對一多變量製程的變異性做監控，必須能夠導出共變異數矩陣的一個合理估計量。在本文中我們考慮樣本數為1的p個品質特性(quality characteristic)之多變量製程變異性的管制，利用指數加權移動平均(exponentially weighted moving average)的方法，我們建構出一個可用來估計共變異數矩陣的正定(positive definite)矩陣，且利用距離的概念，我們定義出製程共變異數矩陣與管制狀態下共變異數矩陣間是否有顯著差異的指標，進而發展出一個新的管制圖來監控製程整個共變異數矩陣的變化。經由實際例子和統計模擬的方法，證實我們的管制圖比Hawkins (1991)利用迴歸調整變數（regression-adjusted variables）方法所提出的管制圖，在製程變異性的大部分改變上都有比較好的偵測效率。

第一章 簡介 1
1.1 統計製程管制的意義 1
1.2 CUSUM管制圖 2
1.3 EWMA管制圖 2
1.4 監控多變量平均數之管制圖 3
1.5 監控變異數之管制圖 4
第二章 多變量製程變異之管制 5
2.1 文獻探討 5
2.2 利用EWMA建構多變量製程之變異數矩陣 7
2.3 多變量變異數和共變異數管制圖 10
2.4 共變數矩陣管制圖 12
第三章 平均連串長度之表現 13
3.1 平均連串長度的定義 13
3.2 管制限界的求法 14
3.3 比較平均連串長度 18
3.4 實例分析 21
第四章 結論與未來發展 28
附錄
1.證明St 為正定矩陣 29
2.D1之期望值和變異數的計算過程 29
3.D2之期望值和變異數的計算過程 31
4.權數w各次方和之相互關係 32
5.動差計算過程 .33
參考文獻 35
附表 37
附圖 49

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