臺灣博碩士論文加值系統

良質率為工業或其他應用領域中常被用來評估品質的一個最重要指標（index），其定義為一個感興趣的品質特徵變數(quality characteristic）落在預先指定規格界限內的機率，品質特徵變數(Y）為統計學上的隨機變數（random variable），規格界限包括規格下限（A）以及規格上限（B），如工業衛生的問題，一位工人在工廠工作，其環境測定放射線物質（Y）是否超過了職業接觸限值（B），職業接觸限值通常是由政府機構設置，這是想要估計一個隨機變量超過某個規格界限，即在估計良質率。本論文是在簡單線性迴歸上來估計單邊良質率的信賴下界，我們使用廣義樞紐量（generalized pivotal quantity）來建構， 經由統計模擬的結果來看，不論是覆蓋率還是期望長度都很合理，在不同設定的樣本數和母體變異數組合下，覆蓋率都接近我們宣稱的信心水準，此外，我們藉由兩個例子來說明本方法在實際應用上的可行性，結果顯示，本論文所使用廣義樞紐量法為適合可靠的方法。

In this study, we investigate the construction of lower confidence limit for unilateral conformance proportions under a simple linear regression model. Let a quality characteristic of interest be denoted by Y, then P(Y≥A) or P(Y≤B) are called the unilateral conformance proportions, where A and B denote the specification acceptance limits. We consider the situation that Y is fitted by the simple linear regression model, and develop an approach for constructing lower confidence limits for the unilateral conformance proportions based on the concept of a generalized pivotal quantity (GPQ). The performance of the proposed method is evaluated through detailed simulation studies and real data analysis. It is shown that the proposed method is easy to implement and reasonably satisfactory for practical use.

謝誌 ii
摘要 iii
Abstract iv
目錄 v
壹、緒論 1
第1節 良質率 1
第1.1節 單邊良質率 1
第1.2節 雙邊良質率 3
第2節 簡單線性迴歸模型 4
第3節 論文架構 6
貳、單邊良質率的信賴下界之估計 7
第1節 廣義樞紐量 7
第2節 簡單線性迴歸模式下單邊良質率的廣義樞紐量 8
第3節 統計模擬 11
表一 13
表二 14
參、實例分析 15
實例1.血液中酒精濃度的估計 15
實例2.化合物的結晶體 17
肆、結果與討論 19
伍、參考文獻 21
附錄 23
附錄I 23
附錄II 25
附錄III 26

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