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 製程損失指Le是以二次損失函數觀點所發展的指標；事實上，Le= Lpe+Lot，其中，Lpe表示潛在相對期望損失，Lot表示偏離目標值相對損失。又Le指標的估計式比Cpm指標的估計式有較優勢的統計推論性質，以及Le指標定義出兩個分離的項式，分別評估製程品質的準確性和精確性。過去學者對於Le指標的研究成果，大都針對單一樣組製程數據進行分析討論；不過，有些時候製程品質數據會以多重樣組的型態收集來呈現。本文就製程品質數據為多重樣組型態所組成時，推導Lpe、Lot和Le指標估計式的動差、期望值、變異數和均方差等分配性質，以及推導Le指標估計式抽樣分配，並且探討與比較各不同指標估計式的推論性質，包含不偏性、一致性和有效性等。 本文亦討論Lpe、Lot和Le指標估計式的漸近分配等相關性質。接著在不同條件下對於Le指標估計式，利用估算信賴水準100(1-α)%的信賴區間上限的方式，提出評估製程品質績效的可靠程序，以利產業實務之應用。並進一步根據信賴區間上限和Le指標估計值的比率，在配合抽樣計畫與檢測成本之情況下，提供實務應用時樣本組合數量決定之參考。
 Process expected loss indices, Lpe, Lot, and Le provide measures to determine the quality performance of a process. In fact, Le= Lpe+Lot, Lpe denotes the potential relative expected loss, Lot is the relative off-target squared. In real situations where the actual values of Lpe, Lot, and Le are unknown one may estimate them by their corresponding sample counterparts. Most of the results obtained regarding the distributional and inferential properties of estimated expected loss indices were based on one single sample. In practice, however, process information is often derived from multiple samples rather than from one single sample. In this paper, we first investigate the distributional and inferential properties of the estimators of process expected loss indices based on multiple samples. We then investigate the performance evaluation of the process based on the determination of 100(1-α)% upper confidence bound of process loss index, Le, for various combinations of sample size, and implement the evaluating procedure. Moreover, this paper provides equation to estimate the approximate the combinations of sample size necessary to achieve a desired upper conference bound with specified confidence level. The technique provided in this paper will be applicable when the process measurements are taken from control chart samples.
 中文摘要...................................................i英文摘要..................................................ii誌謝.....................................................iii目錄......................................................iv表目錄.....................................................v圖目錄....................................................vi第一章 導論................................................1 1.1 研究背景............................................1 1.2 研究動機與目的......................................5 1.3 研究架構............................................7第二章 估計Lpe 和Lot 指標..................................8 2.1 Lpe指標的估計式.....................................8 2.2 Lpe指標估計式的統計性質............................11 2.3 Lot指標的估計式....................................13 2.4 Lot指標估計式的統計性質............................18第三章 估計製程損失指標...................................21 3.1 Le指標的估計式.....................................21 3.2 Le指標估計式的統計性質.............................23第四章 製程損失指標的信賴上限.............................27 4.1 Le指標的信賴上限...................................27 4.2 適當樣本組合數量的決定.............................36第五章 結論與展望.........................................41 5.1 結論...............................................41 5.2 未來展望...........................................42參考文獻..................................................44表目錄表1.1 製程A、B、C、D和E品質績效的比較......................4表1.2 不同的Lpe指標值和Lot指標值組合下的製程良率...........4表4.1 90%信賴水準的信賴區間上限LU，m=10(5)30，n=2(1)10，以及^Le =0.01(0.01)0.10.......................................32表4.2 95%信賴水準的信賴區間上限LU，m=10(5)30，n=2(1)10，以及^Le =0.01(0.01)0.10.......................................33表4.3 97.5%信賴水準的信賴區間上限LU，m=10(5)30，n=2(1)10，以及^Le =0.01(0.01)0.10.....................................34表 4.4 99%信賴水準的信賴區間上限LU，m=10(5)30，n=2(1)10，以及^Le =0.01(0.01)0.10.....................................35表 4.5 90%信賴水準之^Le /LU值，m=5(5)60，n=2(1)15.........38表 4.6 95%信賴水準之^Le /LU值，m=5(5)60，n=2(1)15.........39表 4.7 97.5%信賴水準之^Le /LU值，m=5(5)60，n=2(1)15.......39表 4.8 99%信賴水準之^Le /LU值，m=5(5)60，n=2(1)15.........40圖目錄圖2.1 不同Lpe值的B(~Lpe)曲線，N=60，(m,n)=(a)(10,6)、(b)(12,5)、(c)(15,4)、(d)(20,3)和(e)(30,2)...................10圖2.2 不同Lpe值的MSE(^Lpe)曲線，N=60，(m,n)=(a)(10,6)、(b)(12,5)、(c)(15,4)、(d)(20,3)和(e)(30,2)...................10圖2.3 不同Lpe值的MSE(~Lpe)曲線，N=60，(m,n)=(a)(10,6)、(b)(12,5)、(c)(15,4)、(d)(20,3)和(e)(30,2)...................11圖2.4 不同Lpe值的B(^Lot)曲線，m=10，n=(a)4、(b)5、(c)6、(d)8和(e)10...................................................16圖2.5 不同Lpe值的B(^Lot)曲線，n=5，m=(a)5、(b)10、(c)15、(d)20和(e)30.................................................16圖2.6 不同Lpe值的MSE(^Lot)曲線，Lot=0.06，m=10，n=(a)4、(b)5、(c)6、(d)8和(e)10......................................16圖2.7 不同Lpe值的MSE(^Lot)曲線，Lot=0.06，n=5，m=(a)5、(b)10、(c)15、(d)20和(e)30...................................17圖2.8 不同Lpe值的MSE(~Lot)曲線，Lot=0.06，m=10，n=(a)4、(b)5、(c)6、(d)8和(e)10......................................17圖2.9 不同Lpe值的MSE(~Lot)曲線，Lot=0.06，n=5，m= (a)5、(b)10、(c)15、(d)20和(e)30...................................17圖2.10 不同Lpe值的MSE(^Lot)曲線，(m,n)=(10,6)，Lot =(a)0.56、(b)0.25、(c)0.06、(d)0.03和(e)0.00..................18圖2.11 不同Lpe值的MSE(~Lot)曲線，(m,n)= (10,6)，Lot =(a)0.56、(b)0.25、(c) 0.06、(d)0.03和(e)0.00.................18圖3.1 不同Lpe值的B(^Le)曲線，N=60，(m,n)=(a)(10,6)、(b)(12, 5)、(c)(15,4)、(d)(20,3)和(e)(30,2).......................26圖3.2 不同Lpe值的MSE(^Le)曲線，Le =0.06，N=60，(m,n)=(a)(10,6)、(b)(12,5)、(c)(15,4)、(d)(20,3)和(e)(30,2)........26圖3.3 不同Lpe值的MSE(^Le)曲線，(m,n)=(10,6)，Le =(a)0.11、(b)0.06、(c)0.05、(d)0.04和(e)0.03........................26圖 4.1 不同Lot/Lpe值，95%信賴水準的信賴區間上限LU曲線，^Le=0.11，(m,n)=(10,6)、(12,5)、(15,4)、(20,3)和(30,2) (曲線由上至下依序顯示).........................................30圖 4.2 不同Lot/Lpe值，95%信賴水準的信賴區間上限LU曲線，^Le=0.06，(m,n)=(10,6)、(12,5)、(15,4)、(20,3)和(30,2) (曲線由上至下依序顯示).........................................30圖 4.3 不同Lot/Lpe值，95%信賴水準的信賴區間上限LU曲線，^Le=0.05，(m,n)=(10,6)、(12,5)、(15,4)、(20,3)和(30,2) (曲線由上至下依序顯示).........................................30圖 4.4 不同Lot/Lpe值，95%信賴水準的信賴區間上限LU曲線，^Le=0.04，(m,n)=(10,6)、(12,5)、(15,4)、(20,3)和(30,2) (曲線由上至下依序顯示).........................................31圖 4.5 不同Lot/Lpe值，95%信賴水準的信賴區間上限LU曲線，^Le=0.03，(m,n)=(10,6)、(12,5)、(15,4)、(20,3)和(30,2) (曲線由上至下依序顯示).........................................31圖4.6 不同Lot/Lpe值，90%信賴水準的^Le /LU曲線，(m,n)=(a)(10,6)、(b)(12,5)、(c)(15,4)、(d)(20,3)和(e)(30,2) (曲線由上至下依序顯示).............................................37圖4.7 不同Lot/Lpe值，95%信賴水準的^Le /LU曲線，(m,n)=(a)(10,6)、(b)(12,5)、(c)(15,4)、(d)(20,3)和(e)(30,2) (曲線由上至下依序顯示).............................................37圖4.8 不同Lot/Lpe值，97.5%信賴水準的^Le /LU曲線，(m,n)=(a)(10,6)、(b)(12,5)、(c)(15,4)、(d)(20,3)和(e)(30,2) (曲線由上至下依序顯示).............................................38圖4.9 不同Lot/Lpe值，99%信賴水準的^Le /LU曲線，(m,n)=(a)(10,6)、(b)(12,5)、(c)(15,4)、(d)(20,3)和(e)(30,2) (曲線由上至下依序顯)..............................................38
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