隨著全球化的競爭激烈，以及生活水準的提高所帶來消費者對於產品的品質有更進一步的認識與要求的。因此，生產者必須更重視品質管理，以致於能達到或者超過消費者的需求，以提高與同行的競爭力。由於製程能力指標能夠客觀的表現出製程是否有能力製造出符合消費者所需的產品品質。近幾年來，製程能力指標發展逐漸成熟常被製造業品管上廣大的運用。目前最常使用的製程能力指標 、 、 及 等，而本研究的目的在於針對Chan et al.(1988)等學者所提出的製程能力指標 來進行信賴區間長度的估計。首先第一部份考慮不同事前分配的情況下，並使用Zimmer、Hubble與Zimmer(2001)所提出均分兩尾 信賴區間的方法來建立 的雙尾信賴區間。第二部份則是針對在特殊情況下 使用Non-informative Prior與Gamma Prior的信賴區間長度作模擬比較，同時也針對在一般情況下 使用Non-informative Prior與Gamma Prior的信賴區間長度作模擬比較。本文包含五個章節，第一章說明本文研究動機與目的、研究方法。第二章探討幾個重要的製程能力指標。第三章針對其中一個製程能力指標 ，在考慮Non-informative Prior與Gamma Prior的情況下建立 的雙尾信賴區間。第四章延續第三章的研究，分別針對特殊情況下 與一般情況下 作電腦模擬比較。最後，第五章提出本文的結論以及未來研究的方向。

In pace with the intense global competition, as well as the increase of the living standard makes the consumer to go step further understanding and the request regarding the product quality. Therefore, the producer must to take the quality control seriously, with the result that it can achieve or surpass consumer's demand, meanwhile it enhances colleague's competitive ability. Because Process Capability Index can perform Process whether it can conform with the product quality which the consumer needs objectively.
    Nearly, Process Capability Index develop gradually is mature often by in manufacturing industry the quality control on the general utilization. At present most often uses Process Capability Index such as Cp、Cpk、Cpm and Cpmk 。
    This goal of the research lies in Process Capability Index which is denoted as Cpm to estimate confidence interval length presented by Chan et al.(1988). In the first part, I consider different prior and use the classical two sided approach presented by Zimmer、Hubble and Zimmer(2001) to build on two-sided confidence interval for Cpm. The second part , I aim at using Non-informative Prior and the Gamma Prior confidence interval length and make the simulation to compare in the peculiar circumstance 。Simultaneously, I also aim at uses Non-informative Prior and the Gamma Prior confidence interval length and make the simulation to compare in the ordinary circumstances . This paper contains five chapters, the first chapter include this research objective and research method. The second chapter discuss several important Process Capability Index. The third chapter aims at one of the capability indices, denoted as Cpm. I consider Non-informative Prior and in the Gamma Prior situation and establish two-sided confidence interval for Cpm. The fourth chapter continues the research of the third chapter. I focus on the peculiar circumstance  to compare with the ordinary circumstances  with computer simulation Separately. Finally, the fifth chapter will propose the research conclusion and the future research direction.

目錄
目錄	I
表目錄	III
圖目錄	IV
第一章 緒論	1
1.1 研究背景與動機	1
1.2 研究方法	3
第二章  文獻探討	4
2.1 製程能力指標Cp 4
2.2 製程能力指標Cpk4
2.3 製程能力指標Cpm5
2.4 製程能力指標Cpmk6
第三章  研究方法	7
3.1 利用無訊息事前分配的貝氏估計分析Cpm製程能力指標	7
3.1.1Cpm雙尾信賴區間建立(case 1 特殊情形u=T)	8
3.1.2Cpm雙尾信賴區間建立(case 2 特殊情形   )	12
3.2 利用Gamma事前分配的貝氏估計分析Cpm製程能力指標	17
3.2.1Cpm雙尾信賴區間建立(case 1 特殊情形u=T)	18
3.2.2Cpm雙尾信賴區間建立(case 2 特殊情形   )	23
第四章 Cpm的信賴區間模擬結果比較	29
4.1當u=T(特殊情況下)時，利用無訊息事前分配與Gamma事前分配所建立的Cpm信賴區間模擬比較	29
4.2當 (一般情況下)時，利用無訊息事前分配與Gamma事前分配所建立的Cpm信賴區間模擬比較	35
第五章 結論	41
5.1 結論	41
5.2 未來的研究方向	42
參考文獻	43
 
表目錄
表4.1  當u=T時，使用Non-information Prior在不同的n下建立Cpm95%信賴區間上限與信賴區間下限……………………32
表4.2  當u=T時，使用Gamma Prior在不同的n下建立Cpm95%信賴區間上限與信賴區間下限 …………………………………33
表4.3  在不同樣本數n的情況下，Non-information事前分配所求的信賴區間長度(D1)與Gamma事前分配所求的信賴區間長度(D2)之比值(P12)……………………………………………34
表4.4  在不同樣本數n與不同 的情況下，Non-information事前分配所求的信賴區間長度(D1)與Gamma事前分配所求的信賴區間長度(D2)之比值(P34)……………………………………38




 
圖目錄
圖4.1  當u=T時，在樣本數n=5、不同的 與不同的目標值T情況下，Gamma事前分配所求得的信賴區間長度(D4)減去Non-information事前分配所求的信賴區間長度(D3)之信賴區間長度差 …………………………………………………39
圖4.2   當u=T時，在樣本數n=30、不同的 與不同的目標值T情況下，Gamma事前分配所求得的信賴區間長度(D4)減去Non-information事前分配所求的信賴區間長度(D3)之信賴區間長度差 ………………………………………………39
圖4.3  當u=T時，在樣本數n=100、不同的 與不同的目標值T情況下Gamma事前分配所求得的信賴區間長度(D4)減去Non-information事前分配所求的信賴區間長度(D3)之信賴區間長度差 …………………………………………………40

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