基於韋伯分配下之非常態製程能力指標比較與信賴區間建構

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研究生：	卓思潔 Chuo, Szu-Chieh
論文名稱：	基於韋伯分配下之非常態製程能力指標比較與信賴區間建構 Comparison and Interval Estimation of Non-normal Process Capability Indices under Weibull Distribution
指導教授：	吳建瑋 Wu, Chien-Wei
口試委員:	張英仲蘇明鴻
學位類別：	碩士 Master
系所名稱：	工學院 - 工業工程與工程管理學系 Department of Industrial Engineering and Engineering Management
論文出版年：	2018
畢業學年度：	106
語文別：	中文
論文頁數：	71
中文關鍵詞：	貝氏方法、馬可夫鏈蒙地卡羅、複式抽樣法、信賴區間、製程良率
外文關鍵詞：	Bayesian approach, Markov Chain Monte Carlo, Bootstrap resampling, Confidence intervals, Process yield
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隨著科技的發展，產品品質是現代消費者選擇產品的重要根據之一，也是企業增強自身競爭力不容忽視的環節，因此，產品的品質管理顯得越趨重要。製程能力指標是一個被廣泛使用來改善品質的品質管理工具，然而，傳統的製程能力指標如Cp、Cpk 等都是基於常態分配的假設之下，若是在製程為非常態的情況下使用，會有錯估的情形發生。因此，本研究選擇了韋伯分配為研究主軸，針對在韋伯分配下的非常態製程能力指標使用情形作分析。
研究第一部分比較並分析多個非常態製程能力指標，包含C_Npk、C'_Npk 、C_Npkg、C_NpkG、C_'NpkG 等，在韋伯分配的情境下的使用情形，評估各指標的穩定性以及其是否能有效反映良率好壞。接著，針對指標建構其信賴區間，在此本研究使用貝氏方法來建構區間，並以傳統的無母數方法之複式抽樣法進行比較。貝氏方法結合了馬可夫鏈蒙地卡羅技巧，針對韋伯分配參數進行多次迭代並建構指標之信賴區間，而複式抽樣法則是選擇了標準型複式抽樣法、百分位點複式抽樣法、偏誤修正百分位點複式抽樣法三種計算方式。研究結果顯示，本研究所發展之馬可夫鏈蒙地卡羅方法在涵蓋率與平均寬度兩部分皆有更好的信賴區間建構效果。

Owing to advances in technology, the quality of the product is an important factor for consumers and also the essential factor for a company to enhance their competitiveness. Process capability indices (PCIs) are considered to be useful quality measurement tools. However, the traditional PCIs including Cp and Cpk are appropriate for normal distribution. When the distribution of a process is non-normal, these PCIs often lead to erroneous interpretation. As the result, in this study, we focus on the non-normal process capability indices for Weibull distribution, analyze if these non-normal PCIs are suitable for Weibull distribution.
In the first part of this study, five non-normal PCIs, including C_Npk, C'_Npk, C_Npkg, C_NpkG and C_'NpkG, are compared under Weibull distribution and we also measure each of them to find the most stable and suitable one. In the second part of this study, we use Bayesian method and integrate it with Markov Chain Monte Carlo technique to construct confidence intervals. Then, we compare them with traditional Bootstrap sampling method. For the Bootstrap sampling technique, we use three types of Bootstrap interval estimation methods. Finally, we found out that MCMC technique performed better in both coverage probability and average width.

摘要---------------------------------------i
Abstract----------------------------------ii
致謝-------------------------------------iii
目錄--------------------------------------iv
圖目錄------------------------------------vi
表目錄-----------------------------------vii
第一章    緒論-------------------------------1
1.1    研究背景與動機----------------------1
1.2    研究目的與方法----------------------3
1.3    研究架構----------------------------3
第二章    文獻回顧與探討----------------------6
2.1    製程能力指標------------------------6
2.1.1    基本型製程能力指標-------------------6
2.1.2    非常態製程能力指標-------------------7
2.1.3    韋伯分配之製程能力指標---------------9
2.2    複式抽樣方法------------------------13
2.2.1    標準型複式抽樣法--------------------14
2.2.2    百分位點複式抽樣法------------------14
2.2.3    偏誤修正百分位點複式抽樣法-----------15
2.3    貝氏方法---------------------------15
2.4    馬可夫鏈蒙地卡羅方法----------------17
2.4.1    Gibbs 抽樣法-----------------------18
2.4.2    適應性拒絕抽樣法--------------------19
2.4.3    Metropolis-Hastings演算法----------21
2.4.4    適應性拒絕Metropolis抽樣法----------22
第三章    非常態製程能力指標分析與比較--------25
3.1    非常態製程能力指標之真值分析---------25
3.1.1    參數設定與執行步驟------------------25
3.1.2    固定良率下不同指標穩定度比較---------27
3.1.3    良率與不同指標對應分析---------------29
3.2    不同指標之估計值偏誤分析-------------33
3.3    非常態製程能力指標分析結果-----------37
第四章    非常態製程能力指標區間估計方法------38
4.1    模擬方法及執行步驟-------------------38
4.1.1    參數設計----------------------------40
4.1.2    涵蓋率與平均寬度---------------------41
4.2    複式抽樣方法模擬結果-----------------42
4.3    馬可夫鏈蒙地卡羅---------------------46
4.3.1    馬可夫鏈蒙地卡羅方法執行流程----------46
4.3.2    馬可夫鏈蒙地卡羅模擬結果--------------48
4.4    複式抽樣方法與馬可夫鏈蒙地卡羅比較-----50
4.5    案例分析----------------------------55
第五章    結論與未來研究-----------------------60
5.1    結論--------------------------------60
5.2    未來研究方向-------------------------61
參考文獻------------------------------------62
英文文獻----------------------------62
附錄A---------------------------------------65
附錄B---------------------------------------66
附錄C---------------------------------------68
附錄D---------------------------------------70

                                

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