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研究生： 楊淞壹
Sung-Yi Yang
論文名稱： 非對稱型製程能力指標區間估計方法比較之研究
A Comparative Study on Interval Estimation Methods of Asymmetric Capability Index
指導教授： 吳建瑋
Chien-Wei Wu
口試委員: 林義貴
Yi-Kuei Lin
陳建良
James C. Chen
學位類別： 碩士
Master
系所名稱： 管理學院 - 工業管理系
Department of Industrial Management
論文出版年： 2013
畢業學年度： 101
語文別： 英文
論文頁數： 118
中文關鍵詞： 信賴下界 、涵蓋率 、製程能力指標 、非對稱規格
外文關鍵詞： process capability indices, coverage rate, Lower confidence bound, asymmetric tolerances.
相關次數： 點閱：351  下載：1 
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    • 製程能力指標(process capability indices)能針對製程產出之品質水準提供一個量化的數值，因此已廣泛地被運用於衡量產品品質保證及評估製程產出績效，各種指標中，又以 指標被最廣泛使用。然而， 指標在非對稱製程規格(asymmetric tolerances)下並無法精確地衡量製程的產出績效，因此近年來許多學者開始致力於提出可衡量非對稱規格之製程能力指標，其中以 指標較能有效精確地評估製程產出績效。但由於 指標估計式的抽樣分配過於複雜，導致不易求算出指標精確的區間估計。因此，本研究主要目的是將利用過去文獻上針對 指標所提出的區間估計方法以及可用來建構區間估計的統計方法包含有廣義信賴區間(Generalized Confidence Intervals method, GCI)法，貝氏(Bayesian method, BA)法，四種利用複式抽樣(Bootstrap method)法的模擬技巧(SB method, PB method, BCPB method, PTB method)以及抽樣分配(Frequency distribution approach, FD和FD*)法，來求算 指標之信賴區間進而比較及探討其在非對稱規格下的評估能力。再者，透過模擬方式計算及比較各方法的表現，藉由其所求得的涵蓋率(Coverage Rate, CR)與信賴下界計算平均值(Average Value of Lower Confidence Bound, AVLCB)進行比較與討論。分析結果顯示，整體而言FD*法、GCI法及BA法較俱充分地解釋能力來評估非對稱規格下的製程能力表現。最後，本文透過一案例分析及說明以提供決策者在評估製程之能力的參考依據。

    Several process capability indices have been widely used to provide quantitative numerical measures on process performance. In particular, the index is most commonly used to measure process capability for cases with symmetric tolerances. However, it has been shown that the index is inappropriate to measure process performance for cases with asymmetric tolerances. Therefore, many scholars have devoted to develop new generalizations of process capability index , but only can efficiently evaluate the capability precisely. Unfortunately, the sampling distribution of the estimated is very complicated, which leads to construct exact confidence interval becoming quite difficult. In this thesis, several available methods are examined and discussed for approximate confidence intervals of the index . These methods include Generalized Confidence Intervals method (GCI), Bayesian method (BA), Bootstrap methods (SB, PB, BCPB, PTB), and Frequency Distribution methods (FD, FD*). A series of simulations is conducted to evaluate and compare the performance of these methods in terms of Coverage Rate (CR) and Average Value of Lower Confidence Bound (AVLCB). The results indicate that FD*, GCI and BA methods are recommended to assess process performance for cases with asymmetric tolerances. Finally, an application example is presented for illustration.

    中文摘要 ii Abstract iii 1. Introduction 1 1.1 Research Background and Motivation 1 1.2 Research Objectives 4 1.3 Research Organization 5 2. Literature Review 8 2.1 Process Capability Indices for Symmetric Case 8 2.2 Process Capability Indices for Asymmetric Case 11 2.3 The Eestimated and Its Sampling Distribution 14 3. Methodology 17 3.1 Frequency Distribution (FD/ FD*) Method 17 3.2 Generalized Confidence Interval (GCI) Method 21 3.3 Bootstrap Method 25 3.3.1 The Standard Bootstrap (SB) Method 26 3.3.2 The Percentile Bootstrap (PB) Method 28 3.3.3 The Biased-Corrected Percentile Bootstrap (BCPB) Method 28 3.3.4 The Percentile-T Bootstrap (PTB) Method 30 3.4 Bayesian (BA) Method 33 4. Performance Comparisons 39 4.1. Simulation Layout Setting 39 4.2 Coverage Rate (CR) Analysis 48 4.2.1. The Performance of CR for FD and FD* Method 59 4.2.2. The Performance of CR for GCI Method 60 4.2.3. The Performance of CR for SB, PB, BCPB and PTB Method 61 4.2.4. The Performance of CR for Bayesian Method 62 4.3 Average Value of Lower Confidence Bound (AVLCB) Analysis 64 4.4 Confidence Interval Analysis 74 5. An Application Example 80 6. Conclusions and Future Works 84 References 86 Appendix 88  

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