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研究生: 梁偉賢
Wei-hsien Liang
論文名稱: 應用拔靴法建構多注頭製程能力指標MSpk之信賴區間
The Bootstrap confidence intervals of the process yield index MSpk for multiple streams process
指導教授: 王福琨
Fu-Kwun Wang
口試委員: 林希偉
Shi-Woei Lin
歐陽超
Chao Ou-Yang
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: 中文
論文頁數: 61
中文關鍵詞: 拔靴法多注頭製程製程能力指標信賴區間
外文關鍵詞: Bootstrap method, Multiple streams process, Process capability index, Confidence interval
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  • 這篇論文的目的在應用拔靴法建構在95%信心水準下多注頭製程能力指標MSpk與MSpk,s信賴區間的研究成果。分別以兩種資料型態:單樣本資料與次樣本資料為資料來源並應用標準拔靴法、百分位拔靴法、修正偏度百分位拔靴法以及修正偏度加速度百分位拔靴法,此四種拔靴法信賴區間分別建構製程能力指標MSpk與MSpk,s之信賴區間,此外,模擬研究中針對樣本數、注頭數量、MSpk與MSpk,s真實值與拔靴法信賴區間做變異數分析之研究,以期找出各因子對信賴區間的影響。
    最後則是以覆蓋率,信賴區間平均長度及信賴區間長度標準差三項評量標準找出最佳之拔靴法信賴區間。在研究中發現,無論樣本資料是單樣本或次樣本資料,樣本數越大時會有較優之區間長度,且由模擬研究與實例結果可知,在95%的信心水準下百分位拔靴法為最佳的拔靴法信賴區間。


    The paper aims to present the results of the four 95 percent bootstrap confidence intervals, i.e. standard bootstrap (SB), percentile bootstrap (PB), biased-correction percentile bootstrap (BCPB) and biased-correction and accelerated bootstrap (BCa) for estimating two capability indices MSpk for one single sample and MSpk,s for subsamples which are from multiple streams process. Additionally, an analysis of variance (ANOVA) table is made to study the effects of the bootstrap methods, the true value of MSpk and MSpk,s,the number of streams and the sample size on the bootstrap confidence intervals. Finally, we use the three assessment criteria, that is, coverage percentage, the average length of bootstrap confidence interval and the standard deviation of length interval to get the best result within the four 95 percent bootstrap confidence intervals.
    For multiple process streams, whether the data is the single or subsamples, the greater number of the samples will be better in the average length of bootstrap confidence interval. Percentile bootstrap is the best method of those bootstrap methods in the 95 percent confidence level.

    摘要 I Abstract II 目錄 III 圖目錄 IV 表目錄 V 第一章 緒論 1 1.1 研究動機 1 1.2 研究目的 3 1.3 研究範圍與限制 3 1.4 研究流程 3 第二章 文獻探討 6 2.1 多注頭製程簡介 6 2.2 資料型態 7 2.2.1單樣本資料(One single sample) 7 2.2.2次樣本資料(Subsamples) 7 2.3 多注頭製程之點估計與區間估計 8 2.3.1多注頭之單樣本製程能力指標MSpk 8 2.3.2多注頭之次樣本製程能力指標MSpk,s 11 2.4 拔靴法簡介 12 2.4.1無母數拔靴法 13 2.4.2有母數拔靴法 13 2.5 應用拔靴法建構多注頭製程指標Cpk之信賴區間 14 第三章 應用拔靴法建構多注頭製程能力指標MSpk與MSpk,s之信賴區間 17 3.1 製程能力指標MSpk之拔靴法信賴區間 17 3.2信賴區間評估指標 19 第四章 模擬與實例分析 21 4.1 模擬研究 21 4.1.1單樣本資料之模擬研究 22 4.1.2 次樣本資料之模擬研究 27 4.2 實例驗證 32 4.2.1單樣本資料之實例驗證 32 4.2.2次樣本資料之實例驗證 35 第五章 結論與建議 37 參考文獻 38 附錄 39

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