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 系統識別號 U0002-1206200917100300 中文論文名稱 型二設限貝氏抽樣計畫之提前接受決策規則 英文論文名稱 Bayesian Sampling Plans for Type II Censored Data with an Early Acceptance Decision Rule 校院名稱 淡江大學 系所名稱(中) 統計學系碩士班 系所名稱(英) Department of Statistics 學年度 97 學期 2 出版年 98 研究生中文姓名 莊銘棋 研究生英文姓名 Ming-Chi Chuang 學號 696650067 學位類別 碩士 語文別 英文 口試日期 2009-05-22 論文頁數 49頁 口試委員 指導教授-蔡宗儒委員-林豐澤委員-蘇懿委員-廖敏治 中文關鍵字 貝氏風險  提前接受決策規則  先驗分配  允收抽樣計畫  型二設限檢測 英文關鍵字 Bayes risk  Early acceptance decision rule  Prior distribution  Acceptance sampling plan  Type II censored test 學科別分類 學科別＞自然科學＞統計 中文摘要 本論文對型二設限指數分配壽命資料建立貝氏抽樣計畫之提前接受決策規則。文中並提供一個演算法來尋找最佳的貝氏抽樣計畫的提前接受決策規則。數值分析結果指出，本論文建議的提前接受決策規則有助於縮短壽命檢測之試驗時間。並且，舉出一個實例說明所建議方法之應用。 表單編號：ATRX-Q03-001-FM030-01 英文摘要 In this thesis, an early acceptance decision rule is considered to establish the Bayesian sampling scheme for type II censored exponential data. Algorithms are provided to determine the optimal Bayesian sampling plans with an early acceptance decision rule. Numerical results indicate that the proposed early acceptance decision rule helps to shorten the experimental time of a life test. Moreover, an example is used to illustrate the application of the proposed method. 表單編號：ATRX-Q03-001-FM031-01 論文目次 Contents 1 Introduction 1 2 Bayesian Sampling Plans with Type II Censoring 5 3 Bayesian Sampling Plans with an Early Acceptance Decision Rule 12 4 Example 18 5 Numerical Results 21 6 Conclusions 46 List of Tables 5.1 The minimum Bayes risks RS(nB, rB, deltaB) and optimal sampling plans for alpha = 4, beta = 1.25, a0 = 7, a1 = 5, a2 = 5, and N = 800. . . . . . . . . . . . . 25 5.2 The minimum Bayes risks RS(nB, rB, deltaB) and optimal sampling plans for alpha = 4, beta = 1.25, a0 = 7, a1 = 5, a2 = 5, and N = 1000. . . . . . . . . . . . 26 5.3 The minimum Bayes risks RS(nB, rB, deltaB) and optimal sampling plans for alpha = 4, beta = 1.25, a0 = 7, a1 = 5, a2 = 5, and N = 1500. . . . . . . . . . . . 27 5.4 The minimum Bayes risks RS(nB, rB, deltaB) and optimal sampling plans for alpha = 4, beta = 1.25, a0 = 7, a1 = 5, a2 = 5, and N = 2000. . . . . . . . . . . . 28 5.5 The minimum Bayes risks RS(nB, rB, deltaB) and optimal sampling plans for alpha = 4, beta = 1.25, a0 = 7, a1 = 5, a2 = 5, and N = 3000. . . . . . . . . . . . 29 5.6 The minimum Bayes risks RS(nB, rB, deltaB) and optimal sampling plans for alpha = 4, beta = 1.25, a0 = 7, a1 = 5, a2 = 5, and N = 5000. . . . . . . . . . . . 30 5.7 The minimum Bayes risks RS(nB, rB, deltaB) and optimal sampling plans for alpha = 5, beta = 1.75, a0 = 7, a1 = 5, a2 = 5, and N = 800. . . . . . . . . . . . . 31 5.8 The minimum Bayes risks RS(nB, rB, deltaB) and optimal sampling plans for alpha = 5, beta = 1.75, a0 = 7, a1 = 5, a2 = 5, and N = 1000. . . . . . . . . . . . 32 5.9 The minimum Bayes risks RS(nB, rB, deltaB) and optimal sampling plans for alpha = 5, beta = 1.75, a0 = 7, a1 = 5, a2 = 5, and N = 1500. . . . . . . . . . . . 33 5.10 The minimum Bayes risks RS(nB, rB, deltaB) and optimal sampling plans for alpha = 5, beta = 1.75, a0 = 7, a1 = 5, a2 = 5, and N = 2000. . . . . . . . . . . . 34 5.11 The minimum Bayes risks RS(nB, rB, deltaB) and optimal sampling plans for alpha = 5, beta = 1.75, a0 = 7, a1 = 5, a2 = 5, and N = 3000. . . . . . . . . . . . 35 5.12 The minimum Bayes risks RS(nB, rB, deltaB) and optimal sampling plans for alpha = 5, beta = 1.75, a0 = 7, a1 = 5, a2 = 5, and N = 5000. . . . . . . . . . . . 36 5.13 The correction rate of the early decision rule for C4 = 50 with 1000 repetitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.14 The correction rate of the early decision rule for C4 = 60 with 1000 repetitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 5.15 The correction rate of the early decision rule for C4 = 80 with 1000 repetitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 List of Figures 3.1 Flowchart of the proposed early decision rule. . . . . . . . . . . . . . . . . 17 4.1 The searching procedure of the early decision rule: (a) m = 6, (b) m = 7, (c) m = 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.1 The value of phi for various batch sizes with C4 = 50, alpha = 4 and beta = 1.25. . 40 5.2 The value of phi for various batch sizes with C4 = 50, alpha = 5 and beta = 1.75. . 41 5.3 The value of phi for various batch sizes with C4 = 60, alpha = 4 and beta = 1.25. . 42 5.4 The value of phi for various batch sizes with C4 = 60, alpha = 5 and beta = 1.75. . 43 5.5 The value of phi for various batch sizes with C4 = 80, alpha = 4 and beta = 1.25. . 44 5.6 The value of phi for various batch sizes with C4 = 80, alpha = 5 and beta = 1.75. . 45 參考文獻 [1] Chen, J., Choy, S.T.B., and Li, K.-H. 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