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 系統識別號 U0002-3006201014213000 中文論文名稱 指數型設限資料的貝氏計量值抽樣計畫 英文論文名稱 Bayesian Variable Sampling Plans for the Exponential Distribution Based on Censored Samples 校院名稱 淡江大學 系所名稱(中) 數學學系博士班 系所名稱(英) Department of Mathematics 學年度 98 學期 2 出版年 99 研究生中文姓名 黃彥龍 研究生英文姓名 Yen-Lung Huang 學號 892150029 學位類別 博士 語文別 英文 口試日期 2010-06-25 論文頁數 69頁 口試委員 指導教授-林千代委員-黃連成委員-陳麗霞委員-吳秀芬委員-吳碩傑 中文關鍵字 貝氏風險  離散分割法  最大概似估計法  普通的混合設限  (修正) 逐步混合設限  模擬退火演算法 英文關鍵字 Bayes risk  Discretization method  Maximum likelihood estimation  Ordinary hybrid censoring  (Adaptive) Progressive hybrid censoring  Simulated annealing algorithm 學科別分類 中文摘要 本論文首先提出一個新的修正逐步混合型I設限計畫。然後，我們根據 Childs et al. (2003) 和 Childs et al. (2008) 的結果推導出指數型I設限和修正的逐步混合型I及型II設限資料下之最大概似估計值的分配。利用不同設限資料下所得之最大概似估計值的分配，我們分別針對簡單和一般性的損失函數建立抽樣計畫之貝氏風險函數，再應用 Lam (1994) 的離散分割法或模擬退火演算法找出最佳的抽樣計畫。最後，我們呈現一些數據及比較來驗證本論文所提出的方法之有效性及穩定性。 英文摘要 In this dissertation, we propose a new adaptive Type-I progressive hybrid censoring scheme. We follow the work of Childs et al. (2003) and Childs et al. (2008) to derive the exact distributions of the maximum likelihood estimator of the mean lifetime of an exponential distribution under Type-I censoring and both types of adaptive progressive hybrid censoring schemes. Based on the distributions of maximum likelihood estimator, we obtain the explicit expressions for the Bayes risks of sampling plans when a simple or general loss function is used. The discretization method of Lam (1994) and the simulated annealing algorithm are then used to determine the optimal sampling plans under different censoring schemes. Some numerical examples and comparisons are presented to illustrate the effectiveness of the proposed method. 論文目次 Contents 1 Introduction 1 1.1 Background and Motivation 1 1.2 Censoring Schemes 4 1.3 Overview 10 2 The Distributions of MLE of θ 11 2.1 Pdf of hat{θ} under Type-I censoring 12 2.2 Pdf of hat{θ} under HCS 14 2.3 Pdf of hat{θ} under PHCS 15 2.4 Pdf of hat{θ} under APHCS 16 3 Variable Sampling Plans With a Simple Loss Function 21 3.1 Bayes Risks 22 3.2 Algorithm for Optimal Solutions 25 3.3 Numerical Results 26 3.3.1 Results for Type-I Censoring 27 3.3.2 Results for HCS 28 3.3.3 Results for PHCS 30 4 Variable Sampling Plans With a General Loss Function 45 4.1 Loss function and Bayes Risks 46 4.2 PMF of m* 47 4.3 The expressions of EλEX|λ[m*|λ] and EλEX|λ[τ|λ] 52 4.3.1 Results for Type-II APHCS 52 4.3.2 Results for Type-I APHCS 53 4.3.3 Results for PHCS 54 4.4 Numerical Results 57 5 Concluding Remarks and Areas for Further Research 62 Appendix: Simulated Annealing Algorithm 64 References 66 List of Tables 3.1 The minimum Bayes risks and optimal sampling plans for a0 = 2.0, a1 =2.0, a2 = 2.0, Cs = 0.5, Cr = 30, and some selected values of a and b 32 3.2 The minimum Bayes risks and optimal sampling plans for a = 2.5, b = 0.8, a1 = 2.0, a2 = 2.0, Cs = 0.5, Cr = 30, and some selected values of a0 33 3.3 The minimum Bayes risks and optimal sampling plans for a = 2.5, b = 0.8, a0 = 2.0, a2 = 2.0, Cs = 0.5, Cr = 30, and some selected values of a1 33 3.4 The minimum Bayes risks and optimal sampling plans for a = 2.5, b = 0.8, a0 = 2.0, a1 = 2.0, Cs = 0.5, Cr = 30, and some selected values of a2 34 3.5 The minimum Bayes risks and optimal sampling plans for a = 2.5, b = 0.8, a0 = 2.0, a1 = 2.0, a2 = 2.0, Cs = 0.5, and some selected values of Cr 34 3.6 The minimum Bayes risks and optimal sampling plans for a = 2.5, b = 0.8, a0 = 2.0, a1 = 2.0, a2 = 2.0, Cr = 30, and some selected values of Cs 35 3.7 The minimum Bayes risks and optimal sampling plans for a0 = 2.0, a1 =2.0, a2 = 2.0, Cs = 0.5, Cr = 30, and some selected values of a and b 36 3.8 The minimum Bayes risks and optimal sampling plans for a = 2.5, b = 0.8, a1 = 2.0, a2 = 2.0, Cs = 0.5, Cr = 30, and some selected values of a0 37 3.9 The minimum Bayes risks and optimal sampling plans for a = 2.5, b = 0.8, a0 = 2.0, a2 = 2.0, Cs = 0.5, Cr = 30, and some selected values of a1 38 3.10 The minimum Bayes risks and optimal sampling plans for a = 2.5, b = 0.8, a0 = 2.0, a1 = 2.0, Cs = 0.5, Cr = 30, and some selected values of a2 39 3.11 The minimum Bayes risks and optimal sampling plans for a = 2.5, b = 0.8, a0 = 2.0, a1 = 2.0, a2 = 2.0, Cr = 30, and some selected values of Cs 40 3.12 The minimum Bayes risks and optimal sampling plans for a = 2.5, b = 0.8, a0 = 2.0, a1 = 2.0, a2 = 2.0, Cs = 0.5, and some selected values of Cr 41 3.13 The minimum Bayes risks and optimal sampling plans for some selected values of a, b, a0, a1, a2, Cs, and Cr under Type-I censoring 42 3.14 The minimum Bayes risks and optimal sampling plans for some selected values of a, b, a0, a1, a2, Cs, and Cr under Type-II censoring 43 3.15 The minimum Bayes risks and optimal sampling plans for some selected values of a, b, a0, a1, a2, Cs, and Cr under Type-I censoring 44 4.1 The minimum Bayes risk and optimal sampling plans for some selected values of a, b, a2, C3 and C4 under Type-II censoring 60 4.2 The minimum Bayes risk and optimal sampling plans for some selected values of a, b, a2, C3 and C4 under Type-I censoring 61 List of Figures 1.1 Schematic representation of HCS 5 1.2 Schematic representation of Type-I PHCS 6 1.3 Schematic representation of Type-II PHCS 7 1.4 Schematic representation of Type-II APHCS 8 1.5 Schematic representation of Type-I APHCS 9 參考文獻 Balakrishnan, N. 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The decision theory approach to sampling inspection. Journal of the Royal Statistical Society, Series B 28, 381--416. Wetherill, G. B. and Kollerstrom, J. (1979). Sampling inspection simplified. Journal of the Royal Statistical Society, Series A 142, 1--32. 論文使用權限 同意紙本無償授權給館內讀者為學術之目的重製使用，於2013-07-09公開。同意授權瀏覽/列印電子全文服務，於2013-07-09起公開。 若您有任何疑問，請與我們聯絡！圖書館： 請來電 (02)2621-5656 轉 2487 或 來信 dss@mail.tku.edu.tw 