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系統識別號 U0002-1106200921510500
中文論文名稱 型一設限貝氏抽樣計畫之提前決策規則
英文論文名稱 Bayesian Sampling Plans for Type I Censored Data with an Early 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 周玟菁
研究生英文姓名 Wen-Ching Chou
學號 696650299
學位類別 碩士
語文別 英文
口試日期 2009-05-22
論文頁數 30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  指數分配  損失函數  抽樣計畫  型一設限 
英文關鍵字 Bayes risk  Exponential distribution  loss function  Sampling plan  Type I censoring 
學科別分類 學科別自然科學統計
中文摘要 本論文對型一設限指數分配壽命資料建立貝氏抽樣計畫之提前
決策規則。本提前決策規則有助於決策者在設限時間之前尋找到最
佳的貝氏決策。文中並提供一個執行提前貝氏決策的演算法。我們
舉出兩個實例說明所建議方法之應用,並在模擬研究下利用數值分
析的方法來評估所提出的提前決策規則之績效。數值結果指出,本
文建議的方法很容易使用,並可有效地在型一設限資料下的貝氏抽
樣計畫中達到提前決策。
表單編號:ATRX-Q03-001-FM030-01
英文摘要 The thesis introduces an early decision rule to the design of Bayesian
sampling plans for the exponential distribution with type I censoring. Using
the proposed early decision rule, a Bayesian decision could be reached before
the censoring time. An algorithm for implementing an early Bayesian decision
is provided. Two examples are used for illustrating the proposed method.
An intensive simulation study is conducted, and performance of the proposed
early decision rule is evaluated numerically. Numerical results show that
the proposed method is easy to operate and helps to reach an early decision
for typical Bayesian sampling plans with type I censoring.
表單編號:ATRX-Q03-001-FM031-01
論文目次 Contents
1 Introduction 1
2 Literature Review: Bayesian Sampling Plans with Type I Censoring 4
3 Early Decision Rule and Examples 9
3.1 Early Decision Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4 Numerical Study 18
5 Conclusions 28
List of Tables
3.1 Values of Y1,Y2,am,am(s) for Batch A. . . . . . . . . . . . . . . . . 16
3.2 Values of Y1,Y2,am,am(s) for Batch B. . . . . . . . . . . . . . . . . 16
3.3 Values of Y1,Y2,am,am(s) for Batch
C. . . . . . . . . . . . . . . . . 17
3.4 Values of Y1, Y2, am and am(s) for the Batch of products. . . . . . . . . . . 17
4.1 The minimum Bayes risks r(nB, tB, Delta B) and optimal sampling plans for
a0 = 2, a1 = 2, a2 = 2, arfa = 2.3, bata = 0.6. . . . . . . . . . . . . . . . . . . . 20
4.2 The minimum Bayes risks r(nB, tB, Delta B) and optimal sampling plans for
a0 = 2, a1 = 2, a2 = 2, arfa = 2.5, bata = 0.6. . . . . . . . . . . . . . . . . . . . 21
4.3 The minimum Bayes risks r(nB, tB, Delta B) and optimal sampling plans for
a0 = 2, a1 = 2, a2 = 2, arfa = 2.7, bata = 0.6. . . . . . . . . . . . . . . . . . . . 22
4.4 The minimum Bayes risks r(nB, tB, Delta B) and optimal sampling plans for
a0 = 2, a1 = 2, a2 = 2, arfa = 2.5, bata = 0.8. . . . . . . . . . . . . . . . . . . . 23
4.5 The minimum Bayes risks r(nB, tB, Delta B) and optimal sampling plans for
a0 = 2, a1 = 2, a2 = 2, arfa = 2.5, bata = 1.0. . . . . . . . . . . . . . . . . . . . 24
4.6 Performance checking for the early decision rule with Lamda= 0.8521 , a0 = 2,
a1 = 2, a2 = 2, C1 = 0.2, C2 = 0.5, C3 = 30. . . . . . . . . . . . . . . . . . 25
4.7 Performance checking for the early decision rule with Lamda= 0.9141 , a0 = 2,
a1 = 2, a2 = 2, C1 = 0.2, C2 = 0.5, C3 = 30. . . . . . . . . . . . . . . . . . 25
4.8 Performance checking for the early decision rule with Lamda= 1.5152 , a0 = 2,
a1 = 2, a2 = 2, C1 = 0.2, C2 = 0.5, C3 = 30. . . . . . . . . . . . . . . . . . 25
4.9 Performance checking for the early decision rule with Lamda= 1.7023 , a0 = 2,
a1 = 2, a2 = 2, C1 = 0.2, C2 = 0.5, C3 = 30. . . . . . . . . . . . . . . . . . 26
4.10 Performance checking for the early decision rule with Lamda= 1.7432 , a0 = 2,
a1 = 2, a2 = 2, C1 = 0.2, C2 = 0.5, C3 = 30. . . . . . . . . . . . . . . . . . 26
4.11 Performance checking for the early decision rule with Lamda= 2.1386 , a0 = 2,
a1 = 2, a2 = 2, C1 = 0.2, C2 = 0.5, C3 = 30. . . . . . . . . . . . . . . . . . 26
4.12 Performance checking for the early decision rule with Lamda= 2.2315 , a0 = 2,
a1 = 2, a2 = 2, C1 = 0.2, C2 = 0.5, C3 = 30. . . . . . . . . . . . . . . . . . 27
4.13 Performance checking for the early decision rule with Lamda= 3.2410 , a0 = 2,
a1 = 2, a2 = 2, C1 = 0.2, C2 = 0.5, C3 = 30. . . . . . . . . . . . . . . . . . 27
4.14 Performance checking for the early decision rule with Lamda= 3.5729 , a0 = 2,
a1 = 2, a2 = 2, C1 = 0.2, C2 = 0.5, C3 = 30. . . . . . . . . . . . . . . . . . 27
List of Figures
3.1 Flowchart of the proposed early decision rule. . . . . . . . . . . . . . . . . 13
參考文獻 Bibliography
[1] Chen, J and Lam, Y. (1999a). Bayesian variable sampling plans for a general life
distribution with type I censoring. OR Transaction, 3:29-45.
[2] Chen, J and Lam, Y. (1999b). Bayesian variable sampling plans for the Weibull
distribution with type I censoring. Acta Math. Appl. Sinica, 15:269-280.
[3] Hald, A. (1967). Asymptotic properties of Bayesian single sampling plans. Journal
of the Royal Statistical Society Series, B29:162-173.
[4] Huang, W-T. and Lin, Y.-P. (2002). An improved Bayesian sampling plan for expo-
nential population with type I censoring. Communication in Statistics,Theory and
Methods 31, 2003-2025.
[5] Lam, Y. (1988). Bayesian approach to single variable sampling plans. Biometrika,
75: 387-391.
[6] Lin, Y.-P., Liang, TC and Huang, W.-T. (2002). Bayesian sampling plans for ex-
ponential distribution based on type I censoring data. Annals of the Institute of
Statistical Mathematics, 54(1): 100-113.
[7] Nigm, A.M. and Ismail, M.A. (1985). Bayesian life test sampling plans for the two
parameter exponential distribution. Communications in Statistics-Simulation and Computation, 14: 691-707.
[8] Spurier, J. D. and Wei, L.J. (1980). A test of the parameter of the exponential distri-
bution in the type I censoring case. Journal of the American Statistical Association,
75:405-409.
[9] Thyregod, P. (1975). Bayesian single sampling plans for life testing with truncation
of the number of failures. Scandinavian Journal of Statistics, 2:61-70.
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