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

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

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

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