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

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

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

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