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。

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.

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

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