本論文使用變動鄰域搜索（VNS）演算法，針對對數位置尺度分配，如韋伯(Weibull)分配和對數邏輯斯(log-logistic)分配，討論逐步設限策略下可靠度抽樣計畫所需之最小樣本數，並找尋此樣本數下最佳的逐步設限策略。與文獻存在的方法相比，我們的方法能顯著地減少所需之樣本數。在小樣本的情況下，VNS演算法搜尋的方法與完全搜索方法（CSM）所得到的最小樣本數結果相同或相近。因此，本文所建議的可靠度抽樣計畫樣本數尋找程序是有效且節省計算時間。當所求之最小樣本數找到後，我們繼續討論在四種目標函數(A-最優性、D-最優性、變異數測量值、成本)的最佳逐步設限策略。在韋伯分配下，使用我們找到的最佳逐步設限策略所求得之目標函數值均優於Ng et al.(2004）論文表格呈列的逐步設限策略所求得之目標函數值。最後，我們還討論加上成本上限的限制條件的最優化問題和敏感度分析。藉由所呈現的數據結果，也可以驗證我們的方法相較於過往的方法與CSM，在實際應用上更具實用性和效率。

This thesis introduces a variable neighborhood search algorithm-based approach to determine the minimum sample sizes required for progressively censored reliability sampling plans within the log-location-scale family of distributions, which include Weibull and log-logistic distributions. Our method significantly reduces sample sizes compared to previous approaches, demonstrating its feasibility, especially for small sample sizes, in contrast to complete search methods (CSM). Optimal censoring plans are identified using A- and D-optimality criteria, a variance-measure criterion, and a cost function-based criterion. The proposed  approach consistently outperforms the method proposed by Ng et al. (2004) for the Weibull distribution. Furthermore, we address an additional optimization problem with a cost constraint to illustrate the practicality and efficiency of our method, and we also conduct a sensitivity analysis.

Contents 
1  Introduction                                                  	   1
2  Parameter Estimation for Log-Location-Scale Distribution               4
3  Optimal Progressive Censored Reliability Sampling Plan				   6
4  Numerical Studies                                                9
5  Optimal Progressive Censored Reliability Sampling Plans with Cost Minimization Based Criterion and Cost Constraint					  17
6  Conclusion                                                     25

List of Tables 
1	A comparison of the sample sizes calculated using our method with those tabulated in Table 10 of Ng et al. (2004) for pα = 0.00041 and pβ = 0.01840. 12 
2	Acomparison of the sample sizes and censoring plans derived from our method with those reported in Example 1 of Ng et al. (2004) for pα = 0.00284, 1 −α=0.95, pβ = 0.0311, β = 0.1, and q = 0.58 . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 
3	A comparison between our optimal sampling plans and the sampling plans presented in Table 11 of Ng et al. (2004) under the criterion (C1) . . . . . . . . . . 13 
4	A comparison between our optimal sampling plans and the sampling plans presented in Table 11 of Ng et al. (2004) under the criterion (C2) . . . . . . . . . . 14 
5	A comparison between our optimal sampling plans and the sampling plans presented in Table 11 of Ng et al. (2004) under the criterion (C3) . . . . . . . . . . 15
6	Optimal sampling plans for log-logistic distribution under three criteria . . . . 16 
7	A comparison between our optimal sampling plans and the sampling plans presented in Table 11 of Ng et al. (2004) under the criterion in (4) when (C1,C2,C3) = (5,5,5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 
8	A comparison between our optimal sampling plans and the sampling plans presented in Table 11 of Ng et al. (2004) under the criterion in (4) when (C1,C2,C3) = (11,37,67) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 
9	Optimal sampling plans for log-logistic distribution under under the criterion in (4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22 
10	Acomparison between our optimal sampling plans and the sampling plans presented in Table 11 of Ng et al. (2004) under the criterion (C3) with constraints in Eq. (5) when (C0,C1,C2) = (100,5,5) . . . . . . . . . . . . . . . . . . . . . . .23 
11	Acomparison between our optimal sampling plans and the sampling plans presented in Table 11 of Ng et al. (2004) under the criterion (C3) with constraints in Eq. (5) when (C0,C1,C2) = (250,11,37) . . . . . . . . . . . . . . . . . . . .24 
12	A sensitivity analysis under the criterion (C3) with constraints in Eq. (5) . . . 24

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