臺灣博碩士論文加值系統

本文主要針對exponentiated weibull分配具有參數 γ、β 、λ 的逐步型I分群設限 (progressively type I group-censoring)之壽命試驗 (life testing)，我們使用最大概似法 (maximum likelihood method)來獲得exponentiated weibull分配的參數之估計量。進一步，我們也求得參數之估計量的漸近變異數-共變異數矩陣之行列式或參數之估計量的函數(例如：q 階分位數估計量 (quantile estimator) 和存活函數 (survival function))的漸進變異數 (asymptotic variance)。接著，再根據壽命試驗過程所需消耗的各種成本，設計一個有關成本的壽命試驗之最佳逐步分群設限計劃：在成本限制情況下的exponentiated weibull壽命試驗，我們採用D-optimality方法 (亦即，使得參數之估計量的漸近變異數-共變異數矩陣之行列式值為最小)來決定其最佳試驗個數 (n)、試驗區間個數 (k)以及試驗區間的長度 (τ)；其次，本文也使用另兩個最適性方法(亦即，所考慮未知參數之估計量的函數，例如：q 階分位數估計量和存活函數之估計量，使得參數之估計量的函數之漸進變異數為最小)來決定其最佳試驗個數 (n*)、試驗區間個數 (k*)以及試驗區間的長度(τ*)。最後，我們列舉三個數值範例來闡述所提出的方法，以及探討exponentiated weibull分配參數和成本參數變動時的敏感度分析。

目錄
中文摘要………………………………………………………… I
英文摘要………………………………………………………… II
誌謝辭…………………….………………………………………… IV
目錄……………………………………………………………… V
圖目錄…………………….………………………………………… VII
表目錄……………………….……………………………………… VIII
第一章 緒論……………………………………………………… 1
1-1研究背景與動機及目的……………………………… 1
1-2文獻探討……………………………………………… 4
1-3研究架構與流程……………………………………… 7
第二章 符號說明、試驗進行程序以及模型參數估計……………… 8
2-1符號說明…………………………..…..………………… .8
2-2 逐步型I設限之統計模型與參數估計.………………… .9
2-2-1當 τ=i τ 時…………………....................………….12
2-2-2當 τ=i(2 τ) 時………………....................………30
2-2-3當 τ=i(0.5τ)時………………....................………46
第三章 設計成本限制下壽命試驗的演算法………………….…… 64
3-1最適的計畫…...…………….…………………………… 64
3-2演算法…...………………….…………………………… 71
3-2-1估計 γ、β 、λ ……………....................…… 73
3-2-2未限制總試驗時間或迴圈數…………………… 73
3-2-3限制總試驗時間或迴圈數……………………… 74
第四章 實例探討…………………………………………………… 76
4-1 實例一......………………….……….…………………… 76
4-2實例與文獻結果之比較……………………………… 80
第五章 敏感度分析……………………………………………… 83
5-1實例一......………………….……….…………………… ..83
5-1-1分配參數 γ、β 、λ 與機率 p 改變…..……..……. 83
5-1-2試驗成本改變…...……………. 102
5-1-3試驗長度改變……………………...…..……..… 167
第六章 結論與未來研究…………………………………………… 174
6-1結論…………………………………………………..…… 175
6-2未來研究……...………………………………………… 177
參考文獻……………………………………………………….… 179

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