串聯系統加速壽命試驗之最佳樣本數配置

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姓名

戴志穎(Chih-Ying Tai) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

串聯系統加速壽命試驗之最佳樣本數配置
(Optimal Sample Size Allocation for a Series System under Accelerated Life Tests)

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摘要(中)

在系統可靠度加速壽命試驗中，不同應力水準下的樣本數配置，將會影響正常應力下系統可靠度推論的精準性，是以本文考慮三應力水準加速壽命試驗之最佳化樣本數配置問題。其目標函數可推得為兩個具有相異係數之二階基本對稱函數(Second Elementary Symmetric Function)之乘積，因此在給定總試驗樣本數下，分別推導出最佳樣本數配置為退化至兩應力水準加速試驗以及為均勻分配時的充分條件，並推廣至多元件串聯系統加速壽命試驗，以數值結果猜測最佳化時之充分條件。再以元件壽命具獨立指數分配而成串聯系統為例，說明在其 D-最佳化準則下之樣本數配置，輔以數值分析比較均勻和最佳樣本數配置之相對效率。最後，以B-型絕緣資料為例，實際分析其最佳樣本數配置。

摘要(英)

In accelerated life tests of system reliability, the sample size allocation under different stress levels could affect the accuracy of the reliability inference. Given three stress levels of an accelerated variable, this thesis tackles the issue on the optimal allocation of an accelerated life test of series systems. It turns out that the objective functions frequently are of the form of the product of second elementary symmetric functions. We fist derive the sufficient condition when the optimal plan is reduced to a two-level test with equal sample size allocated at the lowest and the highest levels for systems connected by two components. Under independent exponential life time distributions of the components, more specific results, such as the relative efficiency of the three-level uniform design to the optimal allocation, are developed. The results are also demonstrated and justified by a real example. Generalization to a multi-component series system is conjectured and verified by numerical results.

關鍵字(中)

★ 串聯系統
★ 加速壽命試驗

關鍵字(英)

★ Series system
★ Accelerated life test

論文目次

第一章緒論 .......... 1
1.1 研究動機 .......... 1
1.2 研究背景與文獻討論 .......... 3
1.3 研究方法 .......... 5
1.4 論文架構 .......... 6
第二章基本對稱函數最佳化 .......... 7
2.1 單一基本對稱函數 .......... 7
2.2 兩二階基本對稱函數乘積之最佳化 .......... 10
2.3 最佳解之充分條件的幾何意義 .......... 13
2.4 多個二階基本對稱函數之推廣 .......... 16
第三章指數分配串聯系統之最佳配置 .......... 18
3.1 串聯之加速壽命模型 .......... 18
3.2 D-最佳化之樣本數配置 .......... 21
3.3 兩元件之D-最佳化設計 .......... 21
3.3.1 妥協設計之D-最佳化 .......... 23
3.3.2 單一失效模式與二失效模式係數條件之比較 .......... 26
3.3.3 均勻設計 .......... 29
第四章資料分析與數值驗證 .......... 34
4.1 二失效模式之最佳樣本數配置 .......... 34
4.2 三失效模式 .......... 36
4.3 最佳化應力水準與樣本數配置 .......... 38
4.3.1 二失效模式 .......... 38
4.3.2 三失效模式 .......... 40
第五章結論與未來研究 .......... 41
參考文獻 .......... 42
附錄 .......... 47
附錄A .......... 47
附錄B .......... 57

參考文獻

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指導教授

樊采虹、彭健育(Tsai-Hung Fan Chien-Yu Peng)

審核日期

2017-7-19

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