串聯系統加速壽命試驗之最佳妥協設計

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彭榆恩(Yu-En Peng) 查詢紙本館藏

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統計研究所

論文名稱

串聯系統加速壽命試驗之最佳妥協設計
(Optimal Compromise Design for a Series System Under Accelerated Life Tests)

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摘要(中)

在系統可靠度的加速壽命試驗中，不同應力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。本文考慮兩元件串聯系統之三應力加速壽命試驗的最佳樣本配置問題，其中各元件壽命具獨立指數分配。假設最佳樣本配置比例介於(0, 1/2)，且三應力為妥協設計下，理論推導D-最佳化樣本配置比例之確切解，亦討論其實務意義。此外，三應力中第二應力之兩元件平均壽命若相等，則可理論求其最佳應力水準之設定。最後，輔以實際例子說明使用最佳樣本配置，最多可提高原始設計約40%之相對效率。

摘要(英)

In accelerated life tests of system reliability, the accuracy of the reliability inference can be affected by the sample size allocation under different stress levels. Given three stress levels of an accelerated variable, this thesis considers the problem on the optimal allocation for a series system with two independent exponential distributions of the components under accelerated life tests. For a compromise design with the assumption of all optimal allocations being in (0, 1/2), the exact D-optimal sample size allocations are analytically derived and the experimental implication is provided as well. Furthermore, the optimal stress levels are determined when the mean-time-to-failures of the two components are assumed to be equal at the median stress level. The analytic results are illustrated and verified by two real examples. The numerical results show that the relative efficiency of the three-level optimal allocation to the original design can be enhanced at most 40%.

關鍵字(中)

★ 串聯系統
★ 加速壽命試驗
★ 二階基本對稱函數
★ 妥協設計
★ D-最佳化
★ 結式

關鍵字(英)

★ Series system
★ Accelerated life tests
★ Second elementary symmetric function
★ Compromise design
★ D-optimality
★ Resultant

論文目次

第一章緒論 ............ 1
1.1 研究動機 ............ 1
1.2 文獻回顧 ............ 2
1.3 研究方法 ............ 4
1.4 論文架構 ............ 4
第二章最佳化二階基本對稱函數之相關結果 ............ 6
2.1 串聯之加速壽命模型D-最佳化之樣本配置 ............ 6
2.2 兩元件串聯系統之D-最佳化妥協設計 ............ 9
2.3 二階基本對稱函數之最佳化 ............ 10
第三章妥協設計之D-最佳化樣本配置 ............ 15
3.1 兩二階基本對稱函數乘積之結式與最佳化結果 ............ 15
3.2 三應力為妥協設計之D-最佳化樣本配置 ............ 19
3.3 妥協設計D-最佳化樣本配置之性質 ............ 29
3.4 妥協設計之D-最佳化應力水準............ 33
第四章實例分析 ............ 35
4.1 B-型絕緣資料 ............ 35
4.2 H-型絕緣資料 ............ 38
第五章結論與未來研究 ............ 44
參考文獻 ............ 45
附錄 ............ 49

參考文獻

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指導教授

樊采虹彭健育

審核日期

2018-8-23

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