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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题名:	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
作者:	戴志穎;Tai, Chih-Ying
贡献者:	統計研究所
关键词:	串聯系統;加速壽命試驗;Series system;Accelerated life test
日期:	2017-07-19
上传时间:	2017-10-27 14:01:31 (UTC+8)
出版者:	國立中央大學
摘要:	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。;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.
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