加速壽命試驗 (Accelerated Life Test, ALT) 是工業界最常被拿來使用推估高可靠度產品的可靠度資訊之重要分析工具，例如產品壽命第p百分位數或產品平均失效時間 (Mean Time To Failure, MTTF)。因此規劃有效率的加速壽命模型，尤其是決定加速應力所需之最佳樣本數配置，是可靠度工程師經常面臨到的決策問題。本文以絕緣體的電擊擊穿時間資料為動機例子，建構一加速壽命模型，其模型的隨機誤差項為位置尺度分配，並極小化產品壽命第p百分位數估計量之漸近變異數，進行樣本數最佳化配置的探討。由推導結果可知在進行樣本數最佳化配置，只需要依照比例配置於最高加速應力及最低加速應力上，且不論加速壽命模型的隨機誤差項屬於位置尺度家族裡何種分配，都不影響樣本數最佳化配置的結果。

Accelerated life test is widely used to assess the lifetime information (e.g., p-th quantile or mean-time-to-failure (MTTF)) of the highly reliable products. Hence, how to design an efficient accelerated life test plan for assessing the product’s lifetime information at normal-use stress such as the optimal sample-size allocation turns out to be a challenging issue for reliability analysts. In this paper, motivated by a mylar-polyurethane data, we first proposed an accelerated life model that random error is a location-scale distribution. Next, by using the optimality criterion that minimized the asymptotic variance of the estimator of the product's p-th percentile lifetime, this article derived the analytical expression of the optimal sample-size allocation for a k-stress accelerated life test. We demonstrated that a necessary condition of the sample-size allocation for k-stress based on the criterion is to assign tested units into the lowest and highest stress levels. A Monte Carlo simulation study was conducted to demonstrate the simulated values are quite close to the asymptotic values when sample sizes are large.

第一章 緒論......................1
1.1 前言......................1
1.2 文獻探討......................2
1.2.1 加速壽命模型......................2
1.2.2 樣本數配置最佳化......................2
1.3 研究動機與目的......................3
1.4 研究架構......................6
第二章 問題描述......................7
第三章 模型參數估計......................9
3.1 最大概似估計......................9
3.2 費雪訊息矩陣......................10
第四章 最佳樣本數配置......................15
第五章 實例探討與模擬分析......................17
5.1 實例探討......................17
5.2 模擬分析......................21
第六章 結論及後續研究......................23
附錄......................24
參考文獻......................29

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