隨著產品可靠性的提升, 在一般條件下的壽命試驗會花費很多時間, 進而耗掉很多成本, 唯一的辦法就是降低樣本個數, 此外要短時間內得到產品的資料也相當困難。為了確保實驗單位能加速失效進而縮短實驗時間, 加速壽命測試經常被用來做為進行壽命實驗的主要架構, 但在一些狀況下,失效模型的加速因子參數是未知狀況下, 特別是當試驗對象為新產品時, 部分加速壽命測試則是另一個很好的選擇。
在小樣本下, 本文研究考慮逐步應力部分加速壽命測試方法, 並選擇以Burr XII 分配做為壽命分配, 使用最大概似估計法估計分配及加速因子的參數。分配及加速因子的參數估計值皆是經由推導的聯立方程式計算求得, 除了參數估計外, 本文也同時推導近似變異數且計算參數的信賴區間以比較估計量的實際表現。

The lifetime of products under normal conditions endures a long period of time because of high reliability of products. Reducing the sample size is the only way to solve this problem. It is difficult to obtain information about the lifetime of products under normal conditions. In order to assure rapid failure and then shorten the testing period, accelerated life test (ALT) is commonly used to obtain information about the lifetime of products quickly. In some cases, the failure model relating the lifetime of products and the stress are not known or cannot be assumed, especially for the new products. So step-stress partially accelerated life tests are the optional choice.
This article considers step-stress partially accelerated life tests for small samples under Burr XII distribution. We use maximum likelihood method to estimate the distribution parameters and acceleration factor. The estimates are obtained by solving two nonlinear equations simultaneously. In addition, we also perform simulation of the asymptotic variance and confidence intervals of the parameters to evaluate the empirical performances of our estimators.

目錄
第一章緒論.... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 1
1.1 研究背景.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 1
1.2 研究動機與目的.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 1
1.3 本文架構.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 3
第二章文獻探討及相關研究.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 4
2.1 加速壽命測試.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 4
2.2 逐步部分加速壽命測試.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 6
2.3 Optimization 估計方法.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 8
第三章理論推導.... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 9
3.1 壽命模型之介紹.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 9
3.2 測試模型.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 10
3.3 最大概似估計法.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 12
3.4 漸近變異與共變異.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 16
第四章模擬研究.... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 19
4.1 模擬步驟.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 20
4.2 結果討論.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 21
第五章結論及建議.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 23
參考文獻.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 25
圖目錄
2.1 三種不同應力加速方法. . . . . . . . . . . . . . . . . . . . . . 5
2.2 Optimization 五種估計法. . . . . . . . . . . . . . . . . . . . . 8
3.3 逐步部分加速測試示意圖. . . . . . . . . . . . . . . . . . . . . 11
表目錄
4.1 方法比較(1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 方法比較(2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3 參數估計-第一組參數. . . . . . . . . . . . . . . . . . . . . . . 31
4.4 參數估計-第二組參數. . . . . . . . . . . . . . . . . . . . . . . 32
4.5 估計漸近變異與共變異(第一組參數) . . . . . . . . . . . . . . . . 33
4.6 估計漸近變異與共變異(第二組參數) . . . . . . . . . . . . . . . . 34
4.7 近似信賴區間(第一組參數) . . . . . . . . . . . . . . . . . . . . . 35
4.8 近似信賴區間(第二組參數) . . . . . . . . . . . . . . . . . . . . . 36

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