在第一章，我們提出了一個新的二元分佈族，並提供一些特殊之分佈，如二元指數、二元韋伯等，同時並與已知的二元分佈族做些比較。對於一些相關之統計性質，如期望值、變異數、故障函數等，及參數的估計也作了探討。並舉一實例，應用動差法，估算出其參數值。
在第二章，對於S-N曲線的建立提供了另一種統計模式，並估計模型中的參數，同時考慮測量誤差的迴歸模型方法，以導出疲勞極限的分佈。在此分佈下，以迴歸分析法導出參數的估計。此外，亦提出一實際之實驗數據，以本文方法算出參數的估計值，並與已知的結果比較。最後，進行統計模擬研究。

In chapter 1, we have proposed a new family of bivariate distributions, and also some special distributions such as bivariate exponential, bivariate Weibull etc.. Some comparisons with known results are also made. A real data set is illustrated in which some parameters are estimated by moment method. 
In chapter 2, we consider an error-in-variables regression model for random fatigue-limit problem. Some estimates for the related parameters are also derived. A real data set is also illustrated by the proposed method and some comparisons are also made with known results. Some simulation study is also carried out.

第一章 二元分佈族…………………………………………………..1
1.1 介紹……………………………………………………………….1
1.1.1背景………………………………………………………………1
1.1.2 多元分佈的相關文獻………………………...............2
1.2 一些相關定義及符號…………………………...............3
1.3 二元分佈族……………………………………………………….4
1.3.1二元分佈族與其他相關的二元分佈......................4
1.3.2二元分佈之模型比較………………………………………….10
1.3.3二元分佈的參數估計.................................12
1.4 實例………………………………………………………………15
1.5 結論………………………………………………………………16
第二章 隨機疲勞極限模型………………………………………….18
2.1介紹……………………………………………………………….18
2.1.1 背景……………………………………………………………18
2.1.2 相關的文章……………………………………………………18
2.2 疲勞模型…………………………………………………………19
2.2.1相關符號與定義……………………………………………….19
2.3實例……………………………………………………………….21
2.4與其他的疲勞模型作比較……………………………………...22
2.5 模擬………………………………………………………………23
2.6 結論………………………………………………………………25
參考資料………………………………………………………………26

表目錄：
表一 皮膚燒傷移植手術之生存日數..........................15
表二 疲勞實驗數據資料………………………………………………22
表三 比較各模型的絕對值殘差………………………………………23
表四 模擬結果…………………………………………………………24

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