型I、型II及混合型設限資料所產生的問題，一是觀測樣本個
數太少，使得統計分析效率不高，二是觀測時間過長，導致成本提高。
為了解決這兩難的情形，本論文中，在有一最長觀測時間的設限下，
我們提出了兩階段取樣法，並設定一參考時間及一勉強可接受的樣本數，來作為是否進行第二階段觀測的準則。這樣不僅能得到可接受的樣本數，更能縮短觀測時間，節省長時間觀測下所花費的大量成本。
    當隨機樣本的壽命服從參數theta的指數分配時，我們討論theta的最大概似估計量，及其機率分配、信賴區間…等問題，並用一實例來探討此取樣法。

In a life testing experiment, Type-I, Type-II, and Hybrid censored samples generally lead into some disadvantages, one is that it is inefficient to analyze because of the few number of failures, the other is that the cost becomes higher for a long observing time. In this paper, under the end time of sampling period censored, we propose two-stage sampling and set a criteria to determine whether to proceed to the second stage or not. Using this method, we can not only get an acceptable number of failures but also decrease the observing time to save the cost of the experiment.
    When the n units are put on test and the failure times are independent and identically distributed as exponential with parameter theta, we discuss the maximum likelihood estimator, the probability density function, the confidence interval of theta . We also present one sample to illustrate all the results finally.

目錄
第一章	介紹                                    1
第二章	分段取樣法                              3
第三章	最大概似推論                            5
3.1 參數估計   ...............................   6
3.2 動差母函數   .............................   7
3.3 機率密度函數   ...........................  12
3.4 期望值、變異數及均方差   .................  13
3.5 信賴區間   ...............................  16
第四章	實例說明                               19
4.1 實例說明1   ..............................  19
4.2 實例說明2   ..............................  20
參考文獻                                        22
圖表目錄
表一  ………………………………………………………………   19
表二  ………………………………………………………………   20
圖一 變異數    ……………………………………………  21
圖二 均方差       ……………………………………………  21

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[2]  A. Childs, B. Chandrasekar, N. Balakrishnan,and D. Kundu,Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution,Ann Inst Statist Math 55:319-330(2003). 
[3]  D.J. Bartholomew ,The sampling distribution of an estimate arising in life testing, Technometrics 5:361-374(1963).  
[4]  S. Chen and G.K. Bhattacharyya,Exact confidence bound from an exponential parameter under hybrid censoring, Commun Statist Theory Methods 17:1857-1870(1988).
[5]  王凰妃，兩階段混合型M設限下指數分配的概似推論，淡江大學碩士論文(2006)。