設限資料的取樣法分為型I設限(Type I censoring)、型II設限(Type II censoring)跟混合設限(Mixing censoring)三種，會有觀測時間過長或觀測到壽命的樣本個數不足的問題。要解決觀測到壽命的樣本個數不足的問題，需要設定一較長觀測時間，要改善觀測時間過長會發生觀測到壽命的樣本個數不足的問題。在此，我們在有最長觀測時間的限制下提出兩階段型一混合設限法，將取樣停止時間分成兩階段，並設定一判斷準則，在第一階段取樣停止時，判斷是否進行第二階段取樣，這樣的設限法，可以在改善觀測到壽命的樣本個數不足的缺點時，還有機會縮短觀測時間。另外本論文在這兩階段設限下，討論樣本壽命為指數分配時，其參數的最大概似估計量的分配、期望值、變異數、信賴區間等統計推論。

There are three sampling methods of Type I、Type II and Mixing censoring for censoring data. However, such ways of sampling have problems of over-time observation or the shortcomings of samples. To prevent the defect of the shortcomings of samples, the observed time must be extended; to fix up the problem of over-time observation, the shortcomings of samples may be occurred. To improve the problems of insufficient samples while having less expectation observed time, a two-staged censoring method with the constrain conditional of the maximum of the observed time is thus proposed. In this paper, the end time of sampling period is divided into the first stage and the second stage, and the criteria are set up for determining whether to proceed to the second stage or not. Based on this two-staged sampling method, this paper further argues about the distribution, expectation, variance, and confidence interval of the estimation of the parameter when the distribution of life time is exponential.

1.介紹 ………………………………………………………………..1
2.兩階段混合型I(I)(I)設限資料取樣法……………………………7
2.1參數估計………………………………………………………..7
2.2 動差母函數…………………………………………………….8
2.3 機率密度函數………………………………………………….11
2.4 信賴區間……………………………………………………….13
3.兩階段混合型I(M)(I)設限資料取樣法……………………………15
3.1參數估計………………………………………………………..15
3.2 動差母函數………………………………………………...…..16
3.3 機率密度函數………………………………………………….19
3.4 信賴區間……………………………………………………….22
4.兩階段混合型I(I)(M)設限資料取法…………………………...23
4.1參數估計………………………………………………………..24
4.2 動差母函數…………………………………………………….25
4.3 機率密度函數………………………………………………….27
4.4 信賴區間……………………………………………………….30

5.實例說明 …………………………………………………………..32
6.參考文獻……………………………………………………….34
附錄……………………….……………………………………………35

[1] B. Epstein, Truncated life tests in the exponential case, Ann Math Statist 25 (1954), 555-564.
[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 (2003), 319-330.
[3] S. Chen, B.Bhattacharyya, Exact confidence bounds from an exponential parameter under hybrid censoring, Commun Statist Theory Methods 17 (1988), 1857-1870.
[4] B. Chandrasekar, A. Childs, N. Balakrishnan, Exact likelihood inference for the exponential distribution under generalized Type-I and Type-II hybrid censoring, Naval Research Logistics 51 (2004), 994-1004.
[5] Barlow, R. E., Madansky, A., Proschan, F. and Scheuer, E.(1968). Statistical estimation procedures for the “Burn-in” process, Techonmetrics,1.0, 51-62