在許多領域的問題中，經常會遇到與現狀數據有關的情形。針對一個不易觀察的實際失效時間，而只知道此時間是高於或低於一個隨機的檢測時間。在此篇論文中，我們考慮的是雙變量現狀數據，並且假設我們對此雙變量的失效時間有些先驗訊息。我們最主要的目標，是找到一個最適的檢測時間，來檢定兩者之間的關係。

Current status data are usually obtained with a failure time variable T which is diffcult observed but can be determined to lie below or above a random monitoring time or inspection time t. In this work we consider bivariate current status data ${t,delta_1,delta_2}$ and assume we have some prior information of the bivariate failure time variables T1 and T2. Our main goal is to find an optimal inspection time for testing the relationship between T1 and T2.

Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Optimal design criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Inferences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3. Optimal design for testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1 Under independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 Under association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
4. Numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.1 Test of association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.2 Test under independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.3 Estimate of parameters and association . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.4 Test under association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5. Conclusion and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

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