當兩組的平均餘命函數交叉時，即其中一組的平均餘命函數不會恆大於另一組時，檢定兩組平均餘命函數是否相等的統計方法，其檢定力往往會偏低。在完整資料下，Berger et al. (1988)應用交集-聯集法則(intersection -union principle)來比較兩組的平均餘命函數，並可進一步地找出在哪些時間點上，此兩群體的平均餘命有所差異。當資料具備右設限與左截斷的特性時，本論文沿用Berger et al. (1988)的作法，建構一檢定統計量來比較兩群體的平均餘命函數是否相同。先以模擬的方式來了解此檢定統計量的抽樣分布是否會受到資料的右設限或是左截斷比例的影響。當此檢定統計量受到資料型態的影響時，本論文將以自助重抽法(Bootstrap)的方式進行檢定。最後，以本論文所提的檢定方法來比較台灣地區不同族群以及有無抽菸行為的老年人的平均餘命函數，以提供公衛研究人員做為增進成年人保健行為的參考。

In general, the power of testing the equality of two mean residual life functions will be lower when these two functions cross. Therefore, Berger et al. (1988) proposed a test statistic and employed the intersection-union principle to detect the difference between two mean residual life functions for complete data. Moreover, the test can be inverted to yield confidence set which specified a range of values for which one function dominates the other. We extend their test statistics for left-truncated and right-censored data. Because the asymptotic distribution of the test statistic is affected by censoring distributions, Bootstrap distribution is applied for testing the equality of two mean residual life functions and constructing confidence set. The implementation of the proposed method to one real data set is illustrated.

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