Testing whether new is better than used of a specified age, with randomly censored data

Using randomly censored data, we develop a test of the null hypothesis that a new item has stochastically the same residual lifelength as does a used item of specified age t 0 , versus the alternative hypothesis that a new item has stochastically greater residual lifelength than does a used item of age t 0 . We also compare our test with a related test, developed for a complete‐data model, in order to study the loss in efficiency because of censoring.