Abstract: NBU*t_o class of life distributions, characterized by the fact that a new item has a stochatically larger life length than the residual life length after a certain age t_o＞0, is studied in this.paper, we first provide a characterization for those the residual life of a used one with age not less than t_o＞0 is stochastically equivalent to that of a new one. Furthermore, a nonparametric test is designed so as to test the stochastic equivalence between the life length of a new item and that of a used one with an age greater than t_o, against the alternative, that there is a great tendency for a new item to have a strictly longer life length than does a used one with age not smaller than t_o. Since computer-intensive method is avoided, it is simpler and more convenient than that in Zehui, Li and Xiaohu, Li. Finally, some numerical simulations are presented.