The replacement problems are extensively studied from a number of disciplines including economics, finance, operations research, and decision theory. Much of previous theoretical work is “Bayesian”. In this paper, we restudy the on-line replacement problem by using the competitive analysis. The goal is to minimize the total cost of cumulative payment flow plus changeover costs. Firstly, a refusal strategy is proposed and the competitive ratio for
=1 is obtained. Furthermore, a new time-independent strategy
is presented and we prove that it is
]. Finally, weights are introduced to the original model and some results are achieved.