Abstract: This paper studies a preventive repair policy with two parameters (L,N) for failure waiting time.It is  assumed that when the system fails,it will be replaced in the next preventive repair time rather than at once,and so there will be a failure waiting between failure time and the replaced time.By geometric process,the explicit expression of the average cost rate is derived.Moreover,an appropriate numerical example is given and the optimal (L,N)* policy is derived which makes the average cost rate minimized.

Key words: two parameters preventive repair policy；geometric process, failure waiting, optimal policy