Nonparametric repair-limit replacement policies with imperfect repair

The repair-limit replacement problem is to determine the timing to stop repairing a unit after it fails. In this paper, we consider a generalized repair-limit replacement problem with lead time and imperfect repair, which is subject to a time constraint. In particular, two kinds of solution procedures are discussed to obtain the optimal repair-time limit which minimizes the total expected cost per unit time in the steady state, where one is a straightforward (algebraic) procedure and the other is a geometric one based on the Total Time on Test concept. Finally, a nonparametric solution procedure to estimate the optimal repair-time limit is proposed, and the optimal policies are given directly from the repair-time data. Simulation results tell us that the method proposed gives a good estimate for a sufficiently large number of data set.