Optimizing the repair‐time limit replacement schedule with discounting and imperfect repair

In this paper, we consider a repair‐time limit replacement problem with imperfect repair and develop a graphical method to determine the optimal repair‐time limit which minimizes the expected total discounted cost over an infinite time horizon. The method proposed can be applied to an estimation problem of the optimal repair‐time limit from the empirical repair‐time data. Then, the modified scaled total time on test transform of the underlying repair‐time distribution function is used. Numerical examples are devoted to examine asymptotic properties of the nonparametric estimator for the optimal repair‐time limit.