Statistical estimation algorithms for repairs-time limit replacement scheduling under earning rate criteria

In this paper, we formulate two repair-time limit replacement problems with imperfect repair under earning rate criteria with and without discounting. First, the optimal repair-time limits which maximize the long-run average profit rate and the expected total discounted profit over an infinite time horizon are analytically derived. Next, we develop the nonparametric algorithms for estimating the optimal repair-time limits, provided that the complete sample data of repair time are given. The basic idea is to apply the Lorenz statistics and to transform the underlying algebraic problems to the graphical ones. Finally, we present some numerical examples to show that the proposed algorithms can be useful to estimate the profit-based repair limit replacement schedule.