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The Lorenz Transform approach to the Optimal Repair-Cost limit remplacement Policy with Imperfect Repair

In this paper, we consider a repair-cost limit replacement problem with imperfect repair and develop a graphical method to de- termine the optimal repair-cost limit which minimizes the expected cost per unit time in the steady-state, using the Lorenz transform of the un- derlying repair-cost distribution function. The method proposed can be applied to an estimation problem of the optimal repair-cost limit from empirical repair-cost data. Numerical examples are devoted to examine asymptotic properties of the non-parametric estimator for the optimal repair-cost limit.