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

¹ Department of Industrial and Systems Engineering, Hiroshima University, 4-1 Kagamiyama 1 Chome, Higashi-Hiroshima 739-8527, Japan; osaki@gal.sys.hiroshima-u.ac.jp.
² Department of Economic Informatics, Hiroshima Shudo University, 1-1-1 Ozukahigashi, Asaminami-ku, Hiroshima 731-3195, Japan.

Received: September 2000
Accepted: December 2000

Abstract

In this paper, we consider a repair-cost limit replacement problem with imperfect repair and develop a graphical method to determine the optimal repair-cost limit which minimizes the expected cost per unit time in the steady-state, using the Lorenz transform of the underlying 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.