Age Replacement Under Alternative Cost Criteria

Due to the complexity of optimum replacement problems over finite lime horizons various asymptotic criteria based upon fixed age replacement policies have been employed in the literature and in practice. In this paper the relationships between the optimum policies under three alternative cost criteria are considered. An ordering of the accounting costs under two of these is obtained, and for distributions with Increasing Hazard Rate an ordering of the optimum replacement time is derived. For a finite time horizon the policies are compared to the optimal sequential and fixed-age replacement polices through the example of a gamma distribution previously investigated by Barlow and Proschan (Barlow, R. E., F. Proschan. 1962. Planned replacement. K. J. Arrow, S. Karlin, W. L. Smith, eds. Studies in Applied Probability and Management Science. Stanford University Press, Stanford, Cal.; Barlow, R. E., F. Proschan. 1965. Mathematical Theory of Reliability. Wiley, New York.).