Some necessary and sufficient conditions for age replacement with non-zero downtimes

This paper considers an age replacement strategy, where downtimes are non-zero. Although this model is well known, the literature gives no necessary and sufficient conditions for age replacement to be preferred to replacement on failure. This paper derives such conditions in terms of the minimum of the mean residual life function. When age replacement is indicated, sufficient conditions for the existence of a global minimum to the asymptotic expected cost rate function are derived. These results are illustrated for the Weibull and Gamma distributions.