Some Necessary and Sufficient Conditions for Age Replacement with Non-Zero Downtimes

In this paper we consider 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. In this paper we derive such conditions in terms of the minimum of the mean residual life function. When age replacement is indicated, we derive sufficient conditions for the existence of a global minimum to the asymptotic expected cost rate function. These results are illustrated for the Weibull and Gamma distributions.