Comments on Finite-Period Applications of Age-Based Replacement Models

The age-based replacement problem is considered when a finitetime zone is placed upon the duration of the process and, accordingly,for which an asymptotic model could be of questionable validity.Three models to be optimized with respect to the decision variableare considered: first, the commonly used limiting asymptoticcost per unit time; secondly, the refined asymptotic cost perunit time; and thirdly, the exact expected cost. These modelsare investigated in the case of a negative exponential and Weibullfailure-time distribution. In both cases, it is found that theestimated cumulative cost resulting from the refined model approachesquickly that of the exact formulation. The practical use and decision consequences of this result areinvestigated for a Weibull failure distribution. It is arguedthat, because of the essential illconditioned nature of theage based replacement model, for short time-zone applications,the model should be extended to accommodate non-zero replacementtimes.