A Revisit of Age-Based Replacement Models With Exponential Failure Distributions

This article revisits the optimization problems of age-based replacement models for exponential failure distributions. First, we show the steps how an age replacement time goes to an infinite value when the lifetime of a unit has an exponential distribution, and then, we give two discussions of possible replacement times, by introducing a new concept of cost named as deviation cost per unit of time between replacement and failure. Second, similar discussion is given for a random replacement model when the age replacement time is a random variable with a uniform distribution. Third, the models of age-based replacement first and last with deviation costs are discussed when a random replacement is taken into account for an age replacement model. Numerical examples are illustrated to show the results of the analytical discussions. Finally, necessary proofs are provided in the Appendixes.