On Remaining Lifetimes with Random Initial Age. A New Insight

We consider items that are incepted into operation having already a random (initial) age and define the corresponding remaining lifetime. We show that these lifetimes are identically distributed when the age distribution is equal to the equilibrium distribution of the renewal theory. Then we develop the population studies approach to the problem and generalize the setting in terms of stationary and stable populations of items. We obtain new stochastic comparisons for the corresponding population ages and remaining lifetimes that can be useful in applications.