Lifetime replacement policy in discrete time for a single unit system

We consider, in discrete time, a single unit system which operates for a period of time represented by a general distribution. This unit is subjected to failures during operations. Some of these failures are repairable and the unit is repaired in the repair facility. When the unit experiences a non-repairable failure then it has to be replaced with a new one. We consider a replacement policy based on the lifetime of the unit. This policy can be studied from two different approaches. The first approach, named Model I, is to replace the unit by a new one when the unit attains a predetermined lifetime. The other approach, named Model II, is to close repair facility when the lifetime of the unit attains a predetermined quantity. For each model, we obtain the stationary distribution and some performance measures of interest.