Some renewal theory results with application to fleet warranties

The fleet warranty guarantees the purchaser of a large population of like items that the mean life of the fleet will meet or exceed some negotiated mean μL. If the mean life is less than μL, compensation may be given in terms of a number of free replacement parts R. The expected number of replacements E[R] is studied based upon how the mean life of items in the field is determined and on whether the sampling window starts at time t=0 (ordinary renewal process) or at some arbitrarily large time w (equilibrium renewal process). Properties of E[R] are compared and examples are given.