A cost relationship between age and block replacement policies

The general cost structure of a unit on line is assumed to be governed by a stochastic process where denotes the operating cost on and ζ denotes the time of an unscheduled (or unplanned) replacement by a new unit at a cost c1. For an age replacement maintenance policy, scheduled (or planned) replacements occur whenever an operating unit reaches age T, whereas in the block replacement case, scheduled replacements occur every T units of time. Such scheduled replacements cost c 2. The expected long-run cost per unit time can then be expressed in the form and respectively. Our main result shows that where U is the associated renewal function generated by ζ.