Random Replacement Policies for Two Failure Modes

The extended random replacement policies with two types of failure modes are considered: (a) Unit failure: When the failure has occurred, the unit is replaced immediately. (b) Minimal failure: When the failure has occurred, minimal repair is done. The unit operates for a job with random working cycles, and is replaced at time T, at working cycle N or at unit failure. It is supposed that two policies of replacement first and last are adopted for the above two failure modes. The expected cost rates are obtained, and optimal T
^*
and N
^*
to minimize them are derived analytically and are discussed numerically.