OPTIMAL STOPPING IN A SEMI-MARKOV SHOCK MODEL.

A failure model for a system existing in a random environment is examined. The system accumulates damage through a shock process and the failure time depends on the accumulated damage in the system. The cumulative damage process is assumed to be a semi-Markov process. Upon failure the system must be replaced by a new identical one and a failure cost is incurred. If the system is replaced before failure, a smaller cost is incurred. A controller is allowed to replace the system at any stopping time before failure time. The problem of specifying a replacement rule which minimizes the total long-run average cost per unit time is considered.