In this thesis, preventive replacement policies for a periodically inspected system are considered. It is assumed that the state of system can be detected only by actual inspection which involves a cost and that there is a penalty cost associated with the lapsed time between system failure and its detection.
Three optimum replacement policies are proposed:
Policy A. If the system fails before the $n^{th}$ inspection, the system is replaced. Otherwise, preventive replacement is performed at the $n^{th}$ inspection.
Polic B. If the system fails before the $n^{th}$ inspection, the system is minimally repaired. Preventive replacement is performed at the $n^{th}$ inspection.
Policy C. the first k-1 failures are minimally repaired and at the $k^{th}$ system failure, preventive replacement is performed.
For each model, the expected cost rate are obtained, their behavior are examined, and the ways of obtaining optimal inspection interval and preventive replacement period are explored. Sensitivity analyses of the cost parameters are included.
