This thesis deals with a preventive maintenance model for the systems whose failures are dependent only on their wear levels being checked periodically.
Models developed to solve the problems of this kind are finite state Markovian decision precesses or shock models. Shock models do not assume the finiteness of the state of the system, but the shocks occur discretely in time, so the wears accumulate in discrete amounts at isolated points in time. In our model we forgo the assumption of discreteness, and consider the wear accumulated continuously in time.
In this thesis, a replacement policy is introduced in which a system is replaced before failure when the wear reaches a certain limit during periodic inspections or at failure in operation.
The optimal replacement level which minimizes the expected cost per unit time for an infinite time span is obtained by the application of renewal theory. When the calculations of the optimal solution is difficult, an approximate solution can be used with accuracy in some conditions.