Optimal replacement policy for a cumulative damage model with time deterioration

This paper considers a replacement policy for a cumulative damage model. A unit suffers two kinds of damage which occurs either by shocks or increases with time. It fails only when the total amount of damage exceeds a failure level K. For the purpose of preventing failure, the damage is checked when each shock occurs and a unit is replaced before failure when the total damage exceeds a threshold level k. The expected cost rate is obtained, and an optimal level k∗ which minimizes it is derived, when shocks occur in a Poisson process. Numerical examples are finally given.