Replacement and minimal repair policies for a cumulative damage model with maintenance

This paper considers replacement and minimal repair polices for an extended cumulative damage model with maintenance at each shock: shocks occur at a nonhomogeneous Poisson process. A system undergoes maintenance at each shock when the total damage does not exceed a failure level K, undergoes minimal repair at each shock when the total damage exceeds a failure level K, and is replaced at time T* or at failure N* whichever occurs first. The expected cost rate is obtained and the optimal T* and N* minimizing the expected cost are analytically discussed. It is shown that this model would be applied to the backup of secondary storage files in a database system as an example.