Optimal imperfect preventive maintenance policies for a shock model

This paper applies a preventive maintenance(PM) policy for a used system to a cumulative damage shock model where the PM is imperfect. Shocks occur according to a nonhomogeneous Poisson process. The system is assumed to fail only by degradation, as only when the total amount of damage exceeds a prespecified level K, still the system undergoes only PM where it take the place of replacement and its Cost is C-K. The system undergoes PM where its cost is c(0) at operating time T, or when the total amount of damage exceeds a level k (k <= K), whichever occurs first. The expected cost rate is obtained and optimal T* and k* to minimize the expected cost are analytically discussed when shocks occur at a homogeneous Poisson process. Several examples are presented.