Optimal scheduling of imperfect and perfect inspections for systems subject to continuous degradation

Inspection and Maintenance policies are important in detecting system failures and restoring the system. Most existing researches assume that inspections are perfect. A more realistic situation is that inspections influenced by the environment or technical conditions are imperfect. In this paper, we consider a system subject to continuous degradation with both imperfect and perfect inspections. The system is modeled by a renewal process and expected cost and length of a renewal cycle is derived. A numerical example is presented in the end, which derives the optimal number of imperfect inspection within a cycle by minimizing the long-run cost rate.