Abstract: In view of imperfect inspections in manufacturing systems, a shock model with imperfect inspection is considered. The system is periodically inspected so that a preventive maintenance can be performed when necessary. Assume that the system is deteriorating and has k failure types. An explicit expression of average cost rate C(T,N) of system is given by using renewal process and considering inspection cycle T and replacement policy N. A numerical algorithm is given to obtain the optimal joint strategy. Finally, it provides a numerical example to illustrate the proposed model, and also studies the impact of inspection level on average cost rate.

Key words: imperfect inspection, preventive maintenance, shock model, geometric process, average cost rate, replacement policy