Modeling periodically inspected k/r-out-of-n system

A k/r-out-of-n system undergoing periodic inspection with three states viz. normal, degraded and completely failed is presented in this paper. If at inspection, the system ends up degraded or completely failed then a repair is carried out taking random times. Availability and cost analysis of periodically inspected k/r-out-of-n system is performed specifically propositions on point availability, limiting availability and long-run average cost rate are stated and derived in the study. Conditions for determining the optimal inspection period based on cost rate and availability is also discussed. The derived theorems are illustrated with the help of an example.