Availability of k-out-of-n systems under block replacement sharing limited spares and repair capacity

In this paper we consider an installed base of k-out-of-N systems, each consisting of identical, repairable components. A block replacement policy is used to maintain each system and all components are repaired by a single repair shop. System maintenance consists of replacing all failed and degraded components by spares. We focus on the downtime resulting from the lack of spare parts. The control variables that influence the system availability are the maintenance interval, the spare part inventory level and the repair capacity. We present two approximate methods to analyse the relation between these control variables and the system availability. Comparison with simulation results shows that we can generate nearly accurate approximations for the system availability using one of these models, depending on the system size. The average errors are found to be between 0.1% and 4.3%, compared to simulation. We found that the errors become smaller when the installed base increases and the number of system components becomes larger.