On reliability of systems with periodic maintenance under rare failures of its elements (Q612116)

This paper investigates the reliability of systems with certain times of operation and times of non-operation during which maintenance is performed. System elements may fail during operation, but can be repaired only during the subsequent maintenance period. The system has a certain reserve or redundancy which keeps up operation even after the failure of elements. The system fails if the reserve is completely exhausted during the operation time. If no element failed during operation, then the system reliability is not changed by maintenance, otherwise the reserve is restored during maintenance. Based on some additional assumptions the reliability of systems with exponentially distributed times of failure-free operation and with limited densities of distributions is derived.