Cold Standby Systems With Imperfect Backup

Abstract

Cold standby redundancy is a widely-applied design strategy to achieve high system reliability in numerous applications. To facilitate an effective system recovery in case of an online element failure occurring, the backup mechanism is typically implemented which enables a standby element to take over the mission task from a backup point instead of re-executing the entire mission task from the very beginning. However, the backup mechanism is not perfectly reliable in practice, and effect of its failure on the system reliability can be non-monotonic and is correlated to other system and element parameters. In this paper a new numerical approach is first proposed to evaluate reliability and expected mission completion time for 1-out-of- $N$ : G cold standby systems subject to imperfect even backups. The system elements are non-repairable during the mission. Based on the proposed evaluation algorithm, effects of backup system reliability in connection with other system parameters including backup frequency, data backup and retrieval times, replacement failure probability, replacement time, and number of system elements are investigated through examples. Further, the optimal backup frequency and initiation sequencing problem is formulated and solved for heterogeneous cold standby systems, providing solutions that can maximize mission reliability or minimize expected mission completion time depending on design requirements.