Abstract
This paper models a warm standby system where a single element is online performing a specified mission task (e.g., a computing task) and subject to corrective replacement (CR) by an available standby element upon its failure. During the mission, preventive replacements (PRs) are also performed to renew the aged or worn online operating element before its actual failure according to a predetermined policy. In addition, to facilitate an effective restoration of system function in case of CR or PR happening, backups are also performed periodically so that the mission task can be resumed from the last successful backup point instead of from scratch. The mission succeeds if the specified mission task is accomplished; in other words, the mission fails when no operating elements remain prior to the mission task completion. In this paper, we make new contributions by first proposing an event transition-based numerical method to evaluate mission performance indices of the considered standby system subject to periodic backups, CR and PR. Mission success probability (MSP), expected mission completion time, expected mission operation cost (EMC), and expected uncompleted work fraction are evaluated. Based on the suggested evaluation algorithm, we make another contribution by formulating and solving optimization problems that help to determine the optimal backup-PR policy or the optimal combination of element activation sequencing and backup-PR policy to maximize MSP or minimize EMC. Influence of element performance and reliability parameters, data backup and retrieval complexity parameters on the optimal operation policy is investigated. Findings from this paper can guide the optimal decision making on policies related to element sequencing, backups as well as preventive maintenance planning, contributing toward reliable and cost-effective design and operation of standby computing systems.