Abstract
Some systems work for a job with random working and processing times, and are checked at periodic and random times. When a failure occurs, we execute the backup operation to the latest checking time. First, the expected costs with periodic and random backups are formulated, and comparisons between periodic and random policies are made. Next, we focus on the backup policies when the system is checked at the Nth interval of working times, two total expected costs are obtained and optimal numbers N* which minimize them are derived analytically. Finally, one modified backup model in which failures are detected only at checking times is proposed and two expected costs are obtained.
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