A hard disk has, in recent years, become an essential component for a personal computer as well as a work station. A hard disk stores a variety of files, which are daily updated. The files in a hard disk are, however, lost because of human errors and a failure of the hard disk. This is called a hard disk failure. In order to protect us from such a serious loss, it is important to make a backup copy of files on a magnetic tape or on several floppy disks. Frequent backup operations require much cost in backup operations themselves, while rate backup operations would make the loss at a hard disk failure very large. This indicates that the backup timing should adequately be determined considering the above two factors. This study discusses an economical backup warning strategy, which prescribes the time to give us a warning for a backup operation at age T, where age refers to the elapsed time since the previous backup operation or a recovery operation whichever occurred most recently. When a job accessing the hard disk is being processed at the warning time, the backup operation is conducted after the process of the job is finished. The expected cost per unit time under this strategy is formulated as an objective function. The existence of an economical warning time that minimizes the expected cost is shown. Numerical examples are also presented to illustrate the theoretical underpinnings of the economical backup warning strategy formulation.
