中文摘要：

为了使数据库与计算机等系统发生故障以后的损失降到最低程度,需要对之前的状态进行一个备份。研究了关于检测点的备份策略,系统每次完成工作的时间是随机的,在定期时间进行检测或者在完成工作以后的随机时间进行检测,当系统发生故障时备份操作开始执行直到最近一次检测点。利用几何过程理论求出了系统从开始工作到执行完备份操作的期望费用的表达式,研究结果表明：存在最优的T＊和N＊使期望费用最少。

英文摘要：

In some systems like database and computer system,their failure may cause severe losses.It is very important to make a backup to avoid the losses.This study investigates the backup policy with checkpoint.The time for computer system to complete a job is random.The random time can be checked at planned interval or random time interval after the job is completed.If the system fails,the backup can be carried out until the latest checkpoint.The formula for calculating total expected cost of backup is derived based on geometric process theory.The study result shows that the optimal and exist.