摘要： 对软件的两阶段失效与恢复模型进行了分析，基于特定失效概率求解最优恢复时间间隔，并利用半马尔可夫过程，得到特定失效概率下的平均恢复成本。为了将恢复成本降到更低，采用了嵌套的基于时间的软件恢复策略，同时考虑应用级和系统级的恢复，并求得了特定失效概率下的最大应用级恢复次数、恢复时间间隔序列以及最低年平均恢复成本。

关键词: 软件恢复；系统可靠性；软件老化；软件失效概率

Abstract: A method solving the rejuvenation intervals based on a given failure probability is put forward in this paper. The two-step failure model with rejuvenation interval and semi-Markov process are used for solving the mean rejuvenation cost based on the given-failure-probability. In addition, considering fine-grained rejuvenation consumes lower cost and less downtime, this paper adopts the nested time-based software rejuvenation policy, which takes the application-level and system-level rejuvenation into account simultaneously. And then based on the given-failure-probability, it obtains the maximum times of application-level rejuvenation, the rejuvenation interval sequence, and the minimum mean rejuvenation cost

Key words: Software rejuvenation; Software reliability; Software aging; Software failure probability