This article provides a novel method to solve continuous-time semi-Markov processes by algorithms from discrete-time case, based on the fact that the Markov renewal function in discrete-time case is a finite series. Bounds of approximate errors due to discretization for the transition function matrix of the continuous-time semi-Markov process are investigated. This method is applied to a reliability problem which refers to the availability analysis of the system subject to sequential cyber-attacks. Two cases where sojourn times follow exponential and Weibull distributions are considered and computed in order to verify and illustrate the proposed method.

中文翻译：

---

使用半马尔可夫链求解半马尔可夫过程

本文基于离散时间情形下的马尔可夫更新函数是一个有限级数这一事实，提供了一种通过离散时间情形的算法求解连续时间半马尔可夫过程的新方法。研究了连续时间半马尔可夫过程的转移函数矩阵离散化引起的近似误差界。此方法应用于可靠性问题，该可靠性问题是指受到顺序网络攻击的系统的可用性分析。考虑并计算了逗留时间遵循指数分布和威布尔分布的两种情况，以验证和说明所提出的方法。