马尔可夫更新方程的迭代算法研究

Study on iterative availability algorithm of Markov renewal equation

冷储备系统的动态结构变化使得系统可用度分析必须基于瞬态求解 ,针对频域两部件冷储备系统马尔可夫更新方程解算困难的问题 ,提出基于时域伏尔特拉方程的迭代算法 ,证明了该迭代方程的唯一性和收敛性 ,并给出迭代算法的误差分析 .理论和实例分析表明 ,当冷储备系统部件的工作寿命和维修时间分布是有界函数时 ,利用迭代算法可以容易实现时域马尔可夫更新方程的求解 .

Dynamic structure variance of cool spare system requires the dynamic availability analysis with transient solution. The traditional calculation method of Markov renewal equation based on Laplace transform and inverse Laplace transform makes many difficulties to complex system. The iterative availability algorithm based on Valterra series is presented in time domain to cool spare system with two units, and its uniqueness and convergence are proved. Comparing the iterative algorithm with the algorithm based on Laplace transform, it indicates that the iterative error is small and acceptable. Application results show that the iterative availability algorithm can easily realize the resolution for Markov renewal equation when the life distribution and repair time distribution are bounded functions.