Study on iterative availability algorithm of Markov renewal equation

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.