Bounding steady-state availability models with group repair and phase type repair distributions

We propose an algorithm to obtain bounds for the steady-state availability using Markov models in which only a small portion of the state space is generated. The algorithm is applicable to models with group repair and phase type repair distributions and involves the solution of only four linear systems of the size of the generated state space, independently on the number of “return” states. Numerical examples are presented to illustrate the algorithm and compare it with a previous bounding algorithm.