Bounding Steady-state Availability Models with Group Repair and Phase Type Repair Distributions Juan A. Carrasco Departament d’Enginyeria Electr` onica Universitat Polit` ecnica de Catalunya Diagonal 647, plta. 9 08028 Barcelona, Spain juan.a.carrasco@upc.edu Except for formatting details, this version matches exactly the version published with the same title and authors in Performance Evaluation, vol. 35, no. 3–4, 1999, pp. 193–214 Abstract 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. Keywords: Fault-tolerant systems; Repairable systems; Steady-state availability; Bounds; Group repair; Phase type distributions