Convergence of linear algebraic reliability simulation

In this paper, numerical methods for the solution of a reliability modeling problem are presented by finding the steady state solution of a Markov chain. The reliability modeling problem analyzed is that of a large system made up of two smaller systems each with a varying number of subsystems. The focus of this study is on the optimal choice and formulation of algorithms for the steady-state solution of the generator matrix for the Markov chain associated with the given reliability modeling problem. In this context, iterative linear equation solution algorithms were compared. The Conjugate-Gradient method was determined to have the quickest convergence with the Gauss-Seidel method following close behind for the relevant model structures. Current work associated with this project analyzes the convergence of the Successive Over-Relaxation method. This work is part of a larger program for simulating, processing, and analyzing stochastic processes associated with simulation of naval systems.