The ARIES reliability model, which models a class of repairable and nonrepairable fault-tolerant systems by a continuous-time Markov chain and uses the Lagrange-Sylvester interpolation formula to directly compute the exponential of the state transition rate matrix (STRM) that appears in the solution of the Markov chain, is discussed. The properties of the STRM for ARIES repairable systems are analyzed. Well-established results in matrix theory are used to find an efficient solution for reliability computation when the eigenvalues of the STRM are distinct. A class of systems that ARIES models for which the solution technique is inapplicable is identified. Several transformations which are known to be numerically stable are used in the solution method. The solution method also offers a facility for incrementally computing reliability when the number of spares in the fault-tolerant system is increased by one.
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