AN ANALYSIS OF A RELIABILITY MODEL FOR REPAIRABLE FAULT-TOLERANT SYSTEMS

The ARIES reliability model proposed by Ng and Avizienis [191 models a class of repairable and nonrepairable fault-tolerant systems by a Con tinuous Time Markov Chain. ARIES uses the Lagrange-Sylvester interpola tion Formula to directly compute the exponential of the State Transiti on Rate Matrix (STRM) which appears in the solution of the Markov Chai n. Following have been the main objections to this solution technique [9], [16]. First, that the method is prohibitively expensive in terms of computation; the computational complexity is O(n5) for a state tran sition rate matrix of size n. Second, that it is not clear that the so lution technique is general enough as to handle all repairable fault-t olerant systems which ARIES models. Third, that the numerical stabilit y of this method is unsatisfactory. In this paper, we analyze the prop erties of the STRM for ARIES repairable systems and, drawing from well established results in matrix theory, suggest an efficient solution f or reliability computation when the eigenvalues of the STRM are distin ct. Also, we identify a class of systems that ARIES models for which t he solution technique is inapplicable. We employ several transformatio ns which are known to be numerically stable in our solution method. Ou r solution method also offers a facility for incrementally computing r eliability when the number of spares in the fault-tolerant system is i ncreased by one.