Unification of reliability/availability/repairability models for Markov systems

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Abstract
An examination is made of the structure of the general transition rate matrix from which the model transition rate matrices are obtained. An exact solution to the system-state equations is derived which depends on the eigenvalues of the model transition rate matrix. In order to obtain the exact numerical solution, an algorithm is given which requires a minimal amount of computer storage requirements. An approximate solution is derived which does not require determination of eigenvalues but, instead, is based on the representation of a Markov process by a Markov chain randomized by a Poisson process. This approximation is highly accurate with a controllable error, and its use is particularly effective for large systems