Unification of reliability/availability/repairability models for Markov systems

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