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This article describes an accurate procedure for computing the mean firstpassage times of a finite irreducible Markov chain and a Markov renewalprocess. The method is a refinement to the Kohlas, Zeit fur Oper Res,30,197-207, (1986) procedure. The technique is numerically stable in that itdoesn't involve subtractions. Algebraic expressions for the special cases ofone, two, three and four states are derived. A consequence of the procedure isthat the stationary distribution of the embedded Markov chain does not need tobe derived in advance but can be found accurately from the derived mean firstpassage times. MatLab is utilized to carry out the computations, using sometest problems from the literature.

Accurate calculations of stationary distributions and mean first passage times in Markov renewal processes and Markov chains