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