  In this paper we present the classical results of Kolmogorov's backward and
forward equations to the case of a two-parameter Markov process. These
equations relates the infinitesimal transition matrix of the two-parameter
Markov process. However, solving these equations is not possible and we require
a numerical procedure. In this paper, we give an alternative method by use of
double Laplace transform of the transition probability matrix and of the
infinitesimal transition matrix of the process. An illustrative example is
presented for the method proposed. In this example, we consider a two-parameter
warranty model, in which a system can be any of these states: working, failure.
We calculate the transition density matrix of these states and also the cost of
the warranty for the proposed model.
