The Renewal Process Generated By Return Times of Semi-Markov Process in Reliability Models

Abstract The renewal process generated by the return times of semi-Markov process to a given state is considered in the paper. The return time to a state j and also a first passage time from a given state i to the state j of semi-Markov process are basic concepts that are used to determine this process. The systems of equations for distributions, expectations and secondond moments of these random variables are presented. Theorem concerning the asymptotic distribution of the considered renewal process is presented in this article. Moreover an illustrative example from the reliability theory is presented in the paper.