Semi‐Markov Processes and Hidden Models

Abstract The purpose of this article is to present the semi‐Markov processes focusing on applications, especially in reliability and dependability. The semi‐Markov processes under consideration are both of continuous and discrete time with countable or finite state space. The basic definitions of Markov renewal and semi‐Markov processes are presented, as well as the Markov renewal theorem and the some theory of statistical estimation. In the sequel, we describe a general reliability model and give the corresponding estimations. Finally, we briefly present the semi‐Markov chain and hidden semi‐Markov models. Some bibliographical directions for further relevant topics, which are not included in this article, are given.