Semi-Markov Processes and Hidden Models
Published Online: 15 JUN 2010
Copyright © 2010 John Wiley & Sons, Inc. All rights reserved.
Wiley Encyclopedia of Operations Research and Management Science
How to Cite
Limnios, N. 2010. Semi-Markov Processes and Hidden Models. Wiley Encyclopedia of Operations Research and Management Science. .
- Published Online: 15 JUN 2010
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.
- semi-Markov process;
- Markov renewal process, semi-Markov chain;
- hidden semi-Markov model;
- semi-Markov kernel;
- Markov renewal equation;
- empirical estimator;
- mean time to failure