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Semi-Markov Processes and Hidden Models

  1. Nikolaos Limnios

Published Online: 15 JUN 2010

DOI: 10.1002/9780470400531.eorms0990

Wiley Encyclopedia of Operations Research and Management Science

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. .

Author Information

  1. Université de Technologie de Compiègne, Compiègne, Laboratoire de Mathématiques Appliquées, France

Publication History

  1. Published Online: 15 JUN 2010

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.

Keywords:

  • semi-Markov process;
  • Markov renewal process, semi-Markov chain;
  • hidden semi-Markov model;
  • semi-Markov kernel;
  • Markov renewal equation;
  • empirical estimator;
  • reliability;
  • availability;
  • mean time to failure