Advertisement

Semi-Markov and Markov Renewal Processes

  • Toshio Nakagawa
Chapter
Part of the Springer Series in Reliability Engineering book series (RELIABILITY)

Abstract

State space is usually defined by the number of units that are working satisfactorily. As far as the applications to reliability theory is concerned, we consider only a finite number of states, contrast with a queueing theory. We mention only the theory of stationary Markov processes with a finite-state space. It is shown that transition probabilities, first-passage distributions, and renewal functions are given by forming renewal equations. Furthermore, some limiting properties are summarized when all states communicate.

Keywords

Mass Function System Failure Regeneration Point Renewal Equation Embed Markov Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Osaki S (1992) Applied stochastic system modeling. Springer, BerlinMATHGoogle Scholar
  2. 2.
    Çinlar E (1975) Introduction to stochastic processes. Prentice-Hall, Englewood CliffsMATHGoogle Scholar
  3. 3.
    Nakagawa T (2008) Advanced reliability models and maintenance policies. Springer, LondonGoogle Scholar
  4. 4.
    Takács L (1962) Introduction to the theory of queues. Oxford University Press, New YorkMATHGoogle Scholar
  5. 5.
    Srinivasan VS (1968) First emptiness in the spare parts problem for repairable components. Oper Res 16:407–415MATHCrossRefGoogle Scholar
  6. 6.
    Nakagawa T, Osaki S (1976) Markov renewal process with some nonregeneration points and their applications to reliability theory. Microelectron Reliab 15:633–636CrossRefGoogle Scholar
  7. 7.
    Nakagawa T (2002) Two-unit redundant models. In: Osaki S (ed) Stochastic models in reliability and maintenance. Springer, Berlin, pp 165–185Google Scholar
  8. 8.
    Yasui K, Nakagawa T, Sandoh H (2002) Reliability models in data communication systems. In: Osaki S (ed) Stochastic models in reliability and maintenance. Springer, New York, pp 281–306Google Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of Business AdministrationAichi Institute of TechnologyToyotaJapan

Personalised recommendations