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Markov Chains

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

Abstract

In  Sect. 3.4, we consider the system that repeats up and down such as operating and failed states alternately. Next, as one example of extended models, we take up the system with repair maintenance: The system begins to operate at time 0 and undergoes repair according to two types of failures such as minor and major failures. After the repair completion, the system becomes like new and begins to operate again.

Keywords

Markov Chain Transition Probability Matrix Interarrival Time Kolmogorov Equation Stationary Transition Probability 
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

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    Osaki S (1992) Applied stochastic system modeling. Springer, BerlinGoogle Scholar
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    Kemeny JG, Snell JL (1960) Finite Markov chains. Nostrand Co, PrincetonGoogle Scholar
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    Tijms HC (2003) A first course in stochastic models. Wiley, ChichesterGoogle Scholar
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    Ross SM (1983) Stochastic processes. Wiley, New YorkGoogle Scholar
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    Barlow RE, Proschan F (1965) Mathematical theory of reliability. Wiley, New YorkGoogle Scholar
  6. 6.
    Nakagawa T (2005) Maintenance theory of reliability. Springer, LondonGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of Business AdministrationAichi Institute of TechnologyToyotaJapan

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