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Markov renewal processes in reliability analysis

  • V. S. Korolyuk
Chapter
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Abstract

A Markov renewal processes (MRP) can be defined as a two-dimensional homogeneous Markov chain (xrr; r ⩾ 0), where xr takes its values in the measurable state space E with σ-algebra of measurable sets ε, and θr in [0,+∞) respectively.

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References

  1. Ashby, W. (1964). Introductory remarks at Panel discussion. Views on general system theory. — Views on general system theory. — Proceedings of the 2 systems theory symposium at Case Institute of Technology.Google Scholar
  2. Korolyuk, V.S. and A.F. Turbin (1976). Semi-Markov processes and their applications. Kiev, “Naukova Dumka” (in Russian).Google Scholar
  3. Korolyuk, V.S. and A.F. Turbin (1978). Mathematical foundations of the complex systems phase lumping. Kiev, 22 “Naukova Dumka” (in Russian).Google Scholar
  4. Korolyuk, V.S. and A.F. Turbin (1982). Markov renewal processes in the problems of system’s reliability. Kiev, “aukova Dumka” (in Russian).Google Scholar
  5. Korolyuk, V.S. and A.F. Turbin (1983). Analytic methods to estimate reliability properties of renewal systems. Kiev.Soc. “Znaniye”. Ukr.SSR (in Russian).Google Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • V. S. Korolyuk
    • 1
  1. 1.Ukrainian Academy of SciencesKiev 4USSR

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