Skip to main content
Top

2011 | OriginalPaper | Chapter

8. Markov Processes

Author : Marko Čepin

Published in: Assessment of Power System Reliability

Publisher: Springer London

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

A Markov chain is a type of Markov process in which there are number of finite states that the process may exist at any given time. The probability of the process moving from one state to another is denoted by the transition probability and the probability of the process remaining in the same state is denoted by certain probability. Such modeling provides a clear representation of all the states of a system as well as the transition between these states. One disadvantage is that for large systems with many components, it is difficult to draw a diagram. This is because for a system of n components, each with a failed or operating state, the number of states that exist is equal to 2 n .

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Markov AA (1954) Theory of algorithms (Teoriya algoritmov). Academy of Sciences of the USSR Markov AA (1954) Theory of algorithms (Teoriya algoritmov). Academy of Sciences of the USSR
2.
go back to reference Howard RA (1971) Dynamic probabilistic systems. Wiley, New York Howard RA (1971) Dynamic probabilistic systems. Wiley, New York
3.
go back to reference Kemeny JG, Snell JL, Thompson GL (1974) Introduction to finite mathematics. Prentice-Hall, Englewood Cliffs, NJ Kemeny JG, Snell JL, Thompson GL (1974) Introduction to finite mathematics. Prentice-Hall, Englewood Cliffs, NJ
4.
go back to reference Grinstead C, Snell J (2003) Grinstead and Snell’s introduction to probability, 2nd edn. American Mathematical Society Grinstead C, Snell J (2003) Grinstead and Snell’s introduction to probability, 2nd edn. American Mathematical Society
5.
go back to reference Villemeur A (1992) Reliability, availability, maintainability and safety assessment: methods and techniques. Wiley, New York Villemeur A (1992) Reliability, availability, maintainability and safety assessment: methods and techniques. Wiley, New York
6.
go back to reference Li W (2005) Risk assessment of power systems: models, methods, and applications. Wiley, IEEE, New York Li W (2005) Risk assessment of power systems: models, methods, and applications. Wiley, IEEE, New York
7.
go back to reference Vesely W, Dugan J, Fragola J et al. (2002) Fault tree handbook with aerospace applications. National Aeronautics and Space Administration, NASA Vesely W, Dugan J, Fragola J et al. (2002) Fault tree handbook with aerospace applications. National Aeronautics and Space Administration, NASA
8.
go back to reference Pukite J, Pukite P (1998) Modeling for reliability analysis. IEEE, New YorkCrossRef Pukite J, Pukite P (1998) Modeling for reliability analysis. IEEE, New YorkCrossRef
9.
go back to reference Doeblin W (1937) Exposé de la Théorie des Chaines Simple Constantes de Markov ` un Nombre Fini d’Etats. Rev Mach de l’Union Interbalkanique 2:77?105 Doeblin W (1937) Exposé de la Théorie des Chaines Simple Constantes de Markov ` un Nombre Fini d’Etats. Rev Mach de l’Union Interbalkanique 2:77?105
10.
go back to reference Castelo R, Perlman MD (2002) Learning essential graph Markov models from data. Technical report no. 416 Castelo R, Perlman MD (2002) Learning essential graph Markov models from data. Technical report no. 416
11.
go back to reference Litterman RB (1983) A random walk, Markov model for the distribution of time series. J Business Econ Stat 1(2):169?173 Litterman RB (1983) A random walk, Markov model for the distribution of time series. J Business Econ Stat 1(2):169?173
12.
go back to reference IEC 1165 (1995) Application of Markov techniques. IEC IEC 1165 (1995) Application of Markov techniques. IEC
13.
go back to reference MIL-HDBK-338B (1998) Electronic reliability design handbook. DoD MIL-HDBK-338B (1998) Electronic reliability design handbook. DoD
14.
go back to reference Xie M, Da Y, Poh K (2004) Computing system reliability: models and analysis. Kluwer Academic, New York Xie M, Da Y, Poh K (2004) Computing system reliability: models and analysis. Kluwer Academic, New York
15.
go back to reference Smith DJ (2001) Reliability maintainability and risk. Butterworth-Heinemann, Woburn, MA Smith DJ (2001) Reliability maintainability and risk. Butterworth-Heinemann, Woburn, MA
16.
go back to reference Dhillon BS (2007) Applied reliability and quality: fundamentals, methods and procedures. Springer, London Dhillon BS (2007) Applied reliability and quality: fundamentals, methods and procedures. Springer, London
17.
go back to reference Levitin G (2007) Computational intelligence in reliability engineering, evolutionary techniques in reliability analysis and optimization. Springer, Berlin HeidelbergCrossRefMATH Levitin G (2007) Computational intelligence in reliability engineering, evolutionary techniques in reliability analysis and optimization. Springer, Berlin HeidelbergCrossRefMATH
18.
go back to reference Bertsekas DP, Tsitsiklis JN (2002) Introduction to probability. Athena Scientific, Belmont, MA Bertsekas DP, Tsitsiklis JN (2002) Introduction to probability. Athena Scientific, Belmont, MA
19.
go back to reference Anders GJ (1989) Probability concepts in electric power systems. Wiley, New York Anders GJ (1989) Probability concepts in electric power systems. Wiley, New York
Metadata
Title
Markov Processes
Author
Marko Čepin
Copyright Year
2011
Publisher
Springer London
DOI
https://doi.org/10.1007/978-0-85729-688-7_8