Reliability Measures of Semi-Markov Systems with General State Space

Methodology and Computing in Applied Probability

Volumn 14, Issue 4, 2012, Pages 895-917

  Limnios, Nikolaos ^a  

^a UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

Availability; Failure rate; Mean time to failure; Rate of occurrence of failure; Reliability; Semi Markov process; Survival function

Indexed keywords

EID: 84867897917     PISSN: 13875841     EISSN: 15737713     Source Type: Journal    
DOI: 10.1007/s11009-011-9211-5     Document Type: Article

References (34)

1. Asmussen S (1987) Applied probability and queues. Wiley, Chichester.
2. Aven T, Jensen U (1999) Stochastic models in reliability. Springer, NY.
3. Barbu V, Limnios N (2008) Semi-Markov chains and hidden semi-Markov models. Toward applications. Their use in reliability and DNA analysis, Lecture notes in statistics, vol 191, Springer.
4. Barlow RE, Prochan F (1975) Statistical theory of reliability and life testing: probability models. Holt, Rinehart and Winston, New York.
5. Bhattacharya R, Majumdar M (2007) Random dynamical systems-theory and applications. Cambridge University Press, Cambridge.
6. Chiquet J, Limnios N, Eid M (2009) Piecewise deterministic Markov processes applied to fatigue crack growth modelling. J Stat Plan Inference 139: 1657-1667.
7. Chryssaphinou O, Limnios N, Malefaki S (2010) Multi-state reliability systems under discrete time semi-Markovian hypothesis. IEEE TR (to appear).
8. Csenki A (1995) Dependability for systems with a partitioned state space. Lecture notes in statistics, vol 90, Springer-Verlag, Berlin.
9. Devooght J (1997) Dynamic reliability. Adv Nucl Sci Technol 25: 215-278.
10. Esary JD, Marshal AW, Proschan F (1973) Shock models and wear processes. Ann Probab 1: 627-649.
11. Feller W (1966) An introduction to probability theory and its applications. vol 2, J. Wiley, NY.
12. Gertsbakh I (2000) Reliability theory-with applications to preventive maintenance. Springer, Berlin.
13. Iosifescu M, Limnios N, Oprişan G (2010) Introduction to stochastic models. Iste, J. Wiley, London.
14. Janssen J, Manca R (2006) Applied semi-Markov processes. Springer, New York.
15. Keilson J (1979) Markov chains models-rarity and exponentiality. Springer-Verlag, NY.
16. Korolyuk VS, Limnios N (2004) Average and diffusion approximation for evolutionary systems in an asymptotic split phase space. Ann Appl Probab 14(1): 489-516.
17. Korolyuk VS, Limnios N (2005) Stochastic systems in merging phase space. World Scientific, Singapore.
18. Kovalenko IN, Kuznetsov NYu, Pegg PA (1997) Mathematical theory of reliability of time dependent systems with practical applications. Wiley, Chichester.
19. Limnios N, Nikulin M (eds) (2000) Recent advances in reliability theory: methodology, practice and inference. Birkhäuser, Boston.
20. Limnios N, Oprişan G (2001) Semi-Markov processes and reliability. Birkhäuser, Boston.
21. Limnios N, Ouhbi B (2003) Empirical estimators of reliability and related functions for semi-Markov systems. In: Lindqvist B, Doksum K (eds) Mathematical and statistical methods in reliability, World Scientific.
22. Limnios N, Ouhbi B (2006) Nonparametric estimation of some important indicators in reliability for semi-Markov processes. Statistical Methodology 3(4): 341-350.
23. Lisnianski A, Levitin G (2003) Multi-state system reliability. World Scientific.
24. Neuts MF (1981) Matrix-geometric solution in stochastic models. Johns Hopkins University Press, Baltimore.
25. Osaki S (1985) Stochastic system reliability modeling. World Scientific, Singapore.
26. Ouhbi B, Limnios N (2002) The rate of occurrence of failures for semi-Markov processes and estimation. Stat Probab Lett 59(3): 245-255.
27. Ouhbi B, Limnios N (2003) Nonparametric reliability estimation of semi-Markov processes. J Stat Plan Inference 109(1/2): 155-165.
28. Pérez-Ocón R, Torres-Castro I (2002) A reliability semi-Markov model involving geometric processes. Appl Stoch Models Bus Ind 18: 157-70.
29. Pyke R (1961) Markov renewal processes: definitions and preliminary properties. Ann Math Stat 32: 1231-1242.
30. Ravichandran N (1990) Stochastic methods in reliability theory. Wiley, India.
31. Revuz D (1975) Markov chains. North-Holland, Amsterdam.
32. Shurenkov VM (1984) On the theory of Markov renewal. Theor Probab Appl 19(2): 247-265.
33. Silvestrov DS (1996) Recurrence relations for generalized hitting times for semi-Markov processes, Ann Appl Probab 6(2): 617-649.
34. Wilson A, Limnios N, Keller-McNulty S, Armijo Y (eds) (2005) Modern statistical and mathematical methods in reliability. Series on Quality, Reliability, Engineering Statistics, World Scientific, Singapore.