Discrete-time semi-Markov model for reliability and survival analysis

Communications in Statistics - Theory and Methods

Volumn 33, Issue 11, 2004, Pages 2833-2868

  Barbu, Vlad ^a   Boussemart, Michel ^a   Limnios, Nikolaos ^a  

^a UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

Discrete time Markov renewal process; Discrete time semi Markov process; Generalized ph distribution; Markov renewal theory; Mean hitting times; Monte Carlo method; Reliability; Survival function

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; FUNCTIONS; MARKOV PROCESSES; MATHEMATICAL MODELS; MONTE CARLO METHODS; PROBLEM SOLVING; RELIABILITY; SET THEORY;

DISCRETE-TIME MARKOV RENEWAL PROCESS; DISCRETE-TIME SEMI-MARKOV PROCESS; GENERALIZED PH-DISTRIBUTIONS; MARKOV RENEWAL THEORY; MEAN HITTING TIMES; SURVIVAL FUNCTION;

DISCRETE TIME CONTROL SYSTEMS;

EID: 11444261174     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1081/STA-200037923     Document Type: Article

References (15)

1. Anderson, P. K., Borgan, O., Gill, R. D., Keiding, N. (1993). Statistical Models Based on Counting Processes. New York: Springer.
2. Anselone, P. M. (1960). Ergodic theory for discrete semi-Markov chains. Duke Math. J. 27:33-40.
3. Çinlar, E. (1975). Introduction to Stochastic Processes. New York: Prentice Hall.
4. Csenki, A. (2002). Transition analysis of semi-Markov reliability models - A tutorial review with emphasis on discrete-parameter approaches. In: Osaki, S., ed. Stochastic Models in Reliability and Maintenance. Berlin: Springer, pp. 219-251.
5. Gerontidis, I. I. (1994). Semi-Markov replacement chains. Adv. Appl. Probab. 26:728-755.
6. Howard, R. (1971). Dynamic Probabilistic Systems. Vol II. New York: Wiley.
7. Janssen, J., De Dominicis, R. (1984). An algorithmic approach to non-homogeneous semi-Markov processes. Insurance Math. Econom. 3:157-165.
8. Janssen, J., Manca, R. (2001). Numerical solution of non homogeneous semi-Markov processes in transient case. Methodol. Comput. Appl. Probab. 3:271-294.
9. Limnios, N., Oprişan, G. (2001). Semi-Markov Processes and Reliability. Boston: Birkhäuser.
10. Mode, C. J., Sleeman, C. K. (2000). Stochastic Processes in Epidemiology. New Jersey: World Scientific.
11. Neuts, M. (1981). Matrix-Geometric Solutions in Stochastic Models. Baltimore: The John Hopkins University Press.
12. Port, S. C. (1994). Theoretical Probability for Applications. New York: Wiley
13. Shiryaev, A. N. (1996). Probability. 3rd ed. New York: Springer.
14. Vassiliou, P.-C. G., Papadopoulou, A. A. (1992). Non-homogeneous semi-Markov systems and maintainability of the state sizes. J. Appl. Probab. 29:519-534.
15. Vassiliou, P.-C. G., Papadopoulou, A. A. (1994). Asymptotic behavior of nonhomogeneous semi-Markov systems. Linear Algebra Appl. 210:153-198.