Dynamic reliability via computational solution of generalized state-transition equations for entry-time processes

Reliability Engineering and System Safety

Volumn 92, Issue 9, 2007, Pages 1281-1293

  Nelson, Paul ^a   Wang, Shuwen ^a  

^a Texas A and M University   (United States)

Author keywords

Chapman Kolmogorov equations; Computational solution; Dynamic reliability; Entry time process; Semi Markov processes; State model

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; COMPUTER SIMULATION; MARKOV PROCESSES; MATHEMATICAL MODELS;

ENTRY TIME PROCESSES; STATE VARIABLES; TRANSITION EQUATIONS; TRANSITION RATES;

DIFFERENTIAL EQUATIONS;

EID: 33847389023     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2006.08.005     Document Type: Article

References (16)

1. Cox D.R. The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. Proc Camb Philos Soc 51 (1955) 433-441
2. Liming J.K., and Grantom C.R. Risk-informed asset management (RIAM) for nuclear power plants. Trans Am Nucl Soc 88 (2003) 55-56
3. Fleming K.N. Markov models for evaluating risk-informed in-service inspection strategies for nuclear power plant piping systems. Reliab Eng Syst Saf 83 (2004) 27-45
4. Gertsbakh G.B. Models of preventive maintenance (1977), North-Holland, Amsterdam
5. Gertsbakh G.B. Reliability theory (2000), Springer, Berlin
6. Anonymous. Generic Aging Lessons Learned Report; vol. 1 (Summary), vol. 2 (Tabulation of Results). US Nuclear Regulatory Commission, Report NUREG-1801, April 2001.
7. Bobbio A., and Cumani A. Modelling wear-out by multistate homogeneous Markov processes. In: Lauger E., and Møltoft J. (Eds). Reliability in electrical and electronic components and systems (1982) 101-106
8. Popova E, Wilson JG. Selecting and implementing the best group replacement policy for a nonMarkovian system. In: Probabilistic safety assessment and management `96, Proceedings of the European safety and reliability conference, Crete, 24-26 June 1996. p. 58-63.
9. Heute N., and Huber-Clark C. Semi-Markov models for quality of life data with censoring. In: Mesbah M. (Ed). Statistical methods for quality of life studies (2002) 207-218
10. DeVooght J, Smidts C. Probabilistic reactor dynamics. Nucl. Sci. Eng: Part I, 1992: 111:229-240; Part II, 111: 241-256; Part III, 112:101-113; Part IV, 112: 114-126.
11. DeVooght J., and Smidts C. Probabilistic dynamics as a tool for dynamic PSA. Rel Eng Syst Saf 52 (1996) 185-196
12. Becker G., Camarinopoulos L., and Zioutas G. A semi-Markovian model allowing for inhomogenities with respect to process time. Rel Eng Syst Saf 70 (2000) 41-48
13. Janssen J., and Manca R. Numerical solution of non-homogeneous semi-Markov processes in transient case. Meth Comp Appl Prob 3 (2002) 271-293
14. Becker G., Camarinopoulos L., and Kabranis D. Dynamic reliability under random shocks. Rel Eng Syst Saf 77 (2002) 239-251
15. Sigman K. Stationary marked point processes: an intuitive approach (1995), Chapman & Hall, US
16. Leveque R. Numerical methods for conservation laws (1992), Birkhäuser-Verlag, Switzerland