Explicit results for wear processes in a Markovian environment

Operations Research Letters

Volumn 31, Issue 3, 2003, Pages 237-244

  Kharoufeh, Jeffrey P ^a  

^a Air Force Institute of Technology   (United States)

Author keywords

Failure time; Random environment; Wear process

Indexed keywords

ALGORITHMS; LAPLACE TRANSFORMS; PARTIAL DIFFERENTIAL EQUATIONS; STOCHASTIC PROGRAMMING;

WEAR PROCESSES;

MARKOV PROCESSES;

EID: 0037402227     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6377(02)00229-8     Document Type: Article

References (17)

1. Abate J., Choudhury G., Whitt W. Numerical inversion of multidimensional Laplace transforms by the Laguerre method. Performance Evaluation. 31:1998;229-243.
2. Abate J., Whitt W. Numerical inversion of Laplace transforms of probability distributions. ORSA J. Comput. 7:1995;36-43.
3. Abdel-Hameed M. Life distribution properties of devices subject to Lévy wear process. Math. Oper. Res. 9:1984;606-614.
4. Çinlar E. Shock and wear models and Markov additive processes. Shimi I.N., Tsokos C.P. The Theory and Applications of Reliability. 1977;193-214 Academic Press, New York.
5. Esary J.D., Marshall A.W., Proschan F. Shock models and wear processes. Ann. Probab. 1:1973;627-649.
6. Gottlieb G. Failure distributions of shock models. J. Appl. Probab. 17:1980;745-752.
7. Igaki I., Sumita U., Kowada M. Analysis of Markov renewal shock models. J. Appl. Probab. 32:1995;821-831.
8. Liminos N., Oprisan G. A unified approach for reliability and performability evaluation of semi-Markov systems. Appl. Stochastic Models Business Industry. 15:1999;353-368.
9. Moorthy M.V. Numerical inversion of two-dimensional Laplace transforms-Fourier series representation. Appl. Numer. Math. 17:1995;119-127.
10. Nakagawa T. Replacement problem of a parallel system in random environment. J. Appl. Probab. 16:1979;203-205.
11. Ráde L. Reliability systems in random environment. J. Appl. Probab. 13:1976;407-410.
12. Ray A., Tangirala S. A nonlinear stochastic model of fatigue crack dynamics. Probab. Eng. Mech. 12:1997;33-40.
13. Shanthikumar J.G., Sumita U. General shock models associated with correlated renewal sequences. J. Appl. Probab. 20:1983;600-614.
14. Singpurwalla N.D. Survival in dynamic environments. Statist. Sci. 10:1995;86-103.
15. Stadje W., Zuckerman D. A random walk model for a multi-component deteriorating system. Oper. Res. Lett. 29:2001;199-205.
16. Valdez-Flores C., Feldman R.M. A survey of preventive maintenance models for stochastically deteriorating single-unit systems. Naval Res. Logistics. 36:1989;419-446.
17. Waldmann K.H. Optimal replacement under additive damage in randomly varying environments. Naval Res. Logistics Quart. 30:1983;377-386.