Evaluating failure time probabilities for a Markovian wear process

Computers and Operations Research

Volumn 32, Issue 5, 2005, Pages 1131-1145

  Kharoufeh, Jeffrey P ^a   Sipe, Jeffrey A ^b  

^a Air Force Institute of Technology   (United States)

^b Scott AFB   (United States)

Author keywords

Laplace Stieltjes transform; Lifetime distribution; Wear process

Indexed keywords

ALGEBRA; ALGORITHMS; EXTRAPOLATION; FOURIER TRANSFORMS; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; POLYMERS; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING; STATISTICAL METHODS;

LAPLACE-STIELTJES TRANSFORMS; LIFETIME DISTRIBUTION; TIME PROBABILITIES; WEAR PROCESSES;

MARKOV PROCESSES;

EID: 7544243413     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2003.09.016     Document Type: Article

References (19)

1. Kharoufeh J.P. Explicit results for wear processes in a Markovian environment. Operations Research Letters. 31:2003;237-244.
2. Gillen K.T., Celina M. The wear-out approach for predicting the remaining lifetime of materials. Polymer Degradation and Stability. 71:2001;15-30.
3. Meeker W.Q., Escobar L.A., Chan V. Using accelerated tests to predict service life in highly variable environments. Bauer D.R., Martin J.W. Service life prediction: methodologies and metrologies. 2002;American Chemical Society, Washington, DC.
4. Singpurwalla N.D. Survival in dynamic environments. Statistical Science. 10:1995;86-103.
5. Bobbio A, Kulkarni VG, Telek M. Partial loss in reward models. In: Proceedings of the Second International Conference on Mathematical Methods in Reliability, Bordeaux, France: July 2000. p. 207-10.
6. Bobbio A., Telek M. The task completion time in degradable sytems. Haverkort G.R.B.R., Marie R., Trivedi K.S. Performability modelling: techniques and tools. 2001;p139-p161 Wiley, New York.
7. Abate J., Whitt W. Numerical inversion of Laplace transforms of probability distributions. ORSA Journal on Computing. 7:1995;36-43.
8. Meeker W.Q., Escobar L.A. Statistical methods for reliability data. 1998;Wiley Inc. New York.
9. Çinlar E. Shock and wear models and Markov additive processes. Shimi I.N., Tsokos C.P. The theory and applications of reliability. 1977;p193-p214 Academic Press, New York.
10. Choudhury G.L., Lucantoni D., Whitt W. Multidimensional transform inversion with applications to the transient M/G/1 queue. The Annals of Applied Probability. 4:1994;719-740.
11. Moorthy M.V. Numerical inversion of two-dimensional Laplace transforms-Fourier series representation. Applied Numerical Mathematics. 17:1995;119-127.
12. Noble B., Daniel J.W. Applied linear algebra. 3rd ed. 1988;Prentice-Hall, Englewood Cliffs, NJ.
13. Bladt M., Neuts M.F. Matrix-exponential distributions. calculus and interpretations via flows Stochastic Models. 19:2003;113-124.
14. Neuts M.F. Algorithmic probability: a collection of problems. 1995;Chapman & Hall, London.
15. Moler C., van Loan C. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years laters. SIAM Review. 45:2003;3-49.
16. Vanden Bosch P.M., Dietz D.C., Pohl E.A. Choosing the best approach to matrix exponentiation. Computers and Operations Research. 29:1999;871-882.
17. Dubner H., Abate J. Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform. Journal of the Association for Computing Machinery. 15:1968;115-123.
18. Macdonald J.R. Accelerated convergence, divergence, iteration, extrapolation, and curve fitting. Journal of Applied Physics. 35:1964;3034-3041.
19. Ray A., Tangirala S. A nonlinear stochastic model of fatigue crack dynamics. Probabilistic Engineering Mechanics. 12:1997;33-40