Semi-Markov models for degradation-based reliability

References

• Abate , J. and Whitt , W. 1995 . Numerical inversion of Laplace transforms of probability distributions . ORSA Journal on Computing , 7 ( 1 ) : 36 – 43 .
   Google Scholar
• Aldous , D. and Shepp , L. 1987 . The least variable phase type distribution is Erlang . Communications in Statistics-Stochastic Models , 3 ( 3 ) : 467 – 473 .
   Google Scholar
• Altiok , T. 1985 . On the phase-type approximations of general distributions . IIE Transactions , 17 ( 2 ) : 110 – 116 .
   Web of Science ®Google Scholar
• Basawa , I. V. and Rao , P. 1980 . Statistical Inference for Stochastic Processes , New York : Wiley .
   Google Scholar
• Çinlar , E. 1977 . “ Shock and wear models and Markov additive processes ” . In The Theory and Applications of Reliability , Edited by: Shimi , I. N. and Tsokos , C. P. 193 – 214 . New York : Academic Press .
   Google Scholar
• Çinlar , E. 1984 . “ Markov and semi-Markov models of deterioration ” . In Reliability Theory and Models , Edited by: Abdel-Hameed , M. , Çinlar , E. and Quinn , J. 3 – 41 . New York : Academic Press .
   Google Scholar
• Conover , W. J. 1999 . Practical Nonparametric Statistics , New York : Wiley .
   Google Scholar
• Cox , D. R. 1955 . A use of complex probabilities in the theory of stochastic processes . Proceedings of the Cambridge Philosophical Society , 55 : 313 – 319 .
   Google Scholar
• Cox , D. R. 1972 . Regression models and life tables . Journal of the Royal Statistical Society, B , 34 : 187 – 220 .
   Web of Science ®Google Scholar
• Cox , D. R. and Oakes , S. 1984 . Analysis of Survival Data , London : Chapman and Hall .
   Google Scholar
• Ebeling , C. E. 1997 . An Introduction to Reliability and Maintainability Engineering , New York : McGraw Hill .
   Google Scholar
• Ebrahimi , N. 2006 . System reliability based on system wear . Stochastic Models , 22 ( 1 ) : 21 – 36 .
   Web of Science ®Google Scholar
• Ejaz , N. and Tauqir , A. 2006 . Failure due to structural degradation in turbine blades . Engineering Failure Analysis , 13 : 452 – 463 .
   Web of Science ®Google Scholar
• Elsayed , E. A. 2000 . Perspectives and challenges for research in quality and reliability engineering . International Journal of Production Research , 38 : 1953 – 1976 .
   Web of Science ®Google Scholar
• Elsayed , E. A. , Liao , H. and Wang , X. 2006 . An extended linear hazard regression model with application to time-dependent dielectric breakdown of thermal oxides . IIE Transactions , 38 : 329 – 340 .
   Web of Science ®Google Scholar
• Esary , J. D. , Marshall , A. W. and Proschan , F. 1973 . Shock models and wear processes . Annals of Probability , 1 : 627 – 649 .
   Web of Science ®Google Scholar
• Gebraeel , N. , Lawley , M. , Li , R. and Ryan , J. 2005 . Residual-life distributions from component degradation signals: a Bayesian approach . IIE Transactions , 37 : 543 – 557 .
   Web of Science ®Google Scholar
• Gebraeel , N. and Pan , J. 2008 . Prognostic degradation models for computing and updating residual life distributions in a time-varying environment . IEEE Transactions on Reliability , 57 : 539 – 550 .
   Web of Science ®Google Scholar
• Jardine , A. K. S. and Anderson , M. 1985 . Use of concomitant variables for reliability estimation . Maintenance Management International , 5 : 135 – 140 .
   Google Scholar
• Jardine , A. K. S. , Anderson , P. M. and Mann , D. S. 1987 . Application of the Weibull proportional hazards model to aircraft and marine engine failure data . Quality and Reliability Engineering International , 3 : 77 – 82 .
   Google Scholar
• Jardine , A. K. S. , Ralston , P. , Reid , N. and Stafford , J. 1989 . Proportional hazards analysis of diesel engine failure data . Quality and Reliability Engineering International , 5 : 207 – 216 .
   Google Scholar
• Johnson , M. A. 1993 . Selecting parameters of phase distributions: combining nonlinear programming, heuristics, and Erlang distributions . ORSA Journal on Computing , 5 ( 1 ) : 69 – 83 .
   Google Scholar
• Kharoufeh , J. P. 2003 . Explicit results for wear processes in a Markovian environment . Operations Research Letters , 31 ( 3 ) : 237 – 244 .
   Web of Science ®Google Scholar
• Kharoufeh , J. P. and Cox , S. M. 2005 . Stochastic models for degradation-based reliability . IIE Transactions , 37 : 533 – 542 .
   Web of Science ®Google Scholar
• Kharoufeh , J. P. , Finkelstein , D. and Mixon , D. 2006 . Availability of periodically inspected systems with Markovian wear and shocks . Journal of Applied Probability , 43 : 303 – 317 .
   Web of Science ®Google Scholar
• Kiessler , P. , Klutke , G. and Yang , Y. 2002 . Availability of periodically inspected systems subject to Markovian degradation . Journal of Applied Probability , 39 : 700 – 711 .
   Web of Science ®Google Scholar
• Klutke , G. , Wortman , M. and Ayhan , H. 1996 . The availability of inspected systems subject to random deterioration . Probability in the Engineering and Informational Sciences , 10 : 109 – 118 .
   Web of Science ®Google Scholar
• Kobbacy , K. A. H. , Fawzi , B. B. , Percy , D. F. and Ascher , H. E. 1997 . A full history proportional hazards model for preventive maintenance scheduling . Quality and Reliability Engineering International , 13 : 187 – 198 .
   Web of Science ®Google Scholar
• Kulkarni , V. G. 1995 . Modeling and Analysis of Stochastic Systems , London : Chapman and Hall .
   Google Scholar
• Lang , A. and Arthur , J. L. 1997 . “ Parameter approximation for phase-type distributions ” . In Matrix-Analytic Methods in Stochastic Models , Edited by: Chakravarthy , S. R. and Alfa , A. S. 151 – 206 . New York : Marcel Dekker .
   Google Scholar
• Lawless , J. F. 1982 . Statistical Models and Methods for Lifetime Data , New York : Wiley .
   Google Scholar
• Li , G. and Luo , J. 2005 . Shock model in Markovian environment . Naval Research Logistics , 52 : 253 – 260 .
   Web of Science ®Google Scholar
• Lu , J. C. and Meeker , W. 1993 . Using degradation measures to estimate a time-to-failure distribution . Technometrics , 35 : 161 – 174 .
   Web of Science ®Google Scholar
• Mallor , F. and Omey , E. 2001 . Shocks, runs, and random sums . Journal of Applied Probability , 38 : 438 – 448 .
   Web of Science ®Google Scholar
• Marie , R. Calculating equilibrium probabilities for λ(n)/C k /1/N queues . Proceedings of the 1980 International Symposium on Computer Performance Modelling, Measurement, and Evaluation . pp. 117 – 125 . New York : ACM .
   Google Scholar
• Mishra , S. and Pecht , M. 2002 . In-situ sensors for product reliability monitoring . Proceedings of SPIE , 4755 : 10 – 19 .
   Google Scholar
• Neuts , M. F. 1981 . Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach , New York : Dover Publications .
   Google Scholar
• Osogami , T. and Harchol-Balter , M. 2006 . Closed-form solutions for mapping general distributions to quasi-minimal PH distributions . Performance Evaluation , 63 ( 6 ) : 524 – 552 .
   Web of Science ®Google Scholar
• Özekici , S. and Soyer , R. 2003 . Bayesian analysis of Markov modulated Bernoulli processes . Mathemathical Methods of Operations Research , 57 : 125 – 140 .
   Web of Science ®Google Scholar
• Özekici , S. and Soyer , R. 2004 . “ Reliability modeling and analysis in random environments ” . In Mathematical Reliability: An Expository Perspective , Edited by: Soyer , R. , Mazzuchi , T. A. and Singpurwalla , N. D. 249 – 273 . Norwell, MA : Kluwer Academic Publishers .
   Google Scholar
• Özekici , S. and Soyer , R. 2006 . Semi-Markov modulated Poisson process: probabilistic and statistical analysis . Mathemathical Methods of Operations Research , 64 : 125 – 144 .
   Web of Science ®Google Scholar
• Perros , H. 1994 . Queueing Networks with Blocking , New York : Oxford University Press .
   Google Scholar
• Persson , C. and Persson , P. O. 1993 . Evaluation of service-induced damage and restoration of cast turbine blades . Journal of Materials Engineering and Performance , 2 : 565 – 570 .
   Web of Science ®Google Scholar
• Singpurwalla , N. D. 1995 . Survival in dynamic environments . Statistical Science , 10 : 86 – 103 .
   Web of Science ®Google Scholar
• Tamarin , Y. 2002 . Protective Coatings for Turbine Blades , Materials Park, OH : ASM International .
   Google Scholar
• Telek , M. and Heindl , A. 2003 . Matching moments for acyclic discrete and continuous phase-type distributions of second order . International Journal of Simulation , 3 : 47 – 57 .
   Google Scholar
• Virkler , D. A. , Hillberry , B. M. and Goel , P. K. 1979 . The statistical nature of fatigue crack propagation . Transaction of the ASME Journal of Engineering Materials and Technology , 101 ( 2 ) : 148 – 153 .
   Web of Science ®Google Scholar
• Whitt , W. 1984 . On approximations for queues III: mixtures of exponential disributions . Bell Labs Technical Journal , 63 ( 1 ) : 163 – 175 .
   Web of Science ®Google Scholar
• Zhan , Y. , Makis , V. and Jardine , A. K. S. 2003 . Adaptive model for vibration monitoring of rotating machinery subject to random deterioration . Journal of Quality in Maintenance Engineering , 9 : 351 – 375 .
   Google Scholar