A switching diffusion model for lifetime estimation in randomly varying environments

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
• Abdel-Hameed, M.S. and Proschan, F. (1973) Nonstationary shock models. Stochastic Processes and Their Applications, 1(4), 383–404.
   Google Scholar
• Banjevic, D. and Jardine, A.K.S. (2006) Calculation of reliability function and remaining useful life for a Markov failure time process. IMA Journal of Management Mathematics, 17(2), 115–130.
   Google Scholar
• Banjevic, D., Jardine, A.K.S., Makis, V. and Ennis, M. (2001) A control-limit policy and software for condition-based maintenance optimization. INFOR, 39, 32–50.
   Web of Science ®Google Scholar
• Baum, E. and Petrie, T. (1966) Statistical inference for probabilistic functions of finite state Markov chains. The Annals of Mathematical Statistics, 37(6), 1554–1563.
   Google Scholar
• Billingsley, P. (1961) Statistical methods in Markov chains. The Annals of Mathematical Statistics, 32(1), 12–40.
   Google Scholar
• Blackwell, P.G. (2003) Bayesian inference for Markov processes with diffusion and discrete components. Biometrika, 90(3), 613–627.
   Web of Science ®Google Scholar
• Cappé, O., Moulines, E. and Rydén, R. (2005) Inference in Hidden Markov Models, Springer, New York, NY.
   Google Scholar
• Cha, J.H. and Mi, J. (2007) Study of a stochastic failure model in a random environment. Journal of Applied Probability, 44(1), 151–163.
   Web of Science ®Google Scholar
• Chib, S. (1996) Calculating posterior distributions and model estimates in Markov mixuture models. Journal of Econometrics, 75(1), 79–97.
   Web of Science ®Google Scholar
• Çinlar, E. (1972) Markov additive processes II. Z. Wahrscheinlichkeitstheorie verw. Geb., 24(2), 95–121.
   Web of Science ®Google Scholar
• Çinlar, E. (1977) Shock and wear models and Markov additive processes, in The Theory and Applications of Reliability, Shimi, I.N. and Tsokos, C.P. (eds), Academic Press, New York, NY, pp. 193–214.
   Google Scholar
• Cox, D.R. (1972) Regression models and life-tables. Journal of the Royal Statistical Society. Series B (Methodological), 34(2), 187–220.
   Web of Science ®Google Scholar
• Doksum, K.A. and Hóyland, A. (1992) Models for variable-stress accelerated life testing experiments based on Wiener processes and the inverse Gaussian distribution. Technometrics, 34(1), 74–82.
   Web of Science ®Google Scholar
• Esary, J.D., Marshall, A.W. and Prochan, F. (1973) Shock models and wear processes. Annals of Probability, 1(4), 627–649.
   Web of Science ®Google Scholar
• Feldman, R.M. (1976) Optimal replacement with semi-Markov shock models. Journal of Applied Probability, 13(1), 108–117.
   Web of Science ®Google Scholar
• Gamerman, D. (1991) Dynamic Bayesian models for survival data. Applied Statistics, 40(1), 63–79.
   Web of Science ®Google Scholar
• Gebraeel, N. (2006) Sensory-updated residual life distributions for components with exponential degradation patterns. IEEE Transactions on Automation Science and Engineering, 3(4), 382–393.
   Web of Science ®Google Scholar
• Gebraeel, N., Lawley, M.A., Li, R. and Ryan, J.K. (2005) Residual-life distributions from component degradation signals: a Bayesian approach. IIE Transactions, 37(6), 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(4), 539–550.
   Web of Science ®Google Scholar
• Gelfand, A.E. and Smith, A.F.M. (1990) Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85(410), 398–409.
   Web of Science ®Google Scholar
• Ghasemi, A., Yacout, S. and Ouali, M.S. (2010) Evaluating the reliability function and the mean residual life for equipment with unobservable states. IEEE Transactions on Reliability, 59(1), 45–54.
   Web of Science ®Google Scholar
• Hahn, M., Frühwirth-Schnatter, S. and Sass, J. (2010) Markov chain Monte Carlo methods for parameter estimation in multidimension continuous time switching diffusion models. Journal of Financial Econometrics, 8(1), 88–121.
   Web of Science ®Google Scholar
• Hahn, M. and Sass, J. (2009) Parameter estimation in continuous-time Markov switching models: a semi-continuous Markov chain Monte Carlo approach. Bayesian Analysis, 4(1), 63–84.
   Web of Science ®Google Scholar
• Igaki, N., Sumita, U. and Kowada, M. (1995) Analysis of Markov renewal shock models. Journal of Applied Probability, 32(3), 821–831.
   Web of Science ®Google Scholar
• Jardine, A.K.S., Banjevic, D. and Makis, V. (1997) Optimal replacement policy and the structure of software for condition-based maintenance. Journal of Quality in Maintenance Engineering, 3(2), 109–119.
   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(6), 533–542.
   Web of Science ®Google Scholar
• Kharoufeh, J.P., Finkelstein, D.E. and Mixon, D.G. (2006) Availability of periodically inspected systems with Markovian wear and shocks. Journal of Applied Probability, 43(2), 303–317.
   Web of Science ®Google Scholar
• Kharoufeh, J.P. and Mixon, D.G. (2009) On a Markov-modulated shock and wear process. Naval Research Logistics, 56(6), 563–576.
   Web of Science ®Google Scholar
• Kharoufeh, J.P., Solo, C.J. and Ulukus, M.Y. (2010) Semi-Markov models for degradation-based reliability. IIE Transactions, 42(8), 599–612.
   Web of Science ®Google Scholar
• Lee, M.L.T. and Whitmore, G.A. (2010) Proportional hazards and threshold regression: their theoretical and practical connections. Lifetime Data Analysis, 16(2), 196–214.
   PubMed Web of Science ®Google Scholar
• Lee, M.L.T., Whitmore, G.A., Laden, F., Hart, J.E. and Garshick, E. (2004) Assessing lung cancer risk in railroad workers using a first hitting time regression model. Environmetrics, 15(5), 501–512.
   PubMed Web of Science ®Google Scholar
• Leichty, J. and Roberts, G. (2001) Markov chain Monte Carlo methods for switching diffusion models. Biometrika, 88(2), 299–315.
   Web of Science ®Google Scholar
• Lemoine, A.J. and Wenocur, M.L. (1986) A note on shot-noise and reliability modeling. Operations Research, 34(2), 320–323.
   Web of Science ®Google Scholar
• Liao, C.M. and Tseng, S.T. (2006) Optimal design for step-stress accelerated degradation tests. IEEE Transactions on Reliability, 55(1), 59–66.
   Web of Science ®Google Scholar
• Liao, H. and Elsayed, E.A. (2006) Reliability inference for field conditions from accelerated degradation testing. Naval Research Logistics, 53(6), 576–587.
   Web of Science ®Google Scholar
• Liao, H. and Tian, Z. (2013) A framework for predicting the remaining useful life of a single unit under time-varying operating conditions. IIE Transactions, 45(9), 964–980.
   Web of Science ®Google Scholar
• Liao, H., Zhao, W. and Guo, H. (2006) Predicting remaining useful life of an individual unit using proportional hazards model and logistic regression model, in Proceedings of annual Reliability and Maintainability Symposium, pp. 127–132.
   Google Scholar
• Myers, L.E. (1981) Survival functions induced by stochastic covariate processes. Journal of Applied Probability, 18(2), 523–529.
   Web of Science ®Google Scholar
• Özekici, S. and Soyer, R. (2003) Bayesian analysis of Markov modulated Bernoulli processes. Mathemathical Methods of Operations Research, 57(1), 125–140.
   Web of Science ®Google Scholar
• Schijve, J. (2009) Fatigue of Structures and Materials, Springer, New York, NY.
   Google Scholar
• Schwartz, G. (1978) Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464.
   Web of Science ®Google Scholar
• Si, X.S., Wang, W., Hu, C.H. and Zhou, D.H. (2011) Remaining useful life estimation: A review on the statistical data driven approaches. European Journal of Operational Research, 213(1), 1–14.
   Web of Science ®Google Scholar
• Singpurwalla, N.D. (1995) Survival in dynamic environments. Statistical Science, 10(1), 86–103.
   Web of Science ®Google Scholar
• Sun, Y., Ma, L., Mathew, J., Wang, W. and Zhang, S. (2006) Mechanical systems hazard estimation using condition monitoring. Mechanical Systems and Signal Processing, 20(5), 1189–1201.
   Web of Science ®Google Scholar
• Sutherland, H.J. and Burwinkle, D.P. (1995) The spectral content of the torque loads on a turbine gear tooth. Wind Energy, 16(1), 91–97.
   Google Scholar
• Tseng, S.T., Balakrishnan, N. and Tsai, C.C. (2009) Optimal step-stress accelerated degradation test plan for Gamma degradation processes. IEEE Transactions on Reliability, 58(4), 611–618.
   Web of Science ®Google Scholar
• Virkler, D.A., Hilberry, B.M. and Goel, P.K. (1979) The statistical nature of fatigue crack propagation. ASME Journal of Engineering Materials and Technology, 101(2), 148–153.
   Web of Science ®Google Scholar
• Vlok, P.J., Wnek, M. and Zygmunt, M. (2004) Utilising statistical residual life estimates of bearings to quantify the influence of preventive maintenance actions. Mechanical Systems and Signal Processing, 18(4), 833–847.
   Web of Science ®Google Scholar
• Whitmore, G.A. and Schenkelberg, F. (1997) Modelling accelerated degradation data using Wiener diffusion with a time scale transformation. Lifetime Data Analysis, 3(1), 27–45.
   PubMedGoogle Scholar
• You, M.Y., Li, L., Meng, G. and Ni, J. (2010) Two-zone proportional hazard model for equipment remaining useful life prediction. Journal of Manufacturing Science and Engineering, 132(4), 041008–1–041008–6.
   Web of Science ®Google Scholar
• Zhao, X., Fouladirad, M., Bérenguer, C. and Bordes, L. (2010) Condition-based inspection/replacement policies for non-monotone deteriorating systems with environmental covariates. Reliability Engineering and System Safety, 95(8), 921–934.
   Web of Science ®Google Scholar