References
- Abate, J. and Whitt, W. (1995) Numerical inversion of Laplace transforms of probability distributions. ORSA Journal on Computing, 7, 36–43.
- Abdel-Hameed, M. and Proschan, F. (1973) Nonstationary shock models. Stochastic Processes and Their Applications, 1(4), 383–404.
- Bae, S. and Kvam, P. (2004) A nonlinear random-coefficients model for degradation testing. Technometrics, 46(4), 460–469.
- Bian, L. and Gebraeel, N. (2011) A stochastic methodology for prognostics under time-varying environmental future profiles, in Proceedings of the 2011 Conference on Intelligent Data Understanding, NASA, Mountain View, CA.
- Bian, L. and Gebraeel, N. (2013) Stochastic methodology for prognostics under continuously varying environmental profiles. Statistical Analysis and Data Mining, 6(3), 260–270.
- Billingsley, P. (1961) Statistical Inference for Markov Processes, University of Chicago Press, Chicago, IL.
- Bu, S., Yu, F. and Liu, P. (2011) Stochastic unit commitment in smart grid communications, in IEEE INFOCOM 2011 Workshop on Green Communications and Networking, IEEE Press, Piscataway, NJ, pp. 307–312.
- Cha, J. and Mi, J. (2007) Study of a stochastic failure model in a random environment. Journal of Applied Probability, 44(1), 151–163.
- Çinlar, E. (1977) Shock and wear models and Markov additive processes, in Theory and Applications of Reliability, Shimi, I. and Tsokos, C. (eds), Academic Press, New York, NY, pp. 193–214.
- Cox, D. (1972) Regression models and life-tables. Journal of the Royal Statistical Society. Series B (Methodological), 34(2), 187–220.
- Doksum, K. 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.
- Esary, J. and Marshall, A. (1973) Shock models and wear processes. The Annals of Probability, 1(4), 627–649.
- Flory, J., Kharoufeh, J. and Gebraeel, N. (2014) A switching diffusion model for lifetime estimation in randomly-varying environments. IIE Transactions, 46(11), 1227–1241.
- Gebraeel, N., Lawley, M., Li, R. and Ryan, J. (2005) Residual-life distributions from component degradation signals: a Bayesian approach. IIE Transactions, 37(6), 543–557.
- 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.
- Ghasemi, A., Yacout, S. and Ouali, M. (2010) Evaluating the reliability function and the mean residual life for equipment with unobservable states. IEEE Transactions on Reliability, 59(1), 45–54.
- Harris, T. (2001) Rolling Bearing Analysis fourth edition, John Wiley & Sons, Inc., New York, NY.
- Igaki, N., Sumita, U. and Kowada, M. (1995) Analysis of Markov renewal shock models. Journal of Applied Probability, 32(3), 821–831.
- Jardine, A., 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.
- Kharoufeh, J. (2003) Explicit results for wear processes in a Markovian environment. Operations Research Letters, 31(3), 237–244.
- Kharoufeh, J. and Cox, S. (2005) Stochastic models for degradation-based reliability. IIE Transactions, 37(6), 533–542.
- Kharoufeh, J., Solo, C. and Ulukus, M. (2010) Semi-Markov models for degradation-based reliability. IIE Transactions, 42(8), 599–612.
- Kiessler, P., Klutke, G. and Yang, Y. (2002) Availability of periodically inspected systems subject to Markovian degradation. Journal of Applied Probability, 39(4), 700–711.
- Kulkarni, V. (1995) Modeling and Analysis of Stochastic Systems, Chapman and Hall/CRC, New York, NY.
- Lee, M., Whitmore, G., Laden, F., Hart, J. and Garshick, E. (2004) Assessing lung cancer risk in railroad workers using a first hitting time regression model. Environmetrics, 15(5), 501–512.
- Liao, C. and Tseng, S. (2006) Optimal design for step-stress accelerated degradation tests. IEEE Transactions on Reliability, 55(1), 59–66.
- 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.
- Meeker, W. and Escobar, L. (1998) Statistical Methods for Reliability Data, John Wiley & Sons, Inc., New York, NY.
- Özekici, S. (1995) Optimal maintenance policies in random environments. European Journal of Operational Research, 82(2), 283–294.
- Robinson, M. and Crowder, M. (2000) Bayesian methods for a growth-curve degradation model with repeated measures. Lifetime Data Analysis, 6(4), 357–374.
- Si, X., Wang, W., Hu, C. and Zhou, D. (2011) Remaining useful life estimation: a review on the statistical data driven approaches. European Journal of Operational Research, 213(1), 1–14.
- Siegmund, D. (1986) Boundary crossing probabilities and statistical applications. The Annals of Statistics, 14(2), 361–404.
- Teng, X. and Pham, H. (2006) A new methodology for predicting software reliability in the random field environments. IEEE Transactions on Reliability, 55(3), 458–468.
- Van Noortwijk, J. (2009) A survey of the application of Gamma processes in maintenance. Reliability Engineering and System Safety, 94(1), 2–21.
- Wang, L. and Potzelberger, K. (1997) Boundary crossing probability for Brownian motion and general boundaries. Journal of Applied Probability, 34(1), 54–65.
- Zhu, L., Yu, F., Ning, B. and Tang, T. (2011) Stochastic charging management for plug-in electric vehicles in smart microgrids fueled by renewable energy sources, in Proceedings of the IEEE Online Conference on Green Communications, IEEE Press, Piscataway, NJ, pp. 7–12.