On some general survival models with delayed failures

References

• A-Hameed, M. S., and F. Proschan. 1973. Nonstationary shock models. Stochastic Processes and Their Applications 1 (4):383–404. doi:10.1016/0304-4149(73)90019-7.
   Google Scholar
• Asfaw, Z. G., and B. H. Lindqvist. 2015. Extending minimal repair models for repairable systems: A comparison of dynamic and heterogeneous extensions of a nonhomogeneous Poisson process. Reliability Engineering & System Safety 140:53–158. doi:10.1016/j.ress.2015.03.025.
   Web of Science ®Google Scholar
• Aven, T., and U. Jensen. 1999. Stochastic models in reliability. New York: Springer.
   Google Scholar
• Aven, T., and U. Jensen. 2000. A general minimal repair model. Journal of Applied Probability 37 (1):187–97. doi:10.1239/jap/1014842276.
   Web of Science ®Google Scholar
• Babykina, G., and V. Couallier. 2014. Modelling pipe failures in water distribution systems: Accounting for harmful repairs and a time-dependent covariate. International Journal of Performability Engineering 10:31–42.
   Google Scholar
• Barbu, V. S., and N. Limnios. 2008. Semi-Markov chains and hidden semi-Markov models toward applications (Their use in reliability and DNA analysis). New York: Springer.
   Google Scholar
• Castro, I. T., N. C. Caballe, and C. J. Perez. 2015. A condition-based maintenance for a system subject to multiple degradation processes and external shocks. International Journal of Systems Science 46 (9):1692–704. doi:10.1080/00207721.2013.828796.
   Web of Science ®Google Scholar
• Cha, J. H. 2014. Characterization of the generalized Polya process and its applications. Advances in Applied Probability 46 (4):1148–71. doi:10.1239/aap/1418396247.
   Web of Science ®Google Scholar
• Cha, J. H., and M. Finkelstein. 2009. On a terminating shock process with independent wear increments. Journal of Applied Probability 46 (2):353–62. doi:10.1239/jap/1245676092.
   Web of Science ®Google Scholar
• Cha, J. H., and M. Finkelstein. 2011. On new classes of extreme shock models and some generalizations. Journal of Applied Probability 48 (1):258–70. doi:10.1239/jap/1300198148.
   Web of Science ®Google Scholar
• Cha, J. H., and M. Finkelstein. 2012. Stochastic survival models with events triggered by external shocks. Probability in the Engineering and Informational Sciences 26 (2):183–95. doi:10.1017/S0269964811000325.
   Web of Science ®Google Scholar
• Cha, J. H., and M. Finkelstein. 2018a. Point processes for reliability analysis. Shocks and repairable systems. London: Springer.
   Google Scholar
• Cha, J. H., and M. Finkelstein. 2018b. On information-based residual lifetime in survival models with delayed failures. Statistics & Probability Letters 137:209–16. doi:10.1016/j.spl.2018.01.028.
   Web of Science ®Google Scholar
• Cui, L., and H. Li. 2006. Opportunistic maintenance for multi-component shock models. Mathematical Methods of Operations Research 63 (3):493–511. doi:10.1007/s00186-005-0058-9.
   Web of Science ®Google Scholar
• Cui, L., and H. Li. 2007. Analytical method for reliability and MTTF assessment of coherent systems with dependent components. Reliability Engineering & System Safety 92 (3):300–307. doi:10.1016/j.ress.2006.04.005.
   Web of Science ®Google Scholar
• Cui, L., Z. Chen, and H. Gao. 2018. Reliability for systems with self-healing effect under shock models. Quality Technology & Quantitative Management 15 (5):551–67. doi:10.1080/16843703.2016.1264146.
   Web of Science ®Google Scholar
• Esary, J. D., A. W. Marshal, and F. Proschan. 1973. Shock models and wear processes. The Annals of Probability 1 (4):627–49. doi:10.1214/aop/1176996891.
   Web of Science ®Google Scholar
• Eryilmaz, S., and F. Yalcin. 2011. On the mean and extreme distances between failures in Markovian binary sequences. Journal of Computational and Applied Mathematics 236:1502–10.
   Web of Science ®Google Scholar
• Eryilmaz, S. 2015. Assessment of a multi-state system under a shock model. Applied Mathematics and Computation 269:1–8. doi:10.1016/j.amc.2015.06.129.
   Web of Science ®Google Scholar
• Finkelstein, M. 2008. Failure rate modelling for reliability and risk. London: Springer.
   Google Scholar
• Finkelstein, M., and J. H. Cha. 2013. Stochastic modelling for reliability. Shocks, burn-in and heterogeneous populations. London: Springer.
   Google Scholar
• Guo, L., D. Landriault, and G. E. Willmot. 2013. On the analysis of a class of loss models incorporating time dependence. European Actuarial Journal 3 (1):273–94. doi:10.1007/s13385-013-0064-x.
   Google Scholar
• Huynh, K. T., I. T. Castro, A. Barros, and C. Bérenguer. 2012. Modeling age-based maintenance strategies with minimal repairs for systems subject to competing failure modes due to degradation and shocks. European Journal of Operational Research 218 (1):140–51. doi:10.1016/j.ejor.2011.10.025.
   Web of Science ®Google Scholar
• Lemoine, A. J., and M. L. Wenocur. 1986. A note on shot-noise and reliability modeling. Operations Research 34 (2):320–23. doi:10.1287/opre.34.2.320.
   Web of Science ®Google Scholar
• Le Gat, Y. 2014. Extending the Yule process to model recurrent pipe failures in water supply networks. Urban Water Journal. 11 (8):617–30. doi:10.1080/1573062X.2013.783088.
   Web of Science ®Google Scholar
• Limnios, N., and G. Oprişan. 2001. Semi-Markov processes and reliability. Birkhüauser, Boston.
   Google Scholar
• Montoro-Cazorla, D., and R. Pérez-Ocón. 2012. Shock and wear degradating systems under three types of repair. Applied Mathematics and Computation 218 (24):11727–37. doi:10.1016/j.amc.2012.05.053.
   Web of Science ®Google Scholar
• Montoro-Cazorla, D., and R. Pérez-Ocón. 2015. A shock and wear model with dependence between the interarrival failures. Applied Mathematics and Computation 259:339–52. doi:10.1016/j.amc.2015.02.005.
   Web of Science ®Google Scholar
• Neuts, M. F., and M. C. Bhattacharjee. 1981. Shock models with phase type survival and shock resistance. Naval Research Logistics Quarterly 28 (2):213–19. doi:10.1002/nav.3800280204.
   Google Scholar
• Sheu, S. H., and W. S. Griffith. 1996. Optimal number of minimal repairs before replacement of a system subject to shocks. Naval Research Logistics 43 (3):319–33. doi:10.1002/(SICI)1520-6750(199604)43:3<319::AID-NAV1>3.0.CO;2-C.
   Web of Science ®Google Scholar
• Wu, Q. 2012. Reliability analysis of a cold standby system attacked by shocks. Applied Mathematics and Computation 218 (23):11654–73. doi:10.1016/j.amc.2012.05.051.
   Web of Science ®Google Scholar
• Wu, Q., and S. Wu. 2011. Reliability analysis of two-unit cold standby repairable systems under Poisson shocks. Applied Mathematics and Computation 218 (1):171–82. doi:10.1016/j.amc.2011.05.089.
   Web of Science ®Google Scholar
• Zuckerman, D. 1980. A note on the optimal replacement time of damaged devices. Naval Research Logistics Quarterly 27 (3):521–24. doi:10.1002/nav.3800270315.
   Google Scholar