Comparison of Three Cumulative Damage Models

References

• Abdel-Hameed, M. (1999). Applications of Semi-Markov processed in reliability and maintenance. The Netherlands, eds. J. Jenssen and N. Limnios Semi-Markov Models and Applications. Kluwer Academic, 337–348.
   Google Scholar
• Abdel-Hameed, M. and Nakhi, Y (1991). Optimal replacement and maintenance of systems subject to Semi-Markov damage. Stochastic Processes and Their Applications, 37, 141–160.
   Google Scholar
• Abedel-Hameed, M. and Shimi, I. N. (1978). Optimal replacement of damaged devices. Journal of Applied Probability, 15, 153–161.
   Google Scholar
• Aven, T. (1996). Condition based replacement policies: A counting process approach. Reliability Engineering and System Safety, 51, 275–281.
   Google Scholar
• Aven, T. and Gaarder, S. (1987). Optimal replacement in a shock model: discrete time. Journal of Applied Probability, 24, 281–287.
   Google Scholar
• Barlow, R. E. and Proschan, F. (1965). Mathematical Theory of Reliability. John Wiley & Sons, New York.
   Google Scholar
• Bergman, B. (1978). Optimal replacement under a general failure model. Journal of Applied Probability, 10, 431–451.
   Google Scholar
• Bogdanoff, J. L. and Kozin, F. (1985). Probabilistic Models of Cumulative Damage. John Wiley & Sons, New York.
   Google Scholar
• Chikte, S. D. and Deshmukh, S. D. (1981). Preventive maintenance and replacement under additive damage. Naval Research Logistics Quarterly, 28, 33–46.
   Google Scholar
• Cinlar, E. (1975). Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ.
   Google Scholar
• Cox, D. R. (1962). Renewal Theory. Methuen, London.
   Google Scholar
• Esary, J. D., Marshall, A. W. and Proschan, F. (1973). Shock models and wear processes, Annals of Probability, 1, 627–649.
   Google Scholar
• Feldman, R. M. (1976). Optimal replacement with Semi-Markov shock models. Journal of Applied Probability, 13, 108–117.
   Google Scholar
• Feldman, R. M. (1977). Optimal replacement for systems governed by Markov additive shock processes. The Annals of Probability, 5, 413–429.
   Google Scholar
• Feldman, R. M. (1977). Optimal replacement with Semi-Markov shock models using discounted costs. Mathematics of Operations Research, 2, 78–90.
   Google Scholar
• Feldman, R. M. and Joo, N. Y. (1985). A state-age dependent policy for a shock process. Stochastic Models, 1, 53–76.
   Google Scholar
• Feng, W., Adachi, K. and Kowada, M. (1994). Dynamically optimal replacement policy for a shock model in a Markov random environment. Journal of Operations Research Society of Japan, 37, 255–270.
   Google Scholar
• Gottlieb, G. (1982). Optimal replacement for shock models with general failure rate. Operations Research, 30, 82–92.
   Google Scholar
• Gottlieb, G. and Levikson, B. (1984). Optimal replacement for self-repairing shock models with general failure rate. Journal of Applied Probability, 21, 108–119.
   Google Scholar
• Hisano, K. (2000). Preventive maintenance and residual life evaluation technique for power plant (I.Preventive Maintenance) (in Japanese). The Thermal and Nuclear Power, 51(4), 491–517.
   Google Scholar
• Hisano, K. (2000). Preventive maintenance and residual life evaluation technique for power plant (I.Preventive Maintenance) (in Japanese). The Thermal and Nuclear Power, 51(8), 81–101.
   Google Scholar
• Klutke, G. A. and Yang, Y. J. (2002). The availability of inspected systems subject to shocks and graceful degradation. IEEE Transactions on Reliability, 51, 371–374.
   Google Scholar
• Kuroishi, T., Minami, Y., Kobayashi, Y., Yokoyama, T., Hasegawa, Y. and Minatomoto, M. (2003). Power systems: A portal to customer services for electric power generation. Mitsubishi Heavy Industries, LTD. Technical Review, 40(2), 86–91.
   Google Scholar
• Lam, C. T. and Yeh, R. H. (1994). Optimal replacement policies for multi-state deteriorating systems. Naval Research Logistics, 41, 303–315.
   Google Scholar
• Li, W. J. and Pham, H. (2005). Reliability modeling of multi-state degraded systems with multi-competing failure and random shocks. IEEE Transactions on Reliability, 54, 297–303.
   Google Scholar
• Li, Z., Chan, L. Y. and Yuan, Z. (1999). Failure time distribution under a £-shock model and its application economic design of systems. International Journal of Reliability, Quality and Safety Engineering, 6, 237–247.
   Google Scholar
• Mizuno, N. (1986). Generalized mathematical programming for optimal replacement in a Semi-Markov shock model. Operations Research, 34, 790–795.
   Google Scholar
• Nakagawa, T. (1980) A summary of imperfect preventive maintenance policies with minimal repair, RAIRo Operations Research, 14, 249–255.
   Google Scholar
• Nakagawa, T. (2007). Shock and Damage Models in Reliability Theory. Springer Verlag, London.
   Google Scholar
• Nakagawa, T. and Osaki, S. (1974). Some aspects of damage model. Microelectronics and Reliability, 13, 253–257.
   Google Scholar
• Perry, D. (2000). Control limit policies in a replacement model with additive phase-type distributed damage and linear restoration. Operations Research Letters, 27, 127–134.
   Google Scholar
• Perry, D. and Posner, M. J. M. (1991). Determining the control limit policy in a replacement model with restoration. Operations Research Letters, 10, 335–341.
   Google Scholar
• Posner, M. J. M. and Zuckerman, D. (1984). A replacement model for an additive damage model with restoration. Operations Research Letters, 3, 141–148.
   Google Scholar
• Posner, M. J. M. and Zuckerman, D. (1986). Semi-Markov shock models with additive damage. Advances in Applied Probability, 18, 772–790.
   Google Scholar
• Ross, S. M. (1983). Stochastic Processes. John Wiley & Sons, New York.
   Google Scholar
• Sheu, S. H. (1997). Extend block replacement policy of a system subject to shocks. IEEE Transactions on Reliability, 46, 375–382.
   Google Scholar
• Sheu, S. H. (1998). A generalized age and block replacement of a system subject to Shocks. Europian Journal of Operational Research, 108, 345–362.
   Google Scholar
• Sheu, S. H. and Chien, Y. H. (2004). Optimal age-replacement policy of a system subject to shocks with random lead-time. European Journal of Operational Research, 159, 132–144.
   Google Scholar
• Sheu, S. H. and Griffith, W. S. (1996). Optimal Number of Minimal Repairs before Replacement of a System Subject to Shocks. Naval Research Logistics, 43, 319–333.
   Google Scholar
• Sheu, S. H. and Griffith, W. S. (2002). Extend block replacement policy with shock models and used items. European Journal of Operational Research, 140, 50–60.
   Google Scholar
• Tang, Y. Y. and Lam, Y. (2006). A £-shock maintenance model for a deterioration system. European Journal of Operational Research, 168, 541–556.
   Google Scholar
• Taylor, H. M. (1975). Optimal replacement under additive damage and other failure models. Naval Research Logistics, 22, 1–18.
   Google Scholar
• Waldmann, K. H. (1983). Optimal replacement under additive damage in randomly varying environments. Naval Research Logistics (Quarterly, 30, 377–386.
   Google Scholar
• Wang, G. J. and Zhang, Y. L. (2005). A shock model with two-type failures and optimal replacement policy. International Journal of Systems Science, 36, 209–214.
   Google Scholar
• Wortman, M. A., Klutke, G. A. and Ayhan, H. (1994). A maintenance strategy for systems subjected to deterioration governed by random shocks. IEEE Transactions on Reliability, 43, 439–445.
   Google Scholar
• Yamada, K. (1980). Explicit formula of optimal replacement under additive shock Processes. Stochastic Processes and Their Applications, 9, 193–208.
   Google Scholar
• Zuckerman, D. (1977). Replacement models under additive damage. Naval Research Logistics Quarterly, 24, 549–558.
   Google Scholar
• Zuckerman, D. (1978). Optimal replacement policy for the case where the damage process is a one-sided Levy Process. Stochastic Processes and Their Applications, 7, 141–151.
   Google Scholar
• Zuckerman, D. (1978). Optimal stopping in a Semi-Markov shock model. Journal of Applied Probability, 15, 629–734.
   Google Scholar
• Zuckerman, D. (1980). A note on the optimal replacement time of damaged devices. Naval Research Logistics Quarterly, 27, 521–524.
   Google Scholar
• Zuckerman, D. (1980). Optimal replacement under additive damage and self-restoration. RAIRO Operations Research, 14, 115–127.
   Google Scholar