Abstract
This chapter summarizes concisely optimum maintenance policies for reliability models without detailed mathematical explanations: First, standard replacement models such as age, block, and periodic replacements are taken up, and are converted to modified models with finite operating times and random replacement times. Furthermore, replacement policies for inspection models, cumulative damage models, and a parallel system are proposed. Secondly, preventive maintenances (PMs) of one-unit and two-unit systems are discussed. Modified models with periodic PM times, imperfect PM, and repair limit are proposed. Optimum policies that minimize the expected costs or maximize availabilities are summarized. Finally, as applications of maintenance models, optimum policies for computer systems with intermittent faults, imperfect maintenance, and restart are discussed. These results should be very helpful in applications of maintenance models and studies of reliability theory.
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References
Barlow RE, Proschan F. Mathematical theory of reliability. Wiley, New York, 1965.
Nakagawa T. Maintenance theory of reliability. Springer, London, 2005.
Barlow RE, Proschan F. Statistical theory of reliability and life testing probability models. Holt, Rinehart and Winston, New York, 1975.
Gertsbakh I. Models of preventive maintenance. North-Holland, Amsterdam, 1997.
Osaki S, Nakagawa T. Bibliography for reliability and availability of stochastic systems. IEEE Transactions on Reliability 1976; R-25:284–287.
Pierskalla WP, Voelker JA. A survey of maintenance models: The control and surveillance of deteriorating systems. Naval Research Logistics 1976; Q 23:353–388.
Sherif YS, Smith ML. Optimal maintenance models for systems subject to failure — A review. Naval Research Logistics 1981; Q 28:47–74.
Thomas LC. A survey of maintenance and replacement models for maintainability and reliability of multi-item systems. Reliability Engineering 1986; 16: 297–309.
Valdez-Fores C, Feldman RM. A survey of preventive maintenance models for stochastically deteriorating single-unit system. Naval Research Logistics 1989; Q 36: 419–446.
Cho DI, Parlar M. A survey of maintenance models for multi-unit systems. European Journal of Operational Research 1991; 51:1–23.
Dekker R. Applications of maintenance optimization models: A review and analysis. Reliability Engineering and System Safety 1996; 51: 229–240.
Wang H. A survey of maintenance policies of deteriorating systems. European Journal of Operational Research 2002; 139:469–489.
Ozekici S (editor). Reliability and maintenance of complex systems. Springer, Berlin, 1996.
Ben-Daya M, Duffuaa SO, Raouf A. (editors). Maintenance, modeling and optimization. Kluwer, Boston, 2000.
Rahin MA, Ben-Daya M. Integrated models in production planning, inventory, quality, and maintenance. Kluwer, Boston, 2001.
Osaki S (editor). Stochastic models in reliability and maintenance. Springer, Berlin, 2002.
Pham H. Handbook of reliability engineering. Springer, London, 2003.
Jensen U. Stochastic models of reliability and maintenance: An overview. In: Ozekici S, editor. Reliability and maintenance of complex systems. Springer, Berlin, 1996; 3–36.
Ben-Daya M, Duffuaa SO. Maintenance modeling areas. In: Ben-Daya M, Duffuaa SO, Raouf A, editors Maintenance, modeling and optimization. Kluwer, Boston, 2000; 3–35.
Kaio N, Dohi T, Osaki S. Classical maintenance models. In: Osaki S, editor. Stochastic models in reliability and maintenance. Springer, Berlin, 2002; 65–87.
Nakagawa T. Maintenance and optimum policy. In: Pham H, editors Handbook of reliability engineering. Springer, London, 367–395.
Wang H, Pham H. Reliability and optimal maintenance. Springer, London, 2006.
Nakagawa T, Mizutani S. A summary of maintenance policies for a finite interval. To appear in Reliability Engineering and System Safety. 2008.
Nakagawa T. Shock and damage models in reliability theory. Springer, London, 2007.
Nakagawa T. Two-unit redundant model. In: Osaki S, editor. Stochastic models in reliability and maintenance. Springer, Berlin, 2002.
Nakagawa T. Modified discrete preventive maintenance policies. Naval Research Logistics 1986;Q 33:703–715.
Nakagawa T. Periodic and sequential preventive maintenance policies. Journal of Applied Probability 1986; 23:536–542.
Nakagawa T. Imperfect preventive maintenance models. In: Osaki S, editor. Stochastic models in reliability and maintenance. Springer, Berlin 2002; 125–143.
Wang H., Pham H. Optimal imperfect maintenance models. In: H. Pham, editor. Handbook of reliability engineering. Springer, London 2003; 397–414.
Nakagawa T, Motoori M, Yasui K. Optimal testing policy for a computer system with intermittent faults. Reliability and Engineering System Safety 1990; 27: 213–218.
Nakagawa T, Yasui K. Optimal testing-policies for intermittent faults. IEEE Transactions on Reliability 1989; 38:577–580.
Nakagawa T, Nishi K, Yasui K. Optimum preventive maintenance policies for a computer system with restart. IEEE Transactions on Reliability 1984; R-33:272–276.
Nakagawa T, Yasui K. Optimum policies for a system with imperfect maintenance. IEEE Transactions on Reliability 1987; R-36:631–633
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Nakagawa, T. (2008). Replacement and Preventive Maintenance Models. In: Misra, K.B. (eds) Handbook of Performability Engineering. Springer, London. https://doi.org/10.1007/978-1-84800-131-2_49
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DOI: https://doi.org/10.1007/978-1-84800-131-2_49
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