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Optimal threshold value of failure-rate for leased products with preventive maintenance actions. (English) Zbl 1127.90019

Summary: This paper investigates the optimal threshold value of failure rates for leased products with a Weibull lifetime distribution. Within a lease period, any product failure is rectified by minimal repairs and the lessor may incur a penalty when the time required to perform a minimal repair exceeds a reasonable time limit. To reduce product failures, additional preventive maintenance actions are carried out when the failure rate reaches a threshold value. Under this maintenance scheme, a mathematical model of the expected total cost is established. Based on the model, the optimal threshold value and the corresponding maintenance degrees are derived such that the expected total cost is minimized. The structural properties of the optimal policy are investigated and an efficient algorithm is provided to search for the optimal policy. Finally, numerical examples are given to illustrate the features of the optimal policy.

MSC:

90B25 Reliability, availability, maintenance, inspection in operations research
60K05 Renewal theory
60K10 Applications of renewal theory (reliability, demand theory, etc.)
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References:

[1] Desai, P.; Purohit, D., Leasing and selling: Optimal marketing strategies for a durable goods firm, Management Science, 44, 19-34 (1998) · Zbl 0989.90533
[2] Barlow, R. E.; Hunter, L. C., Optimum preventive maintenance policies, Operations Research, 8, 90-100 (1960) · Zbl 0095.34304
[3] Chun, Y. H., Optimum number of periodic preventive maintenance operations under warranty, Reliability Engineering and System Safety, 37, 223-225 (1992)
[4] Jack, N.; Dagpunar, J. S., An optimal imperfect maintenance policy over a warranty period, Microelectronics and reliability, 34, 529-534 (1994)
[5] Yeh, R. H.; Lo, H. C., Optimal preventive-maintenance warranty policy for repairable products, European Journal of Operational Research, 134, 59-69 (2001) · Zbl 0978.90036
[6] Nakagawa, T., A summary of periodic replacement with minimal repair at failure, Journal of the Operations Research Society of Japan, 24, 213-227 (1981) · Zbl 0471.90055
[7] Nakagawa, T.; Kowada, M., Analysis of a system with minimal repair and its application to replacement policy, European Journal of Operational Research, 12, 176-182 (1983) · Zbl 0499.90034
[8] Boland, P. J.; Proschan, F., Periodic replacement with increasing minimal repair costs at failure, Operations Research, 30, 1183-1189 (1982) · Zbl 0514.90032
[9] Sheu, S. H., Periodic replacement with minimal repair at failure and general random repair cost for a multi-unit system, Microelectronics Reliability, 31, 1019-1025 (1991)
[10] Nakagawa, T., Imperfect preventive-maintenance, Journal of the Operations Research Society of Japan, 24, 213-227 (1979) · Zbl 0421.90033
[11] Pham, H.; Wang, H., Imperfect maintenance, European Journal of Operational Research, 94, 425-438 (1996) · Zbl 0953.90506
[12] Chan, J. K.; Shaw, L., Modeling repairable systems with failure rates dependent on age and maintenance, IEEE Transactions on Reliability, 42, 566-570 (1993)
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