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Optimal replacement policies for two-unit machines with increasing running costs 1

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  • Berg, Menachem

Abstract

A machine consists of two stochastically failing units. Failure of either of the units causes a failure of the machine and the failed unit has to be replaced immediately. Associated with the units are running costs which increase with the age of the unit because of increasing maintenance costs, decreasing output, etc. A preventive replacement policy is proposed under which, at failure points, we also replace the second unit if its age exceeds a predetermined control limit. It is proved that, for two identical units with exponential life-time distributions and linear running costs, this policy is optimal and the optimal control limit is calculated. In an additional model we take into consideration the length of time it takes to replace one unit or both units. The method of solution is a variation of dynamic semi-Markov programming. Analytical results are obtained and the influence of the various parameters on them is investigated. Finally, we study the saving due to our policy in comparison with a policy in which only failed units are replaced.

Suggested Citation

  • Berg, Menachem, 1976. "Optimal replacement policies for two-unit machines with increasing running costs 1," Stochastic Processes and their Applications, Elsevier, vol. 4(1), pages 89-106, January.
    • Handle: RePEc:eee:spapps:v:4:y:1976:i:1:p:89-106
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    Cited by:

    1. Najafi, Seyedvahid & Zheng, Rui & Lee, Chi-Guhn, 2021. "An optimal opportunistic maintenance policy for a two-unit series system with general repair using proportional hazards models," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    2. Lirong Cui & Haijun Li, 2006. "Opportunistic Maintenance for Multi-component Shock Models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 493-511, July.
    3. Rommert Dekker & Ralph Wildeman & Frank Duyn Schouten, 1997. "A review of multi-component maintenance models with economic dependence," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(3), pages 411-435, October.
    4. Wang, Hongzhou, 2002. "A survey of maintenance policies of deteriorating systems," European Journal of Operational Research, Elsevier, vol. 139(3), pages 469-489, June.
    5. Chunhui Guo & Chuan Lyu & Jiayu Chen & Dong Zhou, 2018. "A multi-event combination maintenance model based on event correlation," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-24, November.

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