Annals of Operations Research

, Volume 263, Issue 1–2, pp 271–310 | Cite as

Joint optimization of ordering and maintenance with condition monitoring data

Data Mining and Analytics


We study a single-unit deteriorating system under condition monitoring for which collected signals are only stochastically related to the actual level of degradation. Failure replacement is costlier than preventive replacement and there is a delay (lead time) between the initiation of the maintenance setup and the actual maintenance, which is closely related to the process of spare parts inventory and/or maintenance setup activities. We develop a dynamic control policy with a two-dimensional decision space, referred to as a warning-replacement policy, which jointly optimizes the replacement time and replacement setup initiation point (maintenance ordering time) using online condition monitoring data. The optimization criterion is the long-run expected average cost per unit of operation time. We develop the optimal structure of such a dynamic policy using a partially observable semi-Markov decision process and provide some important results with respect to optimality and monotone properties of the optimal policy. We also discuss how to find the optimal values of observation/inspection interval and lead time using historical condition monitoring data. Illustrative numerical examples are provided to show thatour joint policy outperforms conventional suboptimal policies commonly used in theliterature.


Real-time analytics Partially observable semi-Markov decision process Condition monitoring Deteriorating systems 


  1. Ahmad, R., & Kamaruddin, S. (2012). A review of condition-based maintenance decision-making. European Journal of Industrial Engineering, 6(5), 519–541.CrossRefGoogle Scholar
  2. Armstrong, M., & Atkins, D. (1996). Joint optimization of maintenance and inventory policies for a simple system. IIE Transactions (Institute of Industrial Engineers), 28(5), 415–424.Google Scholar
  3. Armstrong, M., & Atkins, D. (1998). A note on joint optimization of maintenance and inventory. IIE Transactions (Institute of Industrial Engineers), 30(2), 143–149.Google Scholar
  4. Aven, T., & Bergman, B. (1986). Optimal replacement times: A general set-up. Journal of Applied Probability, 23(2), 432–442.CrossRefGoogle Scholar
  5. Banjevic, D., & Jardine, A. K. S. (2006). Calculation of reliability function and remaining useful life for a markov failure time process. IMA Journal of Management Mathematics, 17(2), 115–130.CrossRefGoogle Scholar
  6. Banjevic, D., Jardine, A., Makis, V., & Ennis, M. (2001). A control-limit policy and software for condition-based maintenance optimization. INFOR, 39(1), 32–50.Google Scholar
  7. Bertsekas, D. P., & Tsitsiklis, J. N. (1996). Neuro-dynamic programming (1st ed.). Belmont: Athena Scientific.Google Scholar
  8. Brezavscek, A., & Hudoklin, A. (2003). Joint optimization of block-replacement and periodic-review spare-provisioning policy. IEEE Transactions on Reliability, 52(1), 112–117.CrossRefGoogle Scholar
  9. Chen, A., & Wu, G. (2007). Real-time health prognosis and dynamic preventive maintenance policy for equipment under aging markovian deterioration. International Journal of Production Research, 45(15), 3351–3379.CrossRefGoogle Scholar
  10. Dong, M., & He, D. (2007). Hidden semi-markov model-based methodology for multi-sensor equipment health diagnosis and prognosis. European Journal of Operational Research, 178(3), 858–878.CrossRefGoogle Scholar
  11. Elwany, A., & Gebraeel, N. (2008). Sensor-driven prognostic models for equipment replacement and spare parts inventory. IIE Transactions (Institute of Industrial Engineers), 40(7), 629–639.Google Scholar
  12. Ghasemi, A., Yacout, S., & Ouali, M. (2007). Optimal condition based maintenance with imperfect information and the proportional hazards model. International Journal of Production Research, 45(4), 989–1012.CrossRefGoogle Scholar
  13. Ghasemi, A., Yacout, S., & Ouali, M. S. (2010). Parameter estimation methods for condition-based maintenance with indirect observations. IEEE Transactions on Reliability, 59(2), 426–439.CrossRefGoogle Scholar
  14. Godoy, D., Pascual, R., & Knights, P. (2013). Critical spare parts ordering decisions using conditional reliability and stochastic lead time. Reliability Engineering and System Safety, 119, 199–206.CrossRefGoogle Scholar
  15. Hsu, B. M., & Shu, M. H. (2010). Reliability assessment and replacement for machine tools under wear deterioration. International Journal of Advanced Manufacturing Technology, 48(1–4), 355–365.CrossRefGoogle Scholar
  16. Ivy, J., & Pollock, S. (2005). Marginally monotonic maintenance policies for a multi-state deteriorating machine with probabilistic monitoring, and silent failures. IEEE Transactions on Reliability, 54(3), 489–497.CrossRefGoogle Scholar
  17. Jardine, A., Lin, D., & Banjevic, D. (2006). A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mechanical Systems and Signal Processing, 20(7), 1483–1510.CrossRefGoogle Scholar
  18. Kabir, A., & Farrash, S. (1996). Simulation of an integrated age replacement and spare provisioning policy using slam. Reliability Engineering and System Safety, 52(2), 129–138.CrossRefGoogle Scholar
  19. Kim, M., & Makis, V. (2013). Joint optimization of sampling and control of partially observable failing systems. Operations Research, 61(3), 777–790.CrossRefGoogle Scholar
  20. Kurt, M., & Kharoufeh, J. (2010). Monotone optimal replacement policies for a markovian deteriorating system in a controllable environment. Operations Research Letters, 38(4), 273–279.CrossRefGoogle Scholar
  21. Lam, C., & Yeh, R. (1994). Optimal replacement policies for multistate deteriorating systems. Naval Research Logistics, 41(3), 303–315.CrossRefGoogle Scholar
  22. Louit, D., Pascual, R., Banjevic, D., & Jardine, A. (2011). Condition-based spares ordering for critical components. Mechanical Systems and Signal Processing, 25(5), 1837–1848.CrossRefGoogle Scholar
  23. Maillart, L. (2006). Maintenance policies for systems with condition monitoring and obvious failures. IIE Transactions (Institute of Industrial Engineers), 38(6), 463–475.Google Scholar
  24. Makis, V., & Jardine, A. (1992). Optimal replacement in the proportional hazards model. INFOR, 30(1), 172183.Google Scholar
  25. Ohnishi, M., Morioka, T., & Ibaraki, T. (1994). Optimal minimal-repair and replacement problem of discrete-time markovian deterioration system under incomplete state information. Computers and Industrial Engineering, 27(1–4), 409–412.CrossRefGoogle Scholar
  26. Panagiotidou, S. (2014). Joint optimization of spare parts ordering and maintenance policies for multiple identical items subject to silent failures. European Journal of Operational Research, 235(1), 300–314.CrossRefGoogle Scholar
  27. Peng, Y., Dong, M., & Zuo, M. (2010). Current status of machine prognostics in condition-based maintenance: A review. International Journal of Advanced Manufacturing Technology, 50(1–4), 297–313.CrossRefGoogle Scholar
  28. Qian, X., & Wu, Y. (2014). Condition based maintenance optimization for the hydro generating unit with dynamic economic dependence. International Journal of Control and Automation, 7(3), 317–326.CrossRefGoogle Scholar
  29. Rosenfield, D. (1976). Markovian deterioration with uncertain information: A more general model. Naval Research Logistics, 23(3), 389–405.CrossRefGoogle Scholar
  30. Sun, J., Zuo, H., Wang, W., & Pecht, M. (2012). Application of a state space modeling technique to system prognostics based on a health index for condition-based maintenance. Mechanical Systems and Signal Processing, 28, 585–596.CrossRefGoogle Scholar
  31. Teng, H., Zhao, J., Jia, X., Jia, Y., Zhang, X., & Cai, L. (2011). Experimental study on gearbox prognosis using total life vibration analysis. In Proceedings of 2011 Prognostics and System Health Managment Conference (pp. 1–6).Google Scholar
  32. Van Horenbeek, A., Bur, J., Cattrysse, D., Pintelon, L., & Vansteenwegen, P. (2013). Joint maintenance and inventory optimization systems: A review. International Journal of Production Economics, 143(2), 499–508.CrossRefGoogle Scholar
  33. Wang, L., Chu, J., & Mao, W. (2008a). A condition-based order-replacement policy for a single-unit system. Applied Mathematical Modelling, 32(11), 2274–2289.CrossRefGoogle Scholar
  34. Wang, L., Chu, J., & Mao, W. (2008b). An optimum condition-based replacement and spare provisioning policy based on markov chains. Journal of Quality in Maintenance Engineering, 14(4), 387–401.CrossRefGoogle Scholar
  35. Wang, L., Chu, J., & Mao, W. (2009). A condition-based replacement and spare provisioning policy for deteriorating systems with uncertain deterioration to failure. European Journal of Operational Research, 194(1), 184–205.CrossRefGoogle Scholar
  36. Wang, Z., Hu, C., Wang, W., Kong, X., & Zhang, W. (2015). A prognostics-based spare part ordering and system replacement policy for a deteriorating system subjected to a random lead time. International Journal of Production Research, 53(15), 4511–4527.CrossRefGoogle Scholar
  37. Wu, X., & Ryan, S. (2014). Joint optimization of asset and inventory management in a product-service system. Engineering Economist, 59(2), 91–115.CrossRefGoogle Scholar
  38. Yeh, R. (1997). Optimal inspection and replacement policies for multi-state deteriorating systems. European Journal of Operational Research, 96(2), 248–259.CrossRefGoogle Scholar
  39. Zhang, L., Li, X., & Yu, J. (2006). A review of fault prognostics in condition based maintenance. In Proceedings of SPIE: The International Society for Optical Engineering 6357 II.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Industrial EngineeringUniversity of MiamiCoral GableUSA
  2. 2.Department of Computer EngineeringMiddle East Technical UniversityAnkaraTurkey
  3. 3.MIT Sloan School of ManagementMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations