Skip to main content
SpringerLink
Log in

Continuous-Time Predictive Maintenance Modeling with Dynamic Decision Framework

  • Chapter
  • First Online:
Springer Handbook of Engineering Statistics

Part of the book series: Springer Handbooks ((SHB))

Abstract

Digital technologies improve the information collected on systems and allow the development of condition-based maintenance policies and models using the remaining useful life. Accordingly, maintenance policies have evolved from a simple time-based to a more complex and competitive predictive approach. However, considering a dynamic maintenance decision framework with a self-adaptive decision rule has not been thoroughly addressed. This chapter deals with continuously deteriorating systems and focuses on dynamic maintenance policies, i.e., policies using real-time information to update the decision rule and handle the model’s uncertainty. The first part presents popular stochastic processes for degradation modeling and condition-based maintenance decision rule. Then, dynamic maintenance policies are described in two different contexts: for groupings of maintenance actions and for reducing uncertainty in modeling. Finally, a particular case of dynamic preventive maintenance model is described in detail for a system with continuous degradation and unknown degradation parameters. It is based on the inverse Gaussian process with a nonperiodic inspection policy and includes parameters update.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 309.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 399.00
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Zhang, Q., Basseville, M., Benveniste, A.: Early Warning of Slight Changes in Systems and Plants with Application to ConditionBased Maintenance RR-1750, (1992)

    Google Scholar 

  2. McCall, J.: Maintenance policies for stochastically failing equipment : a survey. Manag. Sci. 11(5), 493–524 (1965)

    MathSciNet  MATH  Google Scholar 

  3. Pierskalla, W., Voelker, J.: A survey of maintenance models : the control and surveillance of deteriorating systems. Naval Res. Logist. Q. 23, 353–388 (1979)

    MathSciNet  MATH  Google Scholar 

  4. Sherif, Y, Smith, M: Optimal maintenance models for systems subject to failure : a review. Naval Res. Logist. Q. 28, 47–74 (1981)

    MathSciNet  MATH  Google Scholar 

  5. Thomas, L: A survey of maintenance and replacement models for maintainability and reliabilityof multi-item systems. Reliab. Eng. 16, 297–309 (1986)

    Google Scholar 

  6. Valdez-Flores, C., Feldman, R.: A survey of preventive maintenance models for stochastically deteriorating single-unit systems. Naval Res. Logist. 36, 419–446 (1989)

    MathSciNet  MATH  Google Scholar 

  7. Barlow, R., Proschan, F.: Mathematical Theory of Reliability, Classics in Applied Mathematics, vol. 17. SIAM, Society for Industrial and Applied Mathematics, Philadelphia (1996)

    Google Scholar 

  8. van der Duyn Schouten, F.: Maintenance policies for multicomponent systems : an overview. In: Özekici, S. (ed.) Reliability and Maintenance of Complex Systems, NATO ASI Series—Series F: Computer and Systems Sciences, vol. 154, pp. 118–136. Springer, Berlim (1996)

    Google Scholar 

  9. Dekker, R., van der Duyn Schouten, F., Wildeman, R.: A review of multi-component maintenance models with economic dependence. Math. Methods Oper. Res. textbf45, 411–435 (1997)

    MathSciNet  MATH  Google Scholar 

  10. Wang, H.: A survey of maintenance policies of deteriorating systems. Eur. J. Oper. Res. 139, 469–489 (2002). https://doi.org/10.1016/S0377-2217(01)00197-7

    MATH  Google Scholar 

  11. Shafiee, M., Chukova, S.: Maintenance models in warranty: a literature review. Eur. J. Oper. Res. 229(3), 561–572 (2013). https://doi.org/10.1016/j.ejor.2013.01.017

    MathSciNet  MATH  Google Scholar 

  12. Zhao, X., Al-Khalifa, K., Magid Hamouda, A., Nakagawa, T.: Age replacement models: a summary with new perspectives and methods. Reliab. Eng. Syst. Saf. 161, 95–105 (2017)

    Google Scholar 

  13. Alaswad, S., Xiang, Y.: A review on condition-based maintenance optimization models for stochastically deteriorating system. Reliab. Eng. Syst. Saf. 157(Supplement C), 54–63 (2017). https://doi.org/10.1016/j.ress.2016.08.009

  14. Grall, A., Bérenguer C., Dieulle, L.: A condition-based maintenance policy for a stochastically deteriorating system. Reliab. Eng. Syst. Saf. 76(2), 167–180 (2002)

    Google Scholar 

  15. Tan, L., Cheng Z., Guo B., Gong, S.: Condition-based maintenance policy for gamma deteriorating systems. J. Syst. Eng. Electron. 21(1), 57–61 (2010)

    Google Scholar 

  16. Mercier, S., Castro, I.T.: On the modelling of imperfect repairs for a continuously monitored gamma wear process through age reduction. J. Appl. Probab. 50(4), 1057–1076 (2013). https://doi.org/10.1239/jap/1389370099

    MathSciNet  MATH  Google Scholar 

  17. van Noortwijk, J.: A survey of the application of gamma processes in maintenance. Reliab. Eng. Syst. Saf. 94, 2–21 (2009). https://doi.org/10.1016/j.ress.2007.03.019

    Google Scholar 

  18. Chen, N., Ye, Z.-S., Xiang, Y., Zhang, L.: Condition-based maintenance using the inverse Gaussian degradation model. Eur. J. Oper. Res. 243(1), 190–199 (2015)

    MathSciNet  MATH  Google Scholar 

  19. Li, R., Liu, X., Song, Y., Cai, Z., Li, J.: An optimal condition based maintenance strategy using inverse-Gaussian degradation process. In: 2017 Second International Conference on Reliability Systems Engineering (ICRSE), pp. 1–5 (2017). https://doi.org/10.1109/ICRSE.2017.8030762

  20. Wang, C., Xu, J., Wang, H., Zhang, Z.: Condition-based predictive order model for a mechanical component following inverse gaussian degradation process. Math. Probl. Eng. 2018 (2018)

    Google Scholar 

  21. Barker, C., Newby, M.: Optimal non-periodic inspection for multivariate degradation model. Reliab. Eng. Syst. Saf. 94(1), 33–43 (2009)

    Google Scholar 

  22. Guo, C., Wang, W., Guo, B., Si, X.: A maintenance optimization model for mission-oriented systems based on Wiener degradation. Reliab. Eng. Syst. Saf. 111, 183–194 (2013)

    Google Scholar 

  23. Elwany, A.H., Gebraeel, N.Z., Maillart, L.M.: Structured replacement policies for components with complex degradation processes and dedicated sensors. Oper. Res. 59(3), 684–695 (2011)

    MathSciNet  MATH  Google Scholar 

  24. Liu, B., Do, P., Iung, B., Xie, M.: Stochastic filtering approach for condition-based maintenance considering sensor degradation. IEEE Trans. Autom. Sci. Eng. 17(1):177–190 (2019)

    Google Scholar 

  25. Gertsbakh, I.: Reliability Theory - With Applications to Preventive Maintenance. Springer, Berlin (2000)

    MATH  Google Scholar 

  26. Rao, B. (ed.): Handbook of Condition Monitoring. Elsevier, Amsterdam (1996)

    Google Scholar 

  27. de Jonge, B., Teunter, R., Tinga, T.: The influence of practical factors on the benefits of condition-based maintenance over time-based maintenance. Reliab. Eng. Syst. Saf. 158, 21–30 (2017)

    Google Scholar 

  28. Whitmore, G., Seshadri, V.: A heuristic derivation of the inverse Gaussian distribution. Am. Stat. 41(4), 280–281 (1987)

    MathSciNet  Google Scholar 

  29. Park, C., Padgett, W.: Accelerated degradation models for failure based on geometric Brownian motion and gamma processes. Lifetime Data Anal. 11(4), 511–527 (2005)

    MathSciNet  MATH  Google Scholar 

  30. Wang, X., Xu, D.: An inverse Gaussian process model for degradation data. Technometrics 52(2), 188–197 (2010)

    MathSciNet  Google Scholar 

  31. Ye, Z.-S., Chen, N.: The inverse Gaussian process as a degradation model. Technometrics 56(3), 302–311 (2014)

    MathSciNet  Google Scholar 

  32. Dieulle, L., Bérenguer, C., Grall, A., Roussignol, M.: Sequential condition-based maintenance scheduling for a deteriorating system. Eur. J. Oper. Res. 150(2), 451–461 (2003)

    MathSciNet  MATH  Google Scholar 

  33. Zhao, X., Fouladirad, M., Bérenguer, C., Bordes, L.: Nonperiodic inspection/replacement policy for monotone deteriorating system with covariates. In: Proceedings of the 7th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes Barcelona, Spain, June 30–July 3, 2009, pp. 1617–1622. IFAC (2009)

    Google Scholar 

  34. Mercier, S., Meier-Hirmer, C., Roussignol, M.: Bivariate Gamma wear processes for track geometry modelling, with application to intervention scheduling. Struct. Infrastruct. Eng. 8(4), 357–366 (2012). https://doi.org/10.1080/15732479.2011.563090

    Google Scholar 

  35. Grall, A., Dieulle, L., Bérenguer, C., Roussignol, M.: Continuous-time predictive-maintenance scheduling for a deteriorating system. IEEE Trans. Reliab. 51(2), 141–150 (2002) https://doi.org/10.1109/TR.2002.1011518

    MATH  Google Scholar 

  36. Do, P., Voisin, A., Levrat, E., Iung, B.: A proactive condition-based maintenance strategy with both perfect and imperfect maintenance actions. Reliab. Eng. Syst. Saf. 133, 22–32 (2015)

    Google Scholar 

  37. Khoury, E., Grall, A., Bérenguer, C.: A comparison of RUL-based and deterioration-based maintenance policies for gradually deteriorating systems. In: Ale, B., Papazoglou, I., Zio, E. (eds.) Reliability, Risk and Safety: Back to the Future. Proceedings of the European Safety and Reliability Conference, ESREL 2010, Rhodes, Greece, 5–9 september 2010, pp. 530–537. Taylor & Francis Group, London (2010)

    Google Scholar 

  38. Castanier, B., Bérenguer, C., Grall, A.: A sequential condition-based repair/replacement policy with non-periodic inspections. Appl. Stoch. Models Bus. Ind. 19(4), 327–347 (2003). https://doi.org/10.1002/asmb.493

    MathSciNet  MATH  Google Scholar 

  39. Chen, Y., Gong, W., Xu, D., Kang, R.: Imperfect maintenance policy considering positive and negative effects for deteriorating systems with variation of operating conditions. IEEE Trans. Autom. Sci. Eng. 15(2), 872–878 (2017)

    Google Scholar 

  40. Olde Keizer, M.C.A., Flapper, S.D.P., Teunter, R.H.: Condition-based maintenance policies for systems with multiple dependent components: a review. Eur. J. Oper. Res. 261(2), 405–420 (2017)

    MathSciNet  MATH  Google Scholar 

  41. Do Van, P., Barros, A., Bérenguer, C., Bouvard, K., Brissaud, F.: Dynamic grouping maintenance with time limited opportunities. Reliab. Eng. Syst. Saf. 120, 51–59 (2013) https://doi.org/10.1016/j.ress.2013.03.016

    Google Scholar 

  42. Wildeman, R., Dekker, R., Smit, A.: A dynamic policy for grouping maintenance activities. Eur. J. Oper. Res. 99, 530–551 (1997)

    MATH  Google Scholar 

  43. Vu, H.C., Do, P., Barros, A., Bérenguer, C.: Maintenance planning and dynamic grouping for multi-component systems with positive and negative economic dependencies. IMA J. Manag. Math. 26(2), 145–170 (2015)

    MathSciNet  MATH  Google Scholar 

  44. Bouvard, K., Artus, S., Bérenguer, C., Cocquempot, V.: Condition-based dynamic maintenance operations planning & grouping. Appl. Commer. Heavy Veh. Reliab. Eng. Syst. Saf. 96(6), 601–610 (2011)

    Google Scholar 

  45. Horenbeek, A.V., Pintelon, L.: A dynamic predictive maintenance policy for complex multi-component systems. Reliab. Eng. Syst. Saf. 120, 39–50 (2013)

    Google Scholar 

  46. Kallen, M.-J., van Noortwijk, J.M.: Optimal maintenance decisions under imperfect inspection. Reliab. Eng. Syst. Saf. 90(2–3), 177–185 (2005)

    Google Scholar 

  47. Mosayebi Omshi, E., Grall, A., Shemehsavar, S.: A dynamic auto-adaptive predictive maintenance policy for degradation with unknown parameters. Eur. J. Oper. Res. 282(1), 81–92 (2020). https://doi.org/10.1016/j.ejor.2019.08.050

    MathSciNet  MATH  Google Scholar 

  48. Paroissin, C.: Online estimation methods for the gamma degradation process. IEEE Trans. Reliab. 66(4), 1361–1367 (2017)

    Google Scholar 

  49. Gebraeel, N.Z., Lawley, M.A., Li, R., Ryan, J.K.: Residual-life distributions from component degradation signals: a Bayesian approach. IIE Trans. 37(6), 543–557 (2005)

    Google Scholar 

  50. Xua, W., Wangb, W.: RUL estimation using an adaptive inverse Gaussian model. Chem. Eng. 33, 331–336 (2013)

    Google Scholar 

  51. Bian, L., Gebraeel, N.: Computing and updating the first-passage time distribution for randomly evolving degradation signals. IIE Trans. 44(11), 974–987 (2012)

    Google Scholar 

  52. Liu, B., Lin, J., Zhang, L., Kumar, U.: A dynamic prescriptive maintenance model considering system aging and degradation. IEEE Access 7, 94931–94943 (2019)

    Google Scholar 

  53. Flage, R., Coit, D.W., Luxhøj, J.T., Aven, T.: Safety constraints applied to an adaptive Bayesian condition-based maintenance optimization model. Reliab. Eng. Syst. Saf. 102, 16–26 (2012)

    Google Scholar 

  54. Mosayebi Omshi, E., Grall, A., Shemehsavar, S.: Bayesian update and aperiodic maintenance policy for deteriorating systems with unknown parameters. In: H. et al. (eds.), Proceedings of the 28th European Safety and Reliability Conference, ESREL 2018, Trondheim, Norway, 17–21 June 2018. Safety and Reliability—Safe Societies in a Changing World, pp. 687–692. Taylor & Francis Group, London (2018)

    Google Scholar 

  55. Juang, M.-G., Anderson, G.: A Bayesian method on adaptive preventive maintenance problem. Eur. J. Oper. Res. 155(2), 455–473 (2004)

    MathSciNet  MATH  Google Scholar 

  56. Sheu, S.-H., Yeh, R.H., Lin, Y.-B., Juang, M.-G.: A Bayesian approach to an adaptive preventive maintenance model. Reliab. Eng. Syst. Saf. 71(1), 33–44 (2001)

    Google Scholar 

  57. Fouladirad, M., Grall, A.: Condition-based maintenance for a system subject to a non-homogeneous wear process with a wear rate transition. Reliab. Eng. Syst. Saf. 96(6), 611–618 (2011)

    Google Scholar 

  58. Fouladirad, M., Grall, A., Dieulle, L.: On the use of on-line detection for maintenance of gradually deteriorating systems. Reliab. Eng. Syst. Saf. 93(12), 1814–1820 (2008)

    Google Scholar 

  59. Fouladirad, M., Grall., A.: Monitoring and condition-based maintenance with abrupt change in a system’s deterioration rate. Int. J. Syst. Sci. 46(12), 2183–2194 (2015)

    Google Scholar 

  60. Fouladirad, M., Grall, A.: On-line change detection and condition-based maintenance for systems with unknown deterioration parameters. IMA J. Manag. Math. 25(2), 139–158 (2014)

    MathSciNet  MATH  Google Scholar 

  61. Zhang, M., Gaudoin, O., Xie, M.: Degradation-based maintenance decision using stochastic filtering for systems under imperfect maintenance. Eur. J. Oper. Res. 245(2), 531–541 (2015)

    MathSciNet  MATH  Google Scholar 

  62. Zhao, X., Liang, Z., Parlikad, A.K., Xie, M.: Dynamic imperfect condition-based maintenance for systems subject to nonlinear degradation paths (2018)

    Google Scholar 

  63. Shen, J., Cui, L., Ma, Y.: Availability and optimal maintenance policy for systems degrading in dynamic environments. Eur. J. Oper. Res. 276(1), 133–143 (2019)

    MathSciNet  MATH  Google Scholar 

  64. Huynh, K.T.: A hybrid condition-based maintenance model for deteriorating systems subject to nonmemoryless imperfect repairs and perfect replacements. IEEE Trans. Reliab. 69(2), 781–815 (2019)

    Google Scholar 

  65. Huynh, K.T.: Modeling past-dependent partial repairs for condition-based maintenance of continuously deteriorating systems. Eur. J. Oper. Res. 280(1), 152–163 (2020)

    MathSciNet  MATH  Google Scholar 

  66. Peng, C.-Y.: Inverse Gaussian processes with random effects and explanatory variables for degradation data. Technometrics 57(1), 100–111 (2015)

    MathSciNet  Google Scholar 

  67. Asmussen, S.: Applied Probability and Queues, Applications of Mathematics, 2nd edn. Springer, New York (2003)

    MATH  Google Scholar 

  68. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes: The Art of Scientific Computing, 3rd edn. Cambridge University Press, Cambridge (2007)

    MATH  Google Scholar 

  69. Nelder, J., Mead, R.: A simplex method for function minimization. Comput. J. 7, 308–313 (1965)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LIST3N, Université de Technologie de Troyes, Champagne, de Troyes, France

    Antoine Grall & Elham Mosayebi Omshi

Authors
  1. Antoine Grall
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elham Mosayebi Omshi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antoine Grall .

Editor information

Editors and Affiliations

  1. Department of Industrial & Systems Engineering, Rutgers University, Piscataway, NJ, USA

    Hoang Pham

Section Editor information

    Rights and permissions

    Reprints and permissions

    Copyright information

    © 2023 Springer-Verlag London Ltd., part of Springer Nature

    About this chapter

    Check for updates. Verify currency and authenticity via CrossMark

    Cite this chapter

    Grall, A., Omshi, E.M. (2023). Continuous-Time Predictive Maintenance Modeling with Dynamic Decision Framework. In: Pham, H. (eds) Springer Handbook of Engineering Statistics. Springer Handbooks. Springer, London. https://doi.org/10.1007/978-1-4471-7503-2_27

    Download citation

    Publish with us

    Policies and ethics

    Search

    Navigation