IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v218y2012i3p726-734.html
   My bibliography  Save this article

A simulation-based multivariate Bayesian control chart for real time condition-based maintenance of complex systems

Author

Listed:
  • Wang, Wenbin

Abstract

When complex systems are monitored, multi-observations from several sensors or sources may be available. These observations can be fused through Bayesian theory to give a posterior probabilistic estimate of the underlying state which is often not directly observable. This forms the basis of a Bayesian control chart where the estimated posterior probability of the state can be compared with a preset threshold level to assess whether a full inspection is needed or not. Maintenance can then be carried out if indicated as necessary by the inspection. This paper considers the design of such multivariate Bayesian control chart where both the transition between states and the relationship between observed information and the state are not Markovian. Since analytical or numerical solutions are difficult for the case considered in this paper, Monte Carlo simulation is used to obtain the optimal control chart parameters, which are the monitoring interval and the upper control limit. A two-stage failure process characterised by the delay time concept is used to describe the underlying state transition process and Bayesian theory is used to compute the posterior probability of the underlying state, which is embedded in the simulation algorithm. Extensive examples are shown to demonstrate the modelling idea.

Suggested Citation

  • Wang, Wenbin, 2012. "A simulation-based multivariate Bayesian control chart for real time condition-based maintenance of complex systems," European Journal of Operational Research, Elsevier, vol. 218(3), pages 726-734.
  • Handle: RePEc:eee:ejores:v:218:y:2012:i:3:p:726-734
    DOI: 10.1016/j.ejor.2011.12.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711010873
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2011.12.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wenbin Wang, 2008. "Delay Time Modelling," Springer Series in Reliability Engineering, in: Complex System Maintenance Handbook, chapter 14, pages 345-370, Springer.
    2. W Wang & A H Christer, 2000. "Towards a general condition based maintenance model for a stochastic dynamic system," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(2), pages 145-155, February.
    3. V. Makis & X. Jiang, 2003. "Optimal Replacement Under Partial Observations," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 382-394, May.
    4. Wang, Wenbin, 2007. "A two-stage prognosis model in condition based maintenance," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1177-1187, November.
    5. Kim, Michael Jong & Makis, Viliam & Jiang, Rui, 2010. "Parameter estimation in a condition-based maintenance model," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1633-1639, November.
    6. Makis, Viliam, 2009. "Multivariate Bayesian process control for a finite production run," European Journal of Operational Research, Elsevier, vol. 194(3), pages 795-806, May.
    7. Stuart, Michael & Mullins, Eamonn & Drew, Eileen, 1996. "Statistical quality control and improvement," European Journal of Operational Research, Elsevier, vol. 88(2), pages 203-214, January.
    8. Deloux, E. & Castanier, B. & Bérenguer, C., 2009. "Predictive maintenance policy for a gradually deteriorating system subject to stress," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 418-431.
    9. Wenbin Wang, 2008. "Condition-based Maintenance Modelling," Springer Series in Reliability Engineering, in: Complex System Maintenance Handbook, chapter 5, pages 111-131, Springer.
    10. A H Christer, 1999. "Developments in delay time analysis for modelling plant maintenance," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(11), pages 1120-1137, November.
    11. Viliam Makis, 2008. "Multivariate Bayesian Control Chart," Operations Research, INFORMS, vol. 56(2), pages 487-496, April.
    12. Wang, Wenbin & Banjevic, Dragan & Pecht, Michael, 2010. "A multi-component and multi-failure mode inspection model based on the delay time concept," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 912-920.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Peruchi, Rogério Santana & Balestrassi, Pedro Paulo & de Paiva, Anderson Paulo & Ferreira, João Roberto & de Santana Carmelossi, Michele, 2013. "A new multivariate gage R&R method for correlated characteristics," International Journal of Production Economics, Elsevier, vol. 144(1), pages 301-315.
    2. Rebello, Sinda & Yu, Hongyang & Ma, Lin, 2018. "An integrated approach for system functional reliability assessment using Dynamic Bayesian Network and Hidden Markov Model," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 124-135.
    3. Haridy, Salah & Wu, Zhang & Lee, Ka Man & Bhuiyan, Nadia, 2013. "Optimal average sample number of the SPRT chart for monitoring fraction nonconforming," European Journal of Operational Research, Elsevier, vol. 229(2), pages 411-421.
    4. Zio, Enrico & Compare, Michele, 2013. "Evaluating maintenance policies by quantitative modeling and analysis," Reliability Engineering and System Safety, Elsevier, vol. 109(C), pages 53-65.
    5. Wang, Hsiuying & Huwang, Longcheen & Yu, Jeng Hung, 2015. "Multivariate control charts based on the James–Stein estimator," European Journal of Operational Research, Elsevier, vol. 246(1), pages 119-127.
    6. Kampitsis, Dimitris & Panagiotidou, Sofia, 2022. "A Bayesian condition-based maintenance and monitoring policy with variable sampling intervals," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    7. Liping Liu & Lining Jiang & Ding Zhang, 2017. "An integrated model of statistical process control and condition-based maintenance for deteriorating systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1452-1460, November.
    8. Peng, Weiwen & Li, Yan-Feng & Yang, Yuan-Jian & Huang, Hong-Zhong & Zuo, Ming J., 2014. "Inverse Gaussian process models for degradation analysis: A Bayesian perspective," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 175-189.
    9. Özgür-Ünlüakın, Demet & Türkali, Busenur, 2021. "Evaluation of proactive maintenance policies on a stochastically dependent hidden multi-component system using DBNs," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    10. Tang, Diyin & Makis, Viliam & Jafari, Leila & Yu, Jinsong, 2015. "Optimal maintenance policy and residual life estimation for a slowly degrading system subject to condition monitoring," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 198-207.
    11. Rebello, Sinda & Yu, Hongyang & Ma, Lin, 2019. "An integrated approach for real-time hazard mitigation in complex industrial processes," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 297-309.
    12. Jiang, R., 2013. "A multivariate CBM model with a random and time-dependent failure threshold," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 178-185.
    13. Chi, Lixun & Su, Huai & Zio, Enrico & Qadrdan, Meysam & Li, Xueyi & Zhang, Li & Fan, Lin & Zhou, Jing & Yang, Zhaoming & Zhang, Jinjun, 2021. "Data-driven reliability assessment method of Integrated Energy Systems based on probabilistic deep learning and Gaussian mixture Model-Hidden Markov Model," Renewable Energy, Elsevier, vol. 174(C), pages 952-970.
    14. Huda, Shamsul & Abdollahian, Mali & Mammadov, Musa & Yearwood, John & Ahmed, Shafiq & Sultan, Ibrahim, 2014. "A hybrid wrapper–filter approach to detect the source(s) of out-of-control signals in multivariate manufacturing process," European Journal of Operational Research, Elsevier, vol. 237(3), pages 857-870.
    15. Peng, Weiwen & Li, Yan-Feng & Mi, Jinhua & Yu, Le & Huang, Hong-Zhong, 2016. "Reliability of complex systems under dynamic conditions: A Bayesian multivariate degradation perspective," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 75-87.
    16. Wang, Wenbin, 2013. "Models of inspection, routine service, and replacement for a serviceable one-component system," Reliability Engineering and System Safety, Elsevier, vol. 116(C), pages 57-63.
    17. Zhang, Zhengxin & Si, Xiaosheng & Hu, Changhua & Lei, Yaguo, 2018. "Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods," European Journal of Operational Research, Elsevier, vol. 271(3), pages 775-796.
    18. Liu, Liping & Yu, Miaomiao & Ma, Yizhong & Tu, Yiliu, 2013. "Economic and economic-statistical designs of an X¯ control chart for two-unit series systems with condition-based maintenance," European Journal of Operational Research, Elsevier, vol. 226(3), pages 491-499.
    19. Zhou, Wenhui & Zheng, Zhibin & Xie, Wei, 2017. "A control-chart-based queueing approach for service facility maintenance with energy-delay tradeoff," European Journal of Operational Research, Elsevier, vol. 261(2), pages 613-625.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Wenbin & Syntetos, Aris A., 2011. "Spare parts demand: Linking forecasting to equipment maintenance," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 1194-1209.
    2. Wang, Wenbin, 2012. "An overview of the recent advances in delay-time-based maintenance modelling," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 165-178.
    3. Rui Jiang & Michael Kim & Viliam Makis, 2012. "A Bayesian model and numerical algorithm for CBM availability maximization," Annals of Operations Research, Springer, vol. 196(1), pages 333-348, July.
    4. Kim, Michael Jong & Jiang, Rui & Makis, Viliam & Lee, Chi-Guhn, 2011. "Optimal Bayesian fault prediction scheme for a partially observable system subject to random failure," European Journal of Operational Research, Elsevier, vol. 214(2), pages 331-339, October.
    5. W Wang, 2011. "Overview of a semi-stochastic filtering approach for residual life estimation with applications in condition based maintenance," Journal of Risk and Reliability, , vol. 225(2), pages 185-197, June.
    6. Wang, Wenbin & Banjevic, Dragan, 2012. "Ergodicity of forward times of the renewal process in a block-based inspection model using the delay time concept," Reliability Engineering and System Safety, Elsevier, vol. 100(C), pages 1-7.
    7. Wang, Wenbin, 2011. "A joint spare part and maintenance inspection optimisation model using the Delay-Time concept," Reliability Engineering and System Safety, Elsevier, vol. 96(11), pages 1535-1541.
    8. Wang, Wenbin, 2011. "An inspection model based on a three-stage failure process," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 838-848.
    9. Wang, Wenbin, 2012. "A stochastic model for joint spare parts inventory and planned maintenance optimisation," European Journal of Operational Research, Elsevier, vol. 216(1), pages 127-139.
    10. Fu, Bo & Wang, Wenbin & Shi, Xin, 2012. "A risk analysis based on a two-stage delayed diagnosis regression model with application to chronic disease progression," European Journal of Operational Research, Elsevier, vol. 218(3), pages 847-855.
    11. Carr, Matthew J. & Wang, Wenbin, 2011. "An approximate algorithm for prognostic modelling using condition monitoring information," European Journal of Operational Research, Elsevier, vol. 211(1), pages 90-96, May.
    12. Wang, Wenbin, 2013. "Models of inspection, routine service, and replacement for a serviceable one-component system," Reliability Engineering and System Safety, Elsevier, vol. 116(C), pages 57-63.
    13. P A Scarf & H A Majid, 2011. "Modelling warranty extensions: a case study in the automotive industry," Journal of Risk and Reliability, , vol. 225(2), pages 251-265, June.
    14. Wang, Wenbin & Banjevic, Dragan & Pecht, Michael, 2010. "A multi-component and multi-failure mode inspection model based on the delay time concept," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 912-920.
    15. Zhou, Zhi-Jie & Hu, Chang-Hua & Xu, Dong-Ling & Chen, Mao-Yin & Zhou, Dong-Hua, 2010. "A model for real-time failure prognosis based on hidden Markov model and belief rule base," European Journal of Operational Research, Elsevier, vol. 207(1), pages 269-283, November.
    16. Flage, Roger, 2014. "A delay time model with imperfect and failure-inducing inspections," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 1-12.
    17. de Jonge, Bram & Teunter, Ruud & Tinga, Tiedo, 2017. "The influence of practical factors on the benefits of condition-based maintenance over time-based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 21-30.
    18. Wang, Wenbin & Zhao, Fei & Peng, Rui, 2014. "A preventive maintenance model with a two-level inspection policy based on a three-stage failure process," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 207-220.
    19. Lam, Ji Ye Janet & Banjevic, Dragan, 2015. "A myopic policy for optimal inspection scheduling for condition based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 1-11.
    20. Wang, Wenbin, 2007. "A two-stage prognosis model in condition based maintenance," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1177-1187, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:218:y:2012:i:3:p:726-734. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.