IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v179y2018icp97-107.html
   My bibliography  Save this article

Time and magnitude monitoring based on the renewal reward process

Author

Listed:
  • Ali, Sajid
  • Pievatolo, Antonio

Abstract

Time between event (TBE) charts are SPC tools for monitoring the occurrence of unwanted events, such as the appearance of a defective item or a failure of a piece of equipment. In some cases, a magnitude, indicating the severity of the event, is also measured. Time and magnitude charts, which are based on the assumption that the stochastic process underlying the occurrence of events is the marked Poisson process, are the preferred option. However, these charts are not suitable to deal with damage events caused by repeatedly occurring shocks or stress conditions. To bridge this gap, we introduce a new control chart based on the assumption of a renewal process with rewards, where the reward represents magnitude, and a magnitude-over-threshold condition represents the occurrence of an event. In particular, we consider two cases for magnitude: (i) magnitude is cumulative over time and (ii) magnitude is non-cumulative or independent over time. We use known results in renewal theory to provide expressions of the probability distributions needed to compute the control limits and perform a simulation analysis of the control chart performance.

Suggested Citation

  • Ali, Sajid & Pievatolo, Antonio, 2018. "Time and magnitude monitoring based on the renewal reward process," Reliability Engineering and System Safety, Elsevier, vol. 179(C), pages 97-107.
    • Handle: RePEc:eee:reensy:v:179:y:2018:i:c:p:97-107
    DOI: 10.1016/j.ress.2018.01.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832018300632
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2018.01.004?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. Wu, Zhang & Jiao, Jianxin & He, Zhen, 2009. "A single control chart for monitoring the frequency and magnitude of an event," International Journal of Production Economics, Elsevier, vol. 119(1), pages 24-33, May.
    2. Toshio Nakagawa, 2007. "Shock and Damage Models in Reliability Theory," Springer Series in Reliability Engineering, Springer, number 978-1-84628-442-7, January.
    3. Yafen Liu & Zhen He & M. Shamsuzzaman & Zhang Wu, 2010. "A combined control scheme for monitoring the frequency and size of an attribute event," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(12), pages 1991-2013.
    4. L. Qu & Z. Wu & A. Rahim & M.B.C. Khoo, 2015. "A balanced two-sided CUSUM chart for monitoring time between events," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 9(1), pages 1-26.
    5. Qu, Liang & Wu, Zhang & Khoo, Michael B.C. & Castagliola, Philippe, 2013. "A CUSUM scheme for event monitoring," International Journal of Production Economics, Elsevier, vol. 145(1), pages 268-280.
    6. Liu, Yafen & He, Zhen & Shu, Lianjie & Wu, Zhang, 2009. "Statistical computation and analyses for attribute events," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3412-3425, July.
    7. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, January.
    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. Sabri-Laghaie, Kamyar & Fathi, Mahdi & Zio, Enrico & Mazhar, Maryam, 2022. "A novel reliability monitoring scheme based on the monitoring of manufacturing quality error rates," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    2. Liao, Ruoyu & He, Yihai & Zhang, Jishan & Zheng, Xin & Zhang, Anqi & Zhang, Weifang, 2023. "Reliability proactive control approach based on product key reliability characteristics in manufacturing process," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    3. de Oliveira, Cícero Carlos Felix & Firmino, Paulo Renato Alves & Cristino, Cláudio Tadeu, 2019. "A tool for evaluating repairable systems based on Generalized Renewal Processes," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 281-297.
    4. Shamstabar, Yousof & Shahriari, Hamid & Samimi, Yaser, 2021. "Reliability monitoring of systems with cumulative shock-based deterioration process," Reliability Engineering and System Safety, Elsevier, vol. 216(C).

    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. Shamstabar, Yousof & Shahriari, Hamid & Samimi, Yaser, 2021. "Reliability monitoring of systems with cumulative shock-based deterioration process," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    2. Zhao, Xufeng & Qian, Cunhua & Nakagawa, Toshio, 2013. "Optimal policies for cumulative damage models with maintenance last and first," Reliability Engineering and System Safety, Elsevier, vol. 110(C), pages 50-59.
    3. Phalguni Nanda & Prajamitra Bhuyan & Anup Dewanji, 2022. "Optimal replacement policy under cumulative damage model and strength degradation with applications," Annals of Operations Research, Springer, vol. 315(2), pages 1345-1371, August.
    4. van der Weide, J.A.M. & Pandey, M.D., 2011. "Stochastic analysis of shock process and modeling of condition-based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 96(6), pages 619-626.
    5. Xufeng Zhao & Toshio Nakagawa, 2016. "Over-time and over-level replacement policies with random working cycles," Annals of Operations Research, Springer, vol. 244(1), pages 103-116, September.
    6. Zhao, Xufeng & Liu, Hu-Chen & Nakagawa, Toshio, 2015. "Where does “whichever occurs first†hold for preventive maintenance modelings?," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 203-211.
    7. Maxim Finkelstein & Gregory Levitin & Oleg A Stepanov, 2019. "On operation termination for degrading systems with two types of failures," Journal of Risk and Reliability, , vol. 233(3), pages 419-426, June.
    8. Xufeng Zhao & Syouji Nakamura & Toshio Nakagawa, 2012. "Optimal Tenuring And Major Collection Times For A Generational Garbage Collector," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-17.
    9. Zhao, Xufeng & Nakagawa, Toshio, 2012. "Optimization problems of replacement first or last in reliability theory," European Journal of Operational Research, Elsevier, vol. 223(1), pages 141-149.
    10. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2021. "Optimization of cyclic preventive replacement in homogeneous warm-standby system with reusable elements exposed to shocks," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    11. Qu, Liang & Wu, Zhang & Khoo, Michael B.C. & Castagliola, Philippe, 2013. "A CUSUM scheme for event monitoring," International Journal of Production Economics, Elsevier, vol. 145(1), pages 268-280.
    12. Chien, Yu-Hung & Sheu, Shey-Huei & Zhang, Zhe George, 2012. "Optimal maintenance policy for a system subject to damage in a discrete time process," Reliability Engineering and System Safety, Elsevier, vol. 103(C), pages 1-10.
    13. Hashemi, M. & Asadi, M. & Zarezadeh, S., 2020. "Optimal maintenance policies for coherent systems with multi-type components," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    14. Gregory Levitin & Maxim Finkelstein, 2018. "Optimal Mission Abort Policy for Systems Operating in a Random Environment," Risk Analysis, John Wiley & Sons, vol. 38(4), pages 795-803, April.
    15. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Mission abort policy optimization for series systems with overlapping primary and rescue subsystems operating in a random environment," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    16. Chin-Chih Chang, 2023. "Optimal maintenance policy for a k-out-of-n system with replacement first and last," Annals of Operations Research, Springer, vol. 323(1), pages 31-43, April.
    17. Ji Hwan Cha & Maxim Finkelstein, 2019. "New failure and minimal repair processes for repairable systems in a random environment," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(3), pages 522-536, May.
    18. Finkelstein, Maxim & Cha, Ji Hwan & Langston, Amy, 2023. "Improving classical optimal age-replacement policies for degrading items," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    19. Torrado, Nuria, 2022. "Optimal component-type allocation and replacement time policies for parallel systems having multi-types dependent components," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    20. Zhengxin Zhang & Xiaosheng Si & Changhua Hu & Xiangyu Kong, 2015. "Degradation modeling–based remaining useful life estimation: A review on approaches for systems with heterogeneity," Journal of Risk and Reliability, , vol. 229(4), pages 343-355, August.

    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:reensy:v:179:y:2018:i:c:p:97-107. 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: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.