IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i22p2858-d676381.html
   My bibliography  Save this article

Computing the Number of Failures for Fuzzy Weibull Hazard Function

Author

Listed:
  • Hennie Husniah

    (Department of Industrial Engineering, Langlangbuana University, Bandung 40261, Indonesia)

  • Asep K. Supriatna

    (Department of Mathematics, Padjadjaran University, Jatinangor 45363, Indonesia)

Abstract

The number of failures plays an important factor in the study of maintenance strategy of a manufacturing system. In the real situation, this number is often affected by some uncertainties. Many of the uncertainties fall into the possibilistic uncertainty, which are different from the probabilistic uncertainty. This uncertainty is commonly modeled by applying the fuzzy theoretical framework. This paper aims to compute the number of failures for a system which has Weibull failure distribution with a fuzzy shape parameter. In this case two different approaches are used to calculate the number. In the first approach, the fuzziness membership of the shape parameter propagates to the number of failures so that they have exactly the same values of the membership. While in the second approach, the membership is computed through the α-cut or α-level of the shape parameter approach in the computation of the formula for the number of failures. Without loss of generality, we use the Triangular Fuzzy Number ( TFN ) for the Weibull shape parameter. We show that both methods have succeeded in computing the number of failures for the system under investigation. Both methods show that when we consider the function of the number of failures as a function of time then the uncertainty (the fuzziness) of the resulting number of failures becomes larger and larger as the time increases. By using the first method, the resulting number of failures has a TFN form. Meanwhile, the resulting number of failures from the second method does not necessarily have a TFN form, but a TFN-like form. Some comparisons between these two methods are presented using the Generalized Mean Value Defuzzification ( GMVD ) method. The results show that for certain weighting factor of the GMVD , the cores of these fuzzy numbers of failures are identical.

Suggested Citation

  • Hennie Husniah & Asep K. Supriatna, 2021. "Computing the Number of Failures for Fuzzy Weibull Hazard Function," Mathematics, MDPI, vol. 9(22), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2858-:d:676381
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/22/2858/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/22/2858/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Harish Garg & S.P. Sharma & Monica Rani, 2013. "Weibull fuzzy probability distribution for analysing the behaviour of pulping unit in a paper industry," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 14(4), pages 395-413.
    2. Juhyun Lee & Byunghoon Kim & Suneung Ahn, 2019. "Maintenance Optimization for Repairable Deteriorating Systems under Imperfect Preventive Maintenance," Mathematics, MDPI, vol. 7(8), pages 1-17, August.
    3. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, June.
    4. Bermawi P. Iskandar & Nat Jack & D. N. Pra Murthy, 2012. "Two New Servicing Strategies For Products Sold With Warranty," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-16.
    Full references (including those not matched with items on IDEAS)

    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. 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).
    2. 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.
    3. 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).
    4. 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.
    5. 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).
    6. Ji Hwan Cha & Maxim Finkelstein, 2020. "On optimal life extension for degrading systems," Journal of Risk and Reliability, , vol. 234(3), pages 487-495, June.
    7. Safaei, Fatemeh & Taghipour, Sharareh, 2024. "Integrated degradation-based burn-in and maintenance model for heterogeneous and highly reliable items," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    8. Zheng, Junjun & Okamura, Hiroyuki & Dohi, Tadashi, 2021. "Age replacement with Markovian opportunity process," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    9. 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.
    10. Cha, Ji Hwan & Finkelstein, Maxim, 2024. "Preventive maintenance for the constrained multi-attempt minimal repair," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    11. M D Pandey & T Cheng & J A M van der Weide, 2011. "Finite-time maintenance cost analysis of engineering systems affected by stochastic degradation," Journal of Risk and Reliability, , vol. 225(2), pages 241-250, June.
    12. Fu-Min Chang & Yu-Hung Chien, 2012. "Optimal Discrete-Time Periodic Replacement Policy For Repairable Products Under Free Minimal Repair Warranty," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-14.
    13. Doostparast, Mohammad & Kolahan, Farhad & Doostparast, Mahdi, 2014. "A reliability-based approach to optimize preventive maintenance scheduling for coherent systems," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 98-106.
    14. Abdolsaeed Toomaj & Antonio Di Crescenzo, 2020. "Connections between Weighted Generalized Cumulative Residual Entropy and Variance," Mathematics, MDPI, vol. 8(7), pages 1-27, July.
    15. Eryilmaz, Serkan & Ozkut, Murat, 2020. "Optimization problems for a parallel system with multiple types of dependent components," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    16. Hyunju Lee & Ji Hwan Cha & Maxim Finkelstein, 2022. "A Preventive Replacement Policy for a System Subject to Bivariate Generalized Polya Failure Process," Mathematics, MDPI, vol. 10(11), pages 1-15, May.
    17. Sheu, Shey-Huei & Liu, Tzu-Hsin & Zhang, Zhe-George & Tsai, Hsin-Nan, 2018. "The generalized age maintenance policies with random working times," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 503-514.
    18. Badía, F.G. & Berrade, M.D. & Cha, Ji Hwan & Lee, Hyunju, 2018. "Optimal replacement policy under a general failure and repair model: Minimal versus worse than old repair," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 362-372.
    19. Michael Patriksson & Ann-Brith Strömberg & Adam Wojciechowski, 2015. "The stochastic opportunistic replacement problem, part II: a two-stage solution approach," Annals of Operations Research, Springer, vol. 224(1), pages 51-75, January.
    20. Zhang, Qin & Fang, Zhigeng & Cai, Jiajia, 2021. "Preventive replacement policies with multiple missions and maintenance triggering approaches," Reliability Engineering and System Safety, Elsevier, vol. 213(C).

    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:gam:jmathe:v:9:y:2021:i:22:p:2858-:d:676381. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.