IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i22p4337-d977242.html
   My bibliography  Save this article

Three-Parameter Estimation Method of Multiple Hybrid Weibull Distribution Based on the EM Optimization Algorithm

Author

Listed:
  • Xiaowei Dong

    (School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China)

  • Feng Sun

    (School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China)

  • Fangchao Xu

    (School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China)

  • Qi Zhang

    (School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China)

  • Ran Zhou

    (School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China)

  • Liang Zhang

    (Shenyang Machine Tool Co., Ltd., Shenyang 110027, China)

  • Zhongwei Liang

    (School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China)

Abstract

The hybrid Weibull distribution model can describe the failure rules of electromechanical products more accurately than the single Weibull distribution model, and it can improve the accuracy of reliability analysis. However, the hybrid Weibull distribution model is also more complex, and the multi-parameter estimation is more difficult. In this paper, a reliability mathematical model based on the two-fold three-parameter hybrid Weibull distribution model was established, an EM optimization algorithm was derived for its solution, and a practical initial parameter selection scheme was designed. The validity of the model and the algorithm were verified, and goodness-of-fit tests were conducted through an arithmetic example. The results showed that the initial value selection scheme proposed in this paper and the corresponding solution algorithm could solve all the parameters and weight coefficients to be estimated for each sub distribution, and the obtained failure probability fitting curve had a high fit with the actual sample data, which effectively solved the multi-parameter estimation problem of the multiple mixed Weibull distribution model.

Suggested Citation

  • Xiaowei Dong & Feng Sun & Fangchao Xu & Qi Zhang & Ran Zhou & Liang Zhang & Zhongwei Liang, 2022. "Three-Parameter Estimation Method of Multiple Hybrid Weibull Distribution Based on the EM Optimization Algorithm," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4337-:d:977242
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/22/4337/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/22/4337/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. R. Jiang & D. N. P. Murthy, 1998. "Mixture of Weibull distributions—parametric characterization of failure rate function," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 14(1), pages 47-65, March.
    2. Elmahdy, Emad E., 2015. "A new approach for Weibull modeling for reliability life data analysis," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 708-720.
    3. Ping Jiang & Yunyan Xing & Xiang Jia & Bo Guo, 2015. "Weibull Failure Probability Estimation Based on Zero-Failure Data," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-8, May.
    4. José Antonio Roldán-Nofuentes & Saad Bouh Regad, 2021. "Comparison of the Average Kappa Coefficients of Two Binary Diagnostic Tests with Missing Data," Mathematics, MDPI, vol. 9(21), pages 1-24, November.
    5. Lulu Zhang & Guang Jin & Yang You, 2019. "Reliability Assessment for Very Few Failure Data and Weibull Distribution," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-9, September.
    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. Trindade, Graça & Dias, José G. & Ambrósio, Jorge, 2017. "Extracting clusters from aggregate panel data: A market segmentation study," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 277-288.
    2. Bebbington, Mark & Lai, Chin-Diew & Zitikis, RiÄ ardas, 2009. "Balancing burn-in and mission times in environments with catastrophic and repairable failures," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1314-1321.
    3. Christian Acal & Juan E. Ruiz-Castro & David Maldonado & Juan B. Roldán, 2021. "One Cut-Point Phase-Type Distributions in Reliability. An Application to Resistive Random Access Memories," Mathematics, MDPI, vol. 9(21), pages 1-13, October.
    4. Lin, Kunsong & Chen, Yunxia, 2021. "Analysis of two-dimensional warranty data considering global and local dependence of heterogeneous marginals," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    5. Somnath Chattopadhyaya & Brajeshkumar Kishorilal Dinkar & Alok Kumar Mukhopadhyay & Shubham Sharma & José Machado, 2021. "Meta-Analysis and Forest Plots for Sustainability of Heavy Load Carrier Equipment Used in the Industrial Mining Environment," Sustainability, MDPI, vol. 13(15), pages 1-15, August.
    6. Jiang, Renyan & Qi, Faqun & Cao, Yu, 2023. "Relation between aging intensity function and WPP plot and its application in reliability modelling," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    7. Chang, Ping-Chen, 2022. "MC-based simulation approach for two-terminal multi-state network reliability evaluation without knowing d-MCs," Reliability Engineering and System Safety, Elsevier, vol. 220(C).
    8. M Bebbington & C D Lai & D N P Murthy & R Zitikis, 2009. "Modelling N- and W-shaped hazard rate functions without mixing distributions," Journal of Risk and Reliability, , vol. 223(1), pages 59-69, March.
    9. Farcomeni, Alessio & Nardi, Alessandra, 2010. "A two-component Weibull mixture to model early and late mortality in a Bayesian framework," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 416-428, February.
    10. Guzzo, Daniel & Rodrigues, Vinicius Picanço & Mascarenhas, Janaina, 2021. "A systems representation of the Circular Economy: Transition scenarios in the electrical and electronic equipment (EEE) industry," Technological Forecasting and Social Change, Elsevier, vol. 163(C).
    11. Lin, Kunsong & Chen, Yunxia & Xu, Dan, 2017. "Reliability assessment model considering heterogeneous population in a multiple stresses accelerated test," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 134-143.
    12. Baker, Rose, 2019. "New survival distributions that quantify the gain from eliminating flawed components," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 493-501.
    13. Örkcü, H. Hasan & Özsoy, Volkan Soner & Aksoy, Ertugrul & Dogan, Mustafa Isa, 2015. "Estimating the parameters of 3-p Weibull distribution using particle swarm optimization: A comprehensive experimental comparison," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 201-226.
    14. Peng, Xiuyun & Yan, Zaizai, 2014. "Estimation and application for a new extended Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 34-42.
    15. Wendy W. Moe & Peter S. Fader, 2002. "Fast-Track: Article Using Advance Purchase Orders to Forecast New Product Sales," Marketing Science, INFORMS, vol. 21(3), pages 347-364, March.
    16. Eshetu T. Wondmagegnehu, 2004. "On the behavior and shape of mixture failure rates from a family of IFR Weibull distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 491-500, June.
    17. Pan, Donghui & Wei, Yantao & Fang, Houzhang & Yang, Wenzhi, 2018. "A reliability estimation approach via Wiener degradation model with measurement errors," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 131-141.
    18. Tianyu Liu & Lulu Zhang & Guang Jin & Zhengqiang Pan, 2022. "Reliability Assessment of Heavily Censored Data Based on E-Bayesian Estimation," Mathematics, MDPI, vol. 10(22), pages 1-14, November.
    19. Ducros, Florence & Pamphile, Patrick, 2018. "Bayesian estimation of Weibull mixture in heavily censored data setting," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 453-462.
    20. Bebbington, Mark & Lai, Chin-Diew & Zitikis, RiÄ ardas, 2007. "A flexible Weibull extension," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 719-726.

    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:10:y:2022:i:22:p:4337-:d:977242. 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.