IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v268y2015icp201-226.html
   My bibliography  Save this article

Estimating the parameters of 3-p Weibull distribution using particle swarm optimization: A comprehensive experimental comparison

Author

Listed:
  • Örkcü, H. Hasan
  • Özsoy, Volkan Soner
  • Aksoy, Ertugrul
  • Dogan, Mustafa Isa

Abstract

Weibull distribution plays an important role in failure distribution modeling in reliability studies and the estimation of its parameters is essential in the most real applications. Maximum likelihood (ML) estimation is a common method, which is usually used to elaborate on the parameter estimation. The maximizing likelihood function formed for the parameter estimation of a three-parameter (3-p) Weibull distribution is a quite difficult problem. Hence, the heuristic approaches must be used to discover good solutions. Particle swarm optimization (PSO) is a population based heuristic optimization technique developed from swarm intelligence. The performance of PSO greatly depends on its control parameters such as inertia weight and acceleration coefficients. Slightly different parameter settings may direct to very different performance. This paper gives a comprehensive investigation of different PSO variants (according to inertia weight procedures, acceleration coefficients, particle size, and search space) in the parameter estimation problem of 3-p Weibull distribution. Three explanatory numerical examples are given to show that PSO approach variants exhibit a rapid convergence to the maximum value of the likelihood function in less iteration, provides accurate estimates and PSO method is satisfactory for the parameter estimation of the 3-p Weibull distribution.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:201-226
    DOI: 10.1016/j.amc.2015.06.043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315008243
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2015.06.043?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. Jukic, Dragan & Bensic, Mirta & Scitovski, Rudolf, 2008. "On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4502-4511, May.
    2. Almalki, Saad J. & Nadarajah, Saralees, 2014. "Modifications of the Weibull distribution: A review," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 32-55.
    3. Babak Abbasi & Luis Rabelo & Mehdi Hosseinkouchack, 2008. "Estimating parameters of the three-parameter Weibull distribution using a neural network," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 2(4), pages 428-445.
    4. 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.
    5. Örkcü, H. Hasan & Aksoy, Ertugˇrul & Dogˇan, Mustafa İsa, 2015. "Estimating the parameters of 3-p Weibull distribution through differential evolution," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 211-224.
    6. Chang, Tian Pau, 2011. "Performance comparison of six numerical methods in estimating Weibull parameters for wind energy application," Applied Energy, Elsevier, vol. 88(1), pages 272-282, January.
    7. Bartolucci, Alfred A. & Singh, Karan P. & Bartolucci, Anne D. & Bae, Sejong, 1999. "Applying medical survival data to estimate the three-parameter Weibull distribution by the method of probability-weighted moments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(4), pages 385-392.
    8. Nagatsuka, Hideki & Kamakura, Toshinari & Balakrishnan, N., 2013. "A consistent method of estimation for the three-parameter Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 210-226.
    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. Acitas, Sukru & Aladag, Cagdas Hakan & Senoglu, Birdal, 2019. "A new approach for estimating the parameters of Weibull distribution via particle swarm optimization: An application to the strengths of glass fibre data," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 116-127.
    2. Yao Liu & Yashun Wang & Zhengwei Fan & Xun Chen & Chunhua Zhang & Yuanyuan Tan, 2020. "A new universal multi-stress acceleration model and multi-parameter estimation method based on particle swarm optimization," Journal of Risk and Reliability, , vol. 234(6), pages 764-778, December.

    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. Örkcü, H. Hasan & Aksoy, Ertugˇrul & Dogˇan, Mustafa İsa, 2015. "Estimating the parameters of 3-p Weibull distribution through differential evolution," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 211-224.
    2. 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.
    3. Chandel, S.S. & Ramasamy, P. & Murthy, K.S.R, 2014. "Wind power potential assessment of 12 locations in western Himalayan region of India," Renewable and Sustainable Energy Reviews, Elsevier, vol. 39(C), pages 530-545.
    4. He, J.Y. & Chan, P.W. & Li, Q.S. & Huang, Tao & Yim, Steve Hung Lam, 2024. "Assessment of urban wind energy resource in Hong Kong based on multi-instrument observations," Renewable and Sustainable Energy Reviews, Elsevier, vol. 191(C).
    5. Pagnini, Luisa C. & Burlando, Massimiliano & Repetto, Maria Pia, 2015. "Experimental power curve of small-size wind turbines in turbulent urban environment," Applied Energy, Elsevier, vol. 154(C), pages 112-121.
    6. Katinas, Vladislovas & Gecevicius, Giedrius & Marciukaitis, Mantas, 2018. "An investigation of wind power density distribution at location with low and high wind speeds using statistical model," Applied Energy, Elsevier, vol. 218(C), pages 442-451.
    7. Chang, Tian-Pau & Ko, Hong-Hsi & Liu, Feng-Jiao & Chen, Pai-Hsun & Chang, Ying-Pin & Liang, Ying-Hsin & Jang, Horng-Yuan & Lin, Tsung-Chi & Chen, Yi-Hwa, 2012. "Fractal dimension of wind speed time series," Applied Energy, Elsevier, vol. 93(C), pages 742-749.
    8. Dongbum Kang & Kyungnam Ko & Jongchul Huh, 2018. "Comparative Study of Different Methods for Estimating Weibull Parameters: A Case Study on Jeju Island, South Korea," Energies, MDPI, vol. 11(2), pages 1-19, February.
    9. 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).
    10. César Henrique Mattos Pires & Felipe M. Pimenta & Carla A. D'Aquino & Osvaldo R. Saavedra & Xuerui Mao & Arcilan T. Assireu, 2020. "Coastal Wind Power in Southern Santa Catarina, Brazil," Energies, MDPI, vol. 13(19), pages 1-23, October.
    11. Liu, Feng Jiao & Chang, Tian Pau, 2011. "Validity analysis of maximum entropy distribution based on different moment constraints for wind energy assessment," Energy, Elsevier, vol. 36(3), pages 1820-1826.
    12. Kang, Dongbum & Ko, Kyungnam & Huh, Jongchul, 2015. "Determination of extreme wind values using the Gumbel distribution," Energy, Elsevier, vol. 86(C), pages 51-58.
    13. Yolanda M. Gómez & Diego I. Gallardo & Carolina Marchant & Luis Sánchez & Marcelo Bourguignon, 2023. "An In-Depth Review of the Weibull Model with a Focus on Various Parameterizations," Mathematics, MDPI, vol. 12(1), pages 1-19, December.
    14. Hannig, Jan & Lai, Randy C.S. & Lee, Thomas C.M., 2014. "Computational issues of generalized fiducial inference," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 849-858.
    15. Oluseyi O. Ajayi & Richard O. Fagbenle & James Katende & Julius M. Ndambuki & David O. Omole & Adekunle A. Badejo, 2014. "Wind Energy Study and Energy Cost of Wind Electricity Generation in Nigeria: Past and Recent Results and a Case Study for South West Nigeria," Energies, MDPI, vol. 7(12), pages 1-27, December.
    16. Bentaha, Mohand-Lounes & Voisin, Alexandre & Marangé, Pascale, 2020. "A decision tool for disassembly process planning under end-of-life product quality," International Journal of Production Economics, Elsevier, vol. 219(C), pages 386-401.
    17. Toja-Silva, Francisco & Lopez-Garcia, Oscar & Peralta, Carlos & Navarro, Jorge & Cruz, Ignacio, 2016. "An empirical–heuristic optimization of the building-roof geometry for urban wind energy exploitation on high-rise buildings," Applied Energy, Elsevier, vol. 164(C), pages 769-794.
    18. XiaoFei, Lu & Min, Liu, 2014. "Hazard rate function in dynamic environment," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 50-60.
    19. Shu, Z.R. & Li, Q.S. & Chan, P.W., 2015. "Investigation of offshore wind energy potential in Hong Kong based on Weibull distribution function," Applied Energy, Elsevier, vol. 156(C), pages 362-373.
    20. Guedes, Kevin S. & de Andrade, Carla F. & Rocha, Paulo A.C. & Mangueira, Rivanilso dos S. & de Moura, Elineudo P., 2020. "Performance analysis of metaheuristic optimization algorithms in estimating the parameters of several wind speed distributions," Applied Energy, Elsevier, vol. 268(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:eee:apmaco:v:268:y:2015:i:c:p:201-226. 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/applied-mathematics-and-computation .

    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.