IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v158y2017icp93-105.html
   My bibliography  Save this article

On the q-Weibull distribution for reliability applications: An adaptive hybrid artificial bee colony algorithm for parameter estimation

Author

Listed:
  • Xu, Meng
  • Droguett, Enrique López
  • Lins, Isis Didier
  • das Chagas Moura, Márcio

Abstract

The q-Weibull model is based on the Tsallis non-extensive entropy [22] and is able to model various behaviors of the hazard rate function, including bathtub curves, by using a single set of parameters. Despite its flexibility, the q-Weibull has not been widely used in reliability applications partly because of the complicated parameters estimation. In this work, the parameters of the q-Weibull are estimated by the maximum likelihood (ML) method. Due to the intricate system of nonlinear equations, derivative-based optimization methods may fail to converge. Thus, the heuristic optimization method of artificial bee colony (ABC) is used instead. To deal with the slow convergence of ABC, it is proposed an adaptive hybrid ABC (AHABC) algorithm that dynamically combines Nelder-Mead simplex search method with ABC for the ML estimation of the q-Weibull parameters. Interval estimates for the q-Weibull parameters, including confidence intervals based on the ML asymptotic theory and on bootstrap methods, are also developed. The AHABC is validated via numerical experiments involving the q-Weibull ML for reliability applications and results show that it produces faster and more accurate convergence when compared to ABC and similar approaches. The estimation procedure is applied to real reliability failure data characterized by a bathtub-shaped hazard rate.

Suggested Citation

  • Xu, Meng & Droguett, Enrique López & Lins, Isis Didier & das Chagas Moura, Márcio, 2017. "On the q-Weibull distribution for reliability applications: An adaptive hybrid artificial bee colony algorithm for parameter estimation," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 93-105.
    • Handle: RePEc:eee:reensy:v:158:y:2017:i:c:p:93-105
    DOI: 10.1016/j.ress.2016.10.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S095183201630655X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2016.10.012?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. 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.
    2. Fan, Shu-Kai S. & Zahara, Erwie, 2007. "A hybrid simplex search and particle swarm optimization for unconstrained optimization," European Journal of Operational Research, Elsevier, vol. 181(2), pages 527-548, September.
    3. Carrasco, Jalmar M.F. & Ortega, Edwin M.M. & Cordeiro, Gauss M., 2008. "A generalized modified Weibull distribution for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 450-462, December.
    4. He, Bo & Cui, Weimin & Du, Xiaofeng, 2016. "An additive modified Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 28-37.
    5. Lemonte, Artur J., 2013. "A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 149-170.
    6. 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.
    7. Picoli, S. & Mendes, R.S. & Malacarne, L.C., 2003. "q-exponential, Weibull, and q-Weibull distributions: an empirical analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(3), pages 678-688.
    8. Costa, U.M.S. & Freire, V.N. & Malacarne, L.C. & Mendes, R.S. & Picoli Jr., S. & de Vasconcelos, E.A. & da Silva Jr., E.F., 2006. "An improved description of the dielectric breakdown in oxides based on a generalized Weibull distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 209-215.
    9. Márcio das Chagas Moura & Enrique López Droguett & Paulo Renato Alves Firmino & Ricardo José Ferreira, 2014. "A competing risk model for dependent and imperfect condition–based preventive and corrective maintenances," Journal of Risk and Reliability, , vol. 228(6), pages 590-605, December.
    10. Bagheri, S.F. & Bahrami Samani, E. & Ganjali, M., 2016. "The generalized modified Weibull power series distribution: Theory and applications," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 136-160.
    11. Winfried Stute & Wenceslao Manteiga & Manuel Quindimil, 1993. "Bootstrap based goodness-of-fit-tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 243-256, December.
    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. Peña-Ramírez, Fernando A. & Guerra, Renata Rojas & Canterle, Diego Ramos & Cordeiro, Gauss M., 2020. "The logistic Nadarajah–Haghighi distribution and its associated regression model for reliability applications," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    2. Xiang Jia & Saralees Nadarajah & Bo Guo, 2020. "Inference on q-Weibull parameters," Statistical Papers, Springer, vol. 61(2), pages 575-593, April.
    3. Ahmad, Abd EL-Baset A. & Ghazal, M.G.M., 2020. "Exponentiated additive Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    4. Zhu, Tiefeng, 2020. "Reliability estimation for two-parameter Weibull distribution under block censoring," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    5. Negreiros, Ana Cláudia Souza Vidal de & Lins, Isis Didier & Moura, Márcio José das Chagas & Droguett, Enrique López, 2020. "Reliability data analysis of systems in the wear-out phase using a (corrected) q-Exponential likelihood," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    6. Zhang, Fode & Ng, Hon Keung Tony & Shi, Yimin, 2018. "On alternative q-Weibull and q-extreme value distributions: Properties and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1171-1190.
    7. Shakhatreh, Mohammed K. & Lemonte, Artur J. & Moreno–Arenas, Germán, 2019. "The log-normal modified Weibull distribution and its reliability implications," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 6-22.
    8. 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.
    9. Reyes-Santias, Francisco & Reboredo, Juan C. & de Assis, Edilson Machado & Rivera-Castro, Miguel A., 2021. "Does length of hospital stay reflect power-law behavior? A q-Weibull density approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(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. Negreiros, Ana Cláudia Souza Vidal de & Lins, Isis Didier & Moura, Márcio José das Chagas & Droguett, Enrique López, 2020. "Reliability data analysis of systems in the wear-out phase using a (corrected) q-Exponential likelihood," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    2. He, Bo & Cui, Weimin & Du, Xiaofeng, 2016. "An additive modified Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 28-37.
    3. Mehrzad Ghorbani & Seyed Fazel Bagheri & Mojtaba Alizadeh, 2017. "A New Family of Distributions: The Additive Modified Weibull Odd Log-logistic-G Poisson Family, Properties and Applications," Annals of Data Science, Springer, vol. 4(2), pages 249-287, June.
    4. C. Satheesh Kumar & S. Dharmaja, 2014. "On some properties of Kies distribution," METRON, Springer;Sapienza Università di Roma, vol. 72(1), pages 97-122, April.
    5. Ahmad, Abd EL-Baset A. & Ghazal, M.G.M., 2020. "Exponentiated additive Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    6. Filippo Domma & Francesca Condino & Božidar V. Popović, 2017. "A new generalized weighted Weibull distribution with decreasing, increasing, upside-down bathtub, N-shape and M-shape hazard rate," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 2978-2993, December.
    7. Xiang Jia & Saralees Nadarajah & Bo Guo, 2020. "Inference on q-Weibull parameters," Statistical Papers, Springer, vol. 61(2), pages 575-593, April.
    8. Gauss M. Cordeiro & Giovana O. Silva & Edwin M. M. Ortega, 2016. "An extended-G geometric family," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-16, December.
    9. Hassan S. Bakouch & Abdus Saboor & Muhammad Nauman Khan, 2021. "Modified Beta Linear Exponential Distribution with Hydrologic Applications," Annals of Data Science, Springer, vol. 8(1), pages 131-157, March.
    10. Zhang, Tieling & Dwight, Richard, 2013. "Choosing an optimal model for failure data analysis by graphical approach," Reliability Engineering and System Safety, Elsevier, vol. 115(C), pages 111-123.
    11. 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.
    12. Freddy Hernández & Viviana Giampaoli, 2018. "The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model," Stats, MDPI, vol. 1(1), pages 1-29, May.
    13. Mustapha Muhammad & Rashad A. R. Bantan & Lixia Liu & Christophe Chesneau & Muhammad H. Tahir & Farrukh Jamal & Mohammed Elgarhy, 2021. "A New Extended Cosine—G Distributions for Lifetime Studies," Mathematics, MDPI, vol. 9(21), pages 1-29, October.
    14. Maha A Aldahlan & Farrukh Jamal & Christophe Chesneau & Ibrahim Elbatal & Mohammed Elgarhy, 2020. "Exponentiated power generalized Weibull power series family of distributions: Properties, estimation and applications," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-25, March.
    15. Bagheri, S.F. & Bahrami Samani, E. & Ganjali, M., 2016. "The generalized modified Weibull power series distribution: Theory and applications," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 136-160.
    16. Almalki, Saad J. & Yuan, Jingsong, 2013. "A new modified Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 164-170.
    17. K. Jose & Shanoja Naik & Miroslav Ristić, 2010. "Marshall–Olkin q-Weibull distribution and max–min processes," Statistical Papers, Springer, vol. 51(4), pages 837-851, December.
    18. Peña-Ramírez, Fernando A. & Guerra, Renata Rojas & Canterle, Diego Ramos & Cordeiro, Gauss M., 2020. "The logistic Nadarajah–Haghighi distribution and its associated regression model for reliability applications," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    19. Singla, Neetu & Jain, Kanchan & Kumar Sharma, Suresh, 2012. "The Beta Generalized Weibull distribution: Properties and applications," Reliability Engineering and System Safety, Elsevier, vol. 102(C), pages 5-15.
    20. Paranaíba, Patrícia F. & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R., 2011. "The beta Burr XII distribution with application to lifetime data," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1118-1136, February.

    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:158:y:2017:i:c:p:93-105. 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.