IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v176y2018icp13-26.html
   My bibliography  Save this article

A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems

Author

Listed:
  • Prataviera, Fábio
  • Ortega, Edwin M.M.
  • Cordeiro, Gauss M.
  • Pescim, Rodrigo R.
  • Verssani, Bruna A.W.

Abstract

We define and study a four-parameter model called the generalized odd log-logistic flexible Weibull distribution. The new distribution can be used effectively in the context of reliability since it accommodates different hazard rate forms such as monotone, unimodal, bathtub-shaped, increasing-decreasing-increasing, among possible others. We provide an extensive study of the quantile function. Further, we present a parametric regression model based on the new distribution as an alternative to the location-scale regression model. An important property of this new regression model is that it does not need the assumption of proportional risks. We use the method of maximum likelihood for estimating the model parameters and perform various simulations for different parameter settings, sample sizes and censoring percentages. Applications in real engineering data sets illustrate the flexibility of the proposed models.

Suggested Citation

  • Prataviera, Fábio & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R. & Verssani, Bruna A.W., 2018. "A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 13-26.
    • Handle: RePEc:eee:reensy:v:176:y:2018:i:c:p:13-26
    DOI: 10.1016/j.ress.2018.03.034
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832017309584
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2018.03.034?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. Hashimoto, Elizabeth M. & Ortega, Edwin M.M. & Cancho, Vicente G. & Cordeiro, Gauss M., 2010. "The log-exponentiated Weibull regression model for interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1017-1035, April.
    2. 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.
    3. Alexander, Carol & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Sarabia, José María, 2012. "Generalized beta-generated distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1880-1897.
    4. Sangun Park & Jiwhan Park, 2018. "A general class of flexible Weibull distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(4), pages 767-778, February.
    5. 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.
    6. Giovana O. Silva & Edwin M.M. Ortega & Gilberto A. Paula, 2011. "Residuals for log-Burr XII regression models in survival analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1435-1445, June.
    7. Krivtsov, Vasiliy V., 2007. "Practical extensions to NHPP application in repairable system reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 560-562.
    8. Ahmed Z. Afify & Haitham M. Yousof & Gauss M. Cordeiro & Edwin M. M. Ortega & Zohdy M. Nofal, 2016. "The Weibull Fréchet distribution and its applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2608-2626, October.
    9. Rodrigo R. Pescim & Edwin M. M. Ortega & Gauss M. Cordeiro & Morad Alizadeh, 2017. "A new log-location regression model: estimation, influence diagnostics and residual analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(2), pages 233-252, January.
    10. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    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. 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.
    3. José H. Dias Gonçalves & João J. Ferreira Gomes & Lihki Rubio & Filipe R. Ramos, 2023. "A Generalized Log Gamma Approach: Theoretical Contributions and an Application to Companies’ Life Expectancy," Mathematics, MDPI, vol. 11(23), pages 1-23, November.
    4. 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.
    5. 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.
    6. Abba, Badamasi & Wang, Hong & Bakouch, Hassan S., 2022. "A reliability and survival model for one and two failure modes system with applications to complete and censored datasets," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    7. 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.
    8. Ahmad, Abd EL-Baset A. & Ghazal, M.G.M., 2020. "Exponentiated additive Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 193(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. Saralees Nadarajah & Gauss Cordeiro & Edwin Ortega, 2013. "The exponentiated Weibull distribution: a survey," Statistical Papers, Springer, vol. 54(3), pages 839-877, August.
    2. Sanku Dey & Vikas Kumar Sharma & Mhamed Mesfioui, 2017. "A New Extension of Weibull Distribution with Application to Lifetime Data," Annals of Data Science, Springer, vol. 4(1), pages 31-61, March.
    3. Muhammad H. Tahir & Muhammad Adnan Hussain & Gauss M. Cordeiro & M. El-Morshedy & M. S. Eliwa, 2020. "A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension," Mathematics, MDPI, vol. 8(11), pages 1-28, November.
    4. Boikanyo Makubate & Fastel Chipepa & Broderick Oluyede & Peter O. Peter, 2021. "The Marshall-Olkin Half Logistic-G Family of Distributions With Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 120-120, March.
    5. Showkat Ahmad Lone & Tabassum Naz Sindhu & Marwa K. H. Hassan & Tahani A. Abushal & Sadia Anwar & Anum Shafiq, 2023. "Theoretical Structure and Applications of a Newly Enhanced Gumbel Type II Model," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    6. Jiong Liu & R. A. Serota, 2023. "Rethinking Generalized Beta family of distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(2), pages 1-14, February.
    7. Amal S. Hassan & Said G. Nassr, 2019. "Power Lindley-G Family of Distributions," Annals of Data Science, Springer, vol. 6(2), pages 189-210, June.
    8. Fiaz Ahmad Bhatti & G. G. Hamedani & Mustafa Ç. Korkmaz & Munir Ahmad, 2018. "The transmuted geometric-quadratic hazard rate distribution: development, properties, characterizations and applications," Journal of Statistical Distributions and Applications, Springer, vol. 5(1), pages 1-23, December.
    9. 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.
    10. Sajid Hussain & Muhammad Sajid Rashid & Mahmood Ul Hassan & Rashid Ahmed, 2022. "The Generalized Alpha Exponent Power Family of Distributions: Properties and Applications," Mathematics, MDPI, vol. 10(9), pages 1-19, April.
    11. Joseph Thomas Eghwerido & Pelumi E. Oguntunde & Friday Ikechukwu Agu, 2023. "The Alpha Power Marshall-Olkin-G Distribution: Properties, and Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 172-197, February.
    12. 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.
    13. Emrah Altun & Mustafa Ç. Korkmaz & Mahmoud El-Morshedy & Mohamed S. Eliwa, 2021. "A New Flexible Family of Continuous Distributions: The Additive Odd-G Family," Mathematics, MDPI, vol. 9(16), pages 1-17, August.
    14. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    15. Fastel Chipepa & Broderick O. Oluyede & Boikanyo Makubate, 2019. "A New Generalized Family of Odd Lindley-G Distributions With Application," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(6), pages 1-1, November.
    16. Gokarna R. Aryal & Keshav P. Pokhrel & Netra Khanal & Chris P. Tsokos, 2019. "Reliability Models Using the Composite Generalizers of Weibull Distribution," Annals of Data Science, Springer, vol. 6(4), pages 807-829, December.
    17. Francesca Condino & Filippo Domma, 2017. "A new distribution function with bounded support: the reflected generalized Topp-Leone power series distribution," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 51-68, April.
    18. Muhammad H Tahir & Gauss M. Cordeiro, 2016. "Compounding of distributions: a survey and new generalized classes," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-35, December.
    19. M S Eliwa & Emrah Altun & Ziyad Ali Alhussain & Essam A Ahmed & Mukhtar M Salah & Hanan Haj Ahmed & M El-Morshedy, 2021. "A new one-parameter lifetime distribution and its regression model with applications," PLOS ONE, Public Library of Science, vol. 16(2), pages 1-19, February.
    20. Gauss M. Cordeiro & Antonio E. Gomes & Cibele Q. da-Silva & Edwin M. M. Ortega, 2017. "A useful extension of the Burr III distribution," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-15, December.

    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:176:y:2018:i:c:p:13-26. 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.