IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v93y2008i10p1434-1443.html
   My bibliography  Save this article

Weibull extension model: A Bayes study using Markov chain Monte Carlo simulation

Author

Listed:
  • Gupta, Ashutosh
  • Mukherjee, Bhaswati
  • Upadhyay, S.K.

Abstract

Several generalizations of the two-parameter Weibull model have been proposed to model data sets that exhibit complex non-monotone shapes of hazard rate function. The present paper focuses on one such generalization referred to as the Weibull extension model in the literature. Complete Bayesian analysis of the model has been provided using Markov chain Monte Carlo simulation. Finally, a thorough study has been conducted for checking the adequacy of the model for a given data set using some of the graphical and numerical methods based on predictive simulation ideas. A real data set is considered for illustration.

Suggested Citation

  • Gupta, Ashutosh & Mukherjee, Bhaswati & Upadhyay, S.K., 2008. "Weibull extension model: A Bayes study using Markov chain Monte Carlo simulation," Reliability Engineering and System Safety, Elsevier, vol. 93(10), pages 1434-1443.
    • Handle: RePEc:eee:reensy:v:93:y:2008:i:10:p:1434-1443
    DOI: 10.1016/j.ress.2007.10.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832007002542
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2007.10.008?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. Nadarajah, Saralees, 2005. "On the moments of the modified Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 90(1), pages 114-117.
    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. Pang, Wan-Kai & Hou, Shui-Hung & Yu, Wing-Tong, 2007. "On a proper way to select population failure distribution and a stochastic optimization method in parameter estimation," European Journal of Operational Research, Elsevier, vol. 177(1), pages 604-611, February.
    4. Chen, Zhenmin, 2000. "A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 155-161, August.
    5. Zhang, L.F. & Xie, M. & Tang, L.C., 2007. "A study of two estimation approaches for parameters of Weibull distribution based on WPP," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 360-368.
    6. Mark Bebbington & Chin-Diew Lai & Ričardas Zitikis, 2007. "Optimum Burn-in Time for a Bathtub Shaped Failure Distribution," Methodology and Computing in Applied Probability, Springer, vol. 9(1), pages 1-20, March.
    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. Soliman, Ahmed A. & Abd-Ellah, Ahmed H. & Abou-Elheggag, Naser A. & Ahmed, Essam A., 2012. "Modified Weibull model: A Bayes study using MCMC approach based on progressive censoring data," Reliability Engineering and System Safety, Elsevier, vol. 100(C), pages 48-57.
    2. Tien Thanh Thach & Radim Bris, 2020. "Improved new modified Weibull distribution: A Bayes study using Hamiltonian Monte Carlo simulation," Journal of Risk and Reliability, , vol. 234(3), pages 496-511, June.
    3. 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).
    4. Li, Der-Chiang & Lin, Liang-Sian, 2013. "A new approach to assess product lifetime performance for small data sets," European Journal of Operational Research, Elsevier, vol. 230(2), pages 290-298.
    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).

    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. 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.
    2. 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.
    3. 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.
    4. Silva, Rodrigo B. & Bourguignon, Marcelo & Dias, Cícero R.B. & Cordeiro, Gauss M., 2013. "The compound class of extended Weibull power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 352-367.
    5. S. Nadarajah & S. Bakar, 2013. "A new R package for actuarial survival models," Computational Statistics, Springer, vol. 28(5), pages 2139-2160, October.
    6. 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.
    7. Silva, Giovana O. & Ortega, Edwin M.M. & Cordeiro, Gauss M., 2009. "A log-extended Weibull regression model," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4482-4489, October.
    8. 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).
    9. Bebbington, Mark & Lai, Chin-Diew & Wellington, Morgan & Zitikis, RiÄ ardas, 2012. "The discrete additive Weibull distribution: A bathtub-shaped hazard for discontinuous failure data," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 37-44.
    10. 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.
    11. Braglia, Marcello & Carmignani, Gionata & Frosolini, Marco & Zammori, Francesco, 2012. "Data classification and MTBF prediction with a multivariate analysis approach," Reliability Engineering and System Safety, Elsevier, vol. 97(1), pages 27-35.
    12. Barriga, Gladys D.C. & Louzada-Neto, Franscisco & Cancho, Vicente G., 2011. "The complementary exponential power lifetime model," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1250-1259, March.
    13. Li, Der-Chiang & Lin, Liang-Sian, 2013. "A new approach to assess product lifetime performance for small data sets," European Journal of Operational Research, Elsevier, vol. 230(2), pages 290-298.
    14. Wenjie Zhang & Wenhao Gui, 2022. "Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II Censoring," Mathematics, MDPI, vol. 10(9), pages 1-21, May.
    15. Mahmoud M. Mansour & Mohammed A. Farsi & Salah M. Mohamed & Enayat M. Abd Elrazik, 2021. "Modeling the COVID-19 Pandemic Dynamics in Egypt and Saudi Arabia," Mathematics, MDPI, vol. 9(8), pages 1-13, April.
    16. Przemysław Bodziony & Michał Patyk, 2024. "The Influence of the Mining Operation Environment on the Energy Consumption and Technical Availability of Truck Haulage Operations in Surface Mines," Energies, MDPI, vol. 17(11), pages 1-18, May.
    17. Shu-Fei Wu & Meng-Zong Song, 2023. "Experimental Design for Progressive Type I Interval Censoring on the Lifetime Performance Index of Chen Lifetime Distribution," Mathematics, MDPI, vol. 11(6), pages 1-16, March.
    18. 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.
    19. Sarhan, Ammar M. & Apaloo, Joseph, 2013. "Exponentiated modified Weibull extension distribution," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 137-144.
    20. MARK BEBBINGTON & CHIN-DIEW LAI & RIcARDAS ZITIKIS, 2011. "Modelling Deceleration in Senescent Mortality," Mathematical Population Studies, Taylor & Francis Journals, vol. 18(1), pages 18-37.

    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:93:y:2008:i:10:p:1434-1443. 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.