IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i11p1261-d566237.html
   My bibliography  Save this article

E-Bayesian Estimation of Reliability Characteristics of a Weibull Distribution with Applications

Author

Listed:
  • Hassan M. Okasha

    (Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo 11884, Egypt)

  • Heba S. Mohammed

    (Mathematical Sciences Department, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh 11671, Saudi Arabia
    Department of Mathematics, Faculty of Science, New Valley University, El Kharga 72511, Egypt)

  • Yuhlong Lio

    (Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA)

Abstract

Given a progressively type-II censored sample, the E-Bayesian estimates, which are the expected Bayesian estimates over the joint prior distributions of the hyper-parameters in the gamma prior distribution of the unknown Weibull rate parameter, are developed for any given function of unknown rate parameter under the square error loss function. In order to study the impact from the selection of hyper-parameters for the prior, three different joint priors of the hyper-parameters are utilized to establish the theoretical properties of the E-Bayesian estimators for four functions of the rate parameter, which include an identity function (that is, a rate parameter) as well as survival, hazard rate and quantile functions. A simulation study is also conducted to compare the three E-Bayesian and a Bayesian estimate as well as the maximum likelihood estimate for each of the four functions considered. Moreover, two real data sets from a medical study and industry life test, respectively, are used for illustration. Finally, concluding remarks are addressed.

Suggested Citation

  • Hassan M. Okasha & Heba S. Mohammed & Yuhlong Lio, 2021. "E-Bayesian Estimation of Reliability Characteristics of a Weibull Distribution with Applications," Mathematics, MDPI, vol. 9(11), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1261-:d:566237
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/11/1261/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/11/1261/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hassan M. Okasha & Chuanmei Wang & Jianhua Wang, 2020. "E-Bayesian Prediction for the Burr XII Model Based on Type-II Censored Data with Two Samples," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-13, February.
    2. George C. Canavos & Chris P. Taokas, 1973. "Bayesian Estimation of Life Parameters in the Weibull Distribution," Operations Research, INFORMS, vol. 21(3), pages 755-763, June.
    3. L.F. Zhang & M. Xie & L.C. Tang, 2008. "On Weighted Least Squares Estimation for the Parameters of Weibull Distribution," Springer Series in Reliability Engineering, in: Hoang Pham (ed.), Recent Advances in Reliability and Quality in Design, chapter 3, pages 57-84, Springer.
    4. Zhang, Tieling & Xie, Min, 2011. "On the upper truncated Weibull distribution and its reliability implications," Reliability Engineering and System Safety, Elsevier, vol. 96(1), pages 194-200.
    5. Sanjay Kumar Singh & Umesh Singh & Vikas Kumar Sharma, 2013. "Bayesian Estimation and Prediction for Flexible Weibull Model under Type-II Censoring Scheme," Journal of Probability and Statistics, Hindawi, vol. 2013, pages 1-16, July.
    6. Essam A. Ahmed, 2014. "Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 752-768, April.
    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. Ranjan, Rakesh & Sen, Rijji & Upadhyay, Satyanshu K., 2021. "Bayes analysis of some important lifetime models using MCMC based approaches when the observations are left truncated and right censored," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    2. Zhou, Chongwen & Chinnam, Ratna Babu & Dalkiran, Evrim & Korostelev, Alexander, 2017. "Bayesian approach to hazard rate models for early detection of warranty and reliability problems using upstream supply chain information," International Journal of Production Economics, Elsevier, vol. 193(C), pages 316-331.
    3. Nesreen M. Al-Olaimat & Husam A. Bayoud & Mohammad Z. Raqab, 2021. "Record data from Kies distribution and related statistical inferences," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 153-170, December.
    4. Al-Olaimat Nesreen M. & Bayoud Husam A. & Raqab Mohammad Z., 2021. "Record data from Kies distribution and related statistical inferences," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 153-170, December.
    5. Hryniewicz, Olgierd, 2016. "Bayes statistical decisions with random fuzzy data—an application in reliability," Reliability Engineering and System Safety, Elsevier, vol. 151(C), pages 20-33.
    6. C. Satheesh Kumar & Subha R. Nair, 2021. "A generalization to the log-inverse Weibull distribution and its applications in cancer research," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-30, December.
    7. 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.
    8. Jiang, R. & Murthy, D.N.P., 2011. "A study of Weibull shape parameter: Properties and significance," Reliability Engineering and System Safety, Elsevier, vol. 96(12), pages 1619-1626.
    9. Sidibe, I.B. & Khatab, A. & Diallo, C. & Kassambara, A., 2017. "Preventive maintenance optimization for a stochastically degrading system with a random initial age," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 255-263.
    10. Ahtasham Gul & Muhammad Mohsin & Muhammad Adil & Mansoor Ali, 2021. "A modified truncated distribution for modeling the heavy tail, engineering and environmental sciences data," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-24, April.
    11. de Jonge, Bram & Dijkstra, Arjan S. & Romeijnders, Ward, 2015. "Cost benefits of postponing time-based maintenance under lifetime distribution uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 15-21.
    12. Mohammad Z. Raqab & Omar M. Bdair & Fahad M. Al-Aboud, 2018. "Inference for the two-parameter bathtub-shaped distribution based on record data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 229-253, April.
    13. Xuehua Hu & Wenhao Gui, 2018. "Bayesian and Non-Bayesian Inference for the Generalized Pareto Distribution Based on Progressive Type II Censored Sample," Mathematics, MDPI, vol. 6(12), pages 1-26, December.
    14. Pramendra Singh Pundir & Puneet Kumar Gupta, 2018. "Reliability Estimation in Load-Sharing System Model with Application to Real Data," Annals of Data Science, Springer, vol. 5(1), pages 69-91, March.
    15. Ahmad, Abd EL-Baset A. & Ghazal, M.G.M., 2020. "Exponentiated additive Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    16. Ziyad A. Alhussain & Essam A. Ahmed, 2020. "Estimation of exponentiated Nadarajah-Haghighi distribution under progressively type-II censored sample with application to bladder cancer data," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 631-657, June.
    17. Farha Sultana & Yogesh Mani Tripathi & Shuo-Jye Wu & Tanmay Sen, 2022. "Inference for Kumaraswamy Distribution Based on Type I Progressive Hybrid Censoring," Annals of Data Science, Springer, vol. 9(6), pages 1283-1307, December.
    18. Siyi Chen & Wenhao Gui, 2020. "Statistical Analysis of a Lifetime Distribution with a Bathtub-Shaped Failure Rate Function under Adaptive Progressive Type-II Censoring," Mathematics, MDPI, vol. 8(5), pages 1-21, April.
    19. Kousik Maiti & Suchandan Kayal, 2019. "Estimation for the generalized Fréchet distribution under progressive censoring scheme," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(5), pages 1276-1301, October.
    20. Muhammad Ijaz & Syed Muhammad Asim & Alamgir & Muhammad Farooq & Sajjad Ahmad Khan & Sadaf Manzoor, 2020. "A Gull Alpha Power Weibull distribution with applications to real and simulated data," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.

    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:9:y:2021:i:11:p:1261-:d:566237. 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.