IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i2p162-d312322.html
   My bibliography  Save this article

Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution

Author

Listed:
  • Hua Xin

    (School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, Heilongjiang, China)

  • Zhifang Liu

    (School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, Heilongjiang, China)

  • Yuhlong Lio

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

  • Tzong-Ru Tsai

    (Department of Statistics, Tamkang University, Tamsui District, New Taipei City 25137, Taiwan)

Abstract

The Burr type XII (BurrXII) distribution is very flexible for modeling and has earned much attention in the past few decades. In this study, the maximum likelihood estimation method and two Bayesian estimation procedures are investigated based on constant-stress accelerated life test (ALT) samples, which are obtained from the doubly truncated three-parameter BurrXII distribution. Because computational difficulty occurs for maximum likelihood estimation method, two Bayesian procedures are suggested to estimate model parameters and lifetime quantiles under the normal use condition. A Markov Chain Monte Carlo approach using the Metropolis–Hastings algorithm via Gibbs sampling is built to obtain Bayes estimators of the model parameters and to construct credible intervals. The proposed Bayesian estimation procedures are simple for practical use, and the obtained Bayes estimates are reliable for evaluating the reliability of lifetime products based on ALT samples. Monte Carlo simulations were conducted to evaluate the performance of these two Bayesian estimation procedures. Simulation results show that the second Bayesian estimation procedure outperforms the first Bayesian estimation procedure in terms of bias and mean squared error when users do not have sufficient knowledge to set up hyperparameters in the prior distributions. Finally, a numerical example about oil-well pumps is used for illustration.

Suggested Citation

  • Hua Xin & Zhifang Liu & Yuhlong Lio & Tzong-Ru Tsai, 2020. "Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution," Mathematics, MDPI, vol. 8(2), pages 1-23, January.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:162-:d:312322
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/2/162/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/8/2/162/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Liang Wang, 2016. "Interval estimation for a lower-truncated distribution based on the double Type-II censored sample," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(19), pages 5679-5692, October.
    2. Ajit Chaturvedi & Reza Arabi Belaghi & Ananya Malhotra, 2018. "Preliminary test estimators of the reliability characteristics for the three parameters Burr XII distribution based on records," 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. 9(6), pages 1260-1278, December.
    3. repec:bot:journl:v:71:y:2011:i:4:p:421-435 is not listed on IDEAS
    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. Hanieh Panahi & Abdolreza Sayyareh, 2014. "Parameter estimation and prediction of order statistics for the Burr Type XII distribution with Type II censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(1), pages 215-232, January.
    6. Nesar Ahmad & A. Islam, 1996. "Optimal accelerated life test designs for Burr type XII distributions under periodic inspection and type I censoring," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(8), pages 1049-1077, December.
    7. Abdel-Hamid, Alaa H., 2009. "Constant-partially accelerated life tests for Burr type-XII distribution with progressive type-II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2511-2523, May.
    8. Mustafa Nadar & Alexandros Papadopoulos, 2011. "Bayesian analysis for the Burr type XII distribution based on record values," Statistica, Department of Statistics, University of Bologna, vol. 71(4), pages 421-435.
    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. Starling, James K. & Mastrangelo, Christina & Choe, Youngjun, 2021. "Improving Weibull distribution estimation for generalized Type I censored data using modified SMOTE," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    2. Chang, Ping-Chen, 2022. "MC-based simulation approach for two-terminal multi-state network reliability evaluation without knowing d-MCs," Reliability Engineering and System Safety, Elsevier, vol. 220(C).
    3. Hanieh Panahi, 2016. "Model Selection Test for the Heavy-Tailed Distributions under Censored Samples with Application in Financial Data," IJFS, MDPI, vol. 4(4), pages 1-14, December.
    4. Jessie Marie Byrnes & Yu-Jau Lin & Tzong-Ru Tsai & Yuhlong Lio, 2019. "Bayesian Inference of δ = P ( X < Y ) for Burr Type XII Distribution Based on Progressively First Failure-Censored Samples," Mathematics, MDPI, vol. 7(9), pages 1-24, September.
    5. Liang Wang & Sanku Dey & Yogesh Mani Tripathi, 2022. "Classical and Bayesian Inference of the Inverse Nakagami Distribution Based on Progressive Type-II Censored Samples," Mathematics, MDPI, vol. 10(12), pages 1-18, June.
    6. M. M. Mohie El-Din & A. M. Abd El-Raheem & S. O. Abd El-Azeem, 2021. "On Step-Stress Accelerated Life Testing for Power Generalized Weibull Distribution Under Progressive Type-II Censoring," Annals of Data Science, Springer, vol. 8(3), pages 629-644, September.
    7. R. Arabi Belaghi & M. Noori Asl, 2019. "Estimation based on progressively type-I hybrid censored data from the Burr XII distribution," Statistical Papers, Springer, vol. 60(3), pages 761-803, June.
    8. Hanieh Panahi, 2019. "Estimation for the parameters of the Burr Type XII distribution under doubly censored sample with application to microfluidics data," 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(4), pages 510-518, August.
    9. Amal S. Hassan & Said G. Nassr & Sukanta Pramanik & Sudhansu S. Maiti, 2020. "Estimation in Constant Stress Partially Accelerated Life Tests for Weibull Distribution Based on Censored Competing Risks Data," Annals of Data Science, Springer, vol. 7(1), pages 45-62, March.
    10. Xinjing Wang & Wenhao Gui, 2021. "Bayesian Estimation of Entropy for Burr Type XII Distribution under Progressive Type-II Censored Data," Mathematics, MDPI, vol. 9(4), pages 1-19, February.
    11. R. Arabi Belaghi & M. Arashi & S. Tabatabaey, 2014. "Improved confidence intervals for the scale parameter of Burr XII model based on record values," Computational Statistics, Springer, vol. 29(5), pages 1153-1173, October.
    12. Shuto, Susumu & Amemiya, Takashi, 2022. "Sequential Bayesian inference for Weibull distribution parameters with initial hyperparameter optimization for system reliability estimation," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    13. M. M. Mohie El-Din & S. E. Abu-Youssef & Nahed S. A. Ali & A. M. Abd El-Raheem, 2016. "Estimation in constant-stress accelerated life tests for extension of the exponential distribution under progressive censoring," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 253-273, August.
    14. Nagode, Marko & Oman, Simon & Klemenc, Jernej & Panić, Branislav, 2023. "Gumbel mixture modelling for multiple failure data," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    15. Chang, Ping-Chen & Huang, Ding-Hsiang & Lin, Yi-Kuei & Nguyen, Thi-Phuong, 2021. "Reliability and maintenance models for a time-related multi-state flow network via d-MC approach," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    16. M. Nassar & S. G. Nassr & S. Dey, 2017. "Analysis of Burr Type-XII Distribution Under Step Stress Partially Accelerated Life Tests with Type-I and Adaptive Type-II Progressively Hybrid Censoring Schemes," Annals of Data Science, Springer, vol. 4(2), pages 227-248, 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:8:y:2020:i:2:p:162-:d:312322. 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.