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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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