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

Hua Xin, Zhifang Liu, Yuhlong Lio and Tzong-Ru Tsai
Additional contact information
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

Mathematics, 2020, vol. 8, issue 2, 1-23

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.

Keywords: accelerated life test; Burr type XII distribution; Markov chain Monte Carlo; maximum likelihood estimation; Newton–Raphson method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/2/162/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/2/162/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:2:p:162-:d:312322

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().