IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i10p2830-2839.html
   My bibliography  Save this article

Objective Bayesian analysis of accelerated competing failure models under Type-I censoring

Author

Listed:
  • Xu, Ancha
  • Tang, Yincai

Abstract

This paper discusses the Bayesian inference of accelerated life tests (ALT) in the presence of competing failure causes. The time to failure due to a specific cause is described by a Weibull distribution. A two-stage approach is utilized to obtain the estimates of parameters in the model. We use the Bayesian method to estimate the parameters of the distribution of component lifetimes in the first stage, in which two noninformative priors (Jeffreys prior and reference prior) are derived in the case of ALT, and based on these two priors we present the Gibbs sampling procedures to obtain the posterior estimates of the parameters. Besides, to overcome the problem of improper posterior densities under some conditions, we modify the likelihood function to make the posterior densities proper. In the second stage, parameters in the accelerating function are obtained by least squares approach. A numerical example is given to show the effectiveness of the method and a real data from Nelson (1990) is analyzed.

Suggested Citation

  • Xu, Ancha & Tang, Yincai, 2011. "Objective Bayesian analysis of accelerated competing failure models under Type-I censoring," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2830-2839, October.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:10:p:2830-2839
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311001381
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    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. Liudong Xing & Chaonan Wang & Gregory Levitin, 2012. "Competing failure analysis in non-repairable binary systems subject to functional dependence," Journal of Risk and Reliability, , vol. 226(4), pages 406-416, August.
    2. Herbert Hove & Frank Beichelt & Parmod K. Kapur, 2017. "Estimation of the Frank copula model for dependent competing risks in accelerated life testing," 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. 8(4), pages 673-682, December.
    3. Kazianka, Hannes, 2012. "Objective Bayesian analysis for the normal compositional model," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1528-1544.
    4. Guan, Qiang & Tang, Yincai & Xu, Ancha, 2013. "Objective Bayesian analysis for bivariate Marshall–Olkin exponential distribution," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 299-313.

    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. Pang, W. K. & Yang, Z. H. & Hou, S. H. & Leung, P. K., 2002. "Non-uniform random variate generation by the vertical strip method," European Journal of Operational Research, Elsevier, vol. 142(3), pages 595-609, November.
    2. Samantha Leorato & Maura Mezzetti, 2015. "Spatial Panel Data Model with error dependence: a Bayesian Separable Covariance Approach," CEIS Research Paper 338, Tor Vergata University, CEIS, revised 09 Apr 2015.
    3. Z. Rezaei Ghahroodi & M. Ganjali, 2013. "A Bayesian approach for analysing longitudinal nominal outcomes using random coefficients transitional generalized logit model: an application to the labour force survey data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(7), pages 1425-1445, July.
    4. Antonello Loddo & Shawn Ni & Dongchu Sun, 2011. "Selection of Multivariate Stochastic Volatility Models via Bayesian Stochastic Search," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 342-355, July.
    5. Chen, Ming-Hui & Ibrahim, Joseph G. & Sinha, Debajyoti, 2004. "A new joint model for longitudinal and survival data with a cure fraction," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 18-34, October.
    6. Nandram, Balgobin & Zelterman, Daniel, 2007. "Computational Bayesian inference for estimating the size of a finite population," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2934-2945, March.
    7. Samaneh Mahabadi & Mojtaba Ganjali, 2015. "A Bayesian approach for sensitivity analysis of incomplete multivariate longitudinal data with potential nonrandom dropout," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 397-417, December.
    8. Fuentes-García, Ruth & Mena, Ramsés H. & Walker, Stephen G., 2009. "A nonparametric dependent process for Bayesian regression," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1112-1119, April.
    9. Brewer, M. J. & Aitken, C. G. G. & Talbot, M., 1996. "A comparison of hybrid strategies for Gibbs sampling in mixed graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 21(3), pages 343-365, March.
    10. Kozumi, Hideo, 2004. "Posterior analysis of latent competing risk models by parallel tempering," Computational Statistics & Data Analysis, Elsevier, vol. 46(3), pages 441-458, June.
    11. H. Abebe & F. Tan & G. Breukelen & M. Berger, 2014. "Robustness of Bayesian D-optimal design for the logistic mixed model against misspecification of autocorrelation," Computational Statistics, Springer, vol. 29(6), pages 1667-1690, December.
    12. Deschamps, Philippe J., 2012. "Bayesian estimation of generalized hyperbolic skewed student GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3035-3054.
    13. Hattam, Caroline & Holloway, Garth J., 2007. "Bayes Estimates of Time to Organic Certification," 81st Annual Conference, April 2-4, 2007, Reading University, UK 7979, Agricultural Economics Society.
    14. Peter F. Thall & Lurdes Y. T. Inoue & Thomas G. Martin, 2002. "Adaptive Decision Making in a Lymphocyte Infusion Trial," Biometrics, The International Biometric Society, vol. 58(3), pages 560-568, September.
    15. M. Ghosh & B. Carlin & M. Srivastava, 1995. "Probability matching priors for linear calibration," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(2), pages 333-357, December.
    16. Pang, Wan Kai & Yu, Bosco Wing-Tong & Troutt, Marvin D. & Hou, Shui Hung, 2008. "A simulation-based approach to the study of coefficient of variation of dividend yields," European Journal of Operational Research, Elsevier, vol. 189(2), pages 559-569, September.
    17. Martijn G. de Jong & Donald R. Lehmann & Oded Netzer, 2012. "State-Dependence Effects in Surveys," Marketing Science, INFORMS, vol. 31(5), pages 838-854, September.
    18. David B. Dunson, 2001. "Bayesian Modeling of the Level and Duration of Fertility in the Menstrual Cycle," Biometrics, The International Biometric Society, vol. 57(4), pages 1067-1073, December.
    19. Chakraborty, Sounak, 2009. "Simultaneous cancer classification and gene selection with Bayesian nearest neighbor method: An integrated approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1462-1474, February.
    20. Mike G. Tsionas, 2023. "Linex and double-linex regression for parameter estimation and forecasting," Annals of Operations Research, Springer, vol. 323(1), pages 229-245, April.

    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:csdana:v:55:y:2011:i:10:p:2830-2839. 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: http://www.elsevier.com/locate/csda .

    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.