IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v64y2017i6p490-501.html
   My bibliography  Save this article

Statistical analysis for masked system life data from Marshall‐Olkin Weibull distribution under progressive hybrid censoring

Author

Listed:
  • Jing Cai
  • Yimin Shi
  • Bin Liu

Abstract

This paper considers the statistical analysis of masked data in a series system, where the components are assumed to have Marshall‐Olkin Weibull distribution. Based on type‐I progressive hybrid censored and masked data, we derive the maximum likelihood estimates, approximate confidence intervals, and bootstrap confidence intervals of unknown parameters. As the maximum likelihood estimate does not exist for small sample size, Gibbs sampling is used to obtain the Bayesian estimates and Monte Carlo method is employed to construct the credible intervals based on Jefferys prior with partial information. Numerical simulations are performed to compare the performances of the proposed methods and one data set is analyzed.

Suggested Citation

  • Jing Cai & Yimin Shi & Bin Liu, 2017. "Statistical analysis for masked system life data from Marshall‐Olkin Weibull distribution under progressive hybrid censoring," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(6), pages 490-501, September.
    • Handle: RePEc:wly:navres:v:64:y:2017:i:6:p:490-501
    DOI: 10.1002/nav.21769
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.21769
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.21769?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Kundu, Debasis & Gupta, Arjun K., 2013. "Bayes estimation for the Marshall–Olkin bivariate Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 271-281.
    2. Ye Liang & Dongchu Sun, 2016. "Identifiability of masking probabilities in competing risks models with emphasis on Weibull models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(7), pages 2143-2157, April.
    3. Bin Liu & Yimin Shi & Jing Cai & Ruibing Wang, 2017. "Reliability analysis of masked data in adaptive step-stress partially accelerated lifetime tests with progressive removal," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(12), pages 6174-6191, June.
    4. Jing Cai & Yimin Shi & Bin Liu, 2017. "Inference for a series system with dependent masked data under progressive interval censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(1), pages 3-15, January.
    5. 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)

    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. Rakesh Ranjan & Vastoshpati Shastri, 2019. "Posterior and predictive inferences for Marshall Olkin bivariate Weibull distribution via Markov chain Monte Carlo methods," 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(6), pages 1535-1543, December.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Deschamps, Philippe J., 2012. "Bayesian estimation of generalized hyperbolic skewed student GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3035-3054.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:64:y:2017:i:6:p:490-501. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.