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

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
    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.
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