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Lower confidence limit for reliability based on grouped data using a quantile-filling algorithm

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  • Zhang, Mimi
  • Hu, Qingpei
  • Xie, Min
  • Yu, Dan

Abstract

The aim of this paper is to propose an approach to constructing lower confidence limits for a reliability function and investigate the effect of a sampling scheme on the performance of the proposed approach. This is accomplished by using a data-completion algorithm and certain Monte Carlo methods. The data-completion algorithm fills in censored observations with pseudo-complete data while the Monte Carlo methods simulate observations for complicated pivotal quantities. The Birnbaum–Saunders distribution, the lognormal distribution and the Weibull distribution are employed for illustrative purpose. The results of three cases of data-analysis are presented to validate the applicability and effectiveness of the proposed methods. The first case is illustrated through simulated data, and the last two cases are illustrated through two real-data sets.

Suggested Citation

  • Zhang, Mimi & Hu, Qingpei & Xie, Min & Yu, Dan, 2014. "Lower confidence limit for reliability based on grouped data using a quantile-filling algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 96-111.
  • Handle: RePEc:eee:csdana:v:75:y:2014:i:c:p:96-111
    DOI: 10.1016/j.csda.2014.01.010
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    References listed on IDEAS

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    1. Barros, Michelli & Paula, Gilberto A. & Leiva, Víctor, 2009. "An R implementation for generalized Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1511-1528, February.
    2. Hapfelmeier, A. & Hothorn, T. & Ulm, K., 2012. "Recursive partitioning on incomplete data using surrogate decisions and multiple imputation," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1552-1565.
    3. Azevedo, Cecilia & Leiva, Víctor & Athayde, Emilia & Balakrishnan, N., 2012. "Shape and change point analyses of the Birnbaum–Saunders-t hazard rate and associated estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3887-3897.
    4. Chen, Ling & Sun, Jianguo, 2010. "A multiple imputation approach to the analysis of interval-censored failure time data with the additive hazards model," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1109-1116, April.
    5. Daniel, Rhian M. & Kenward, Michael G., 2012. "A method for increasing the robustness of multiple imputation," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1624-1643.
    6. Vilca, Filidor & Santana, Lucia & Leiva, Víctor & Balakrishnan, N., 2011. "Estimation of extreme percentiles in Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1665-1678, April.
    7. Ng, H. K. T. & Kundu, D. & Balakrishnan, N., 2003. "Modified moment estimation for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 43(3), pages 283-298, July.
    8. Leiva, Victor & Riquelme, Marco & Balakrishnan, N. & Sanhueza, Antonio, 2008. "Lifetime analysis based on the generalized Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2079-2097, January.
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    Cited by:

    1. Xun Xiao & Amitava Mukherjee & Min Xie, 2016. "Estimation procedures for grouped data – a comparative study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(11), pages 2110-2130, August.

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