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Hybrid censoring: Models, inferential results and applications

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  • Balakrishnan, N.
  • Kundu, Debasis

Abstract

A hybrid censoring scheme is a mixture of Type-I and Type-II censoring schemes. In this review, we first discuss Type-I and Type-II hybrid censoring schemes and associated inferential issues. Next, we present details on developments regarding generalized hybrid censoring and unified hybrid censoring schemes that have been introduced in the literature. Hybrid censoring schemes have been adopted in competing risks set-up and in step-stress modeling and these results are outlined next. Recently, two new censoring schemes, viz., progressive hybrid censoring and adaptive progressive censoring schemes have been introduced in the literature. We discuss these censoring schemes and describe inferential methods based on them, and point out their advantages and disadvantages. Determining an optimal hybrid censoring scheme is an important design problem, and we shed some light on this issue as well. Finally, we present some examples to illustrate some of the results described here. Throughout the article, we mention some open problems and suggest some possible future work for the benefit of readers interested in this area of research.

Suggested Citation

  • Balakrishnan, N. & Kundu, Debasis, 2013. "Hybrid censoring: Models, inferential results and applications," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 166-209.
    • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:166-209
    DOI: 10.1016/j.csda.2012.03.025
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    References listed on IDEAS

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    1. Park, Sangun & Balakrishnan, N., 2009. "On simple calculation of the Fisher information in hybrid censoring schemes," Statistics & Probability Letters, Elsevier, vol. 79(10), pages 1311-1319, May.
    2. N. Balakrishnan & G. Iliopoulos, 2010. "Stochastic monotonicity of the MLEs of parameters in exponential simple step-stress models under Type-I and Type-II censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 89-109, July.
    3. Ng, H. K. T. & Chan, P. S. & Balakrishnan, N., 2002. "Estimation of parameters from progressively censored data using EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 371-386, June.
    4. N. Balakrishnan & Qihao Xie & D. Kundu, 2009. "Exact inference for a simple step-stress model from the exponential distribution under time constraint," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 251-274, March.
    5. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
    6. Balakrishnan, N. & Kateri, M., 2008. "On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2971-2975, December.
    7. Park, Sangun & Balakrishnan, N. & Zheng, Gang, 2008. "Fisher information in hybrid censored data," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2781-2786, November.
    8. Debasis Kundu & Rameshwar Gupta, 2007. "Analysis of Hybrid Life-tests in Presence of Competing Risks," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(2), pages 159-170, February.
    9. Yao Zhang & William Q. Meeker, 2005. "Bayesian life test planning for the Weibull distribution with given shape parameter," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(3), pages 237-249, June.
    10. Kundu, Debasis & Joarder, Avijit, 2006. "Analysis of Type-II progressively hybrid censored data," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2509-2528, June.
    11. N. Balakrishnan & G. Iliopoulos, 2009. "Stochastic monotonicity of the MLE of exponential mean under different censoring schemes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 753-772, September.
    12. Wang, Yanhua & He, Shuyuan, 2005. "Fisher information in censored data," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 199-206, June.
    13. A. Childs & B. Chandrasekar & N. Balakrishnan & D. Kundu, 2003. "Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 319-330, June.
    14. Yu-Pin Lin & TaChen Liang & Wen-Tao Huang, 2002. "Bayesian Sampling Plans for Exponential Distribution Based on Type I Censoring Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 100-113, March.
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