Progressive Censoring: Data and Models

  • N. Balakrishnan
  • Erhard Cramer
Part of the Statistics for Industry and Technology book series (SIT)


The notion of progressive censoring is explained by introducing progressive Type-I and Type-II censoring in detail. The presentation includes detailed descriptions of the procedures as well as graphical illustrations and data. Additionally, progressive hybrid censoring is discussed. Finally, the chapter is supplemented by introducing particular probability models assumed in progressive censoring.


Failure Time Admissible Scheme Progressive Censoring Censoring Scheme Censor Order Statistic 
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  1. 11.
    Aggarwala R (2001) Progressive interval censoring: some mathematical results with applications to inference. Comm Stat Theory Meth 30:1921–1935CrossRefMATHMathSciNetGoogle Scholar
  2. 58.
    Arnold BC, Balakrishnan N, Nagaraja HN (1992) A first course in order statistics. Wiley, New YorkMATHGoogle Scholar
  3. 86.
    Balakrishnan N, Aggarwala R (2000) Progressive censoring: theory, methods, and applications. Birkhäuser, BostonCrossRefGoogle Scholar
  4. 123.
    Balakrishnan N, Sandhu RA (1996) Best linear unbiased and maximum likelihood estimation for exponential distributions under general progressive Type-II censored samples. Sankhyā Ser B 58:1–9MATHMathSciNetGoogle Scholar
  5. 246.
    Chatterjee SK, Sen PK (1973) Nonparametric testing under progressive censoring. Calcutta Stat Assoc Bull 22:13–50MATHMathSciNetGoogle Scholar
  6. 259.
    Childs A, Chandrasekar B, Balakrishnan N, Kundu D (2003) Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution. Ann Inst Stat Math 55:319–330MATHMathSciNetGoogle Scholar
  7. 260.
    Childs A, Chandrasekar B, Balakrishnan N (2008) Exact likelihood inference for an exponential parameter under progressive hybrid censoring schemes. In: Vonta F, Nikulin M, Limnios N, Huber-Carol C (eds) Statistical models and methods for biomedical and technical systems. Birkhäuser, Boston, pp 323–334Google Scholar
  8. 303.
    Cramer E, Lenz U (2010) Association of progressively Type-II censored order statistics. J Stat Plan Infer 140:576–583CrossRefMATHMathSciNetGoogle Scholar
  9. 327.
    David HA, Nagaraja HN (2003) Order statistics, 3rd edn. Wiley, HobokenCrossRefMATHGoogle Scholar
  10. 352.
    Epstein B (1954) Truncated life tests in the exponential case. Ann Math Stat 25:555–564CrossRefMATHGoogle Scholar
  11. 440.
    Herd RG (1956) Estimation of parameters of a population from a multi-censored sample. Ph.D. thesis, Iowa State College, Ames, IowaGoogle Scholar
  12. 483.
    Johnson NL, Kotz S, Balakrishnan N (1994) Continuous univariate distributions, vol 1, 2nd edn. Wiley, New YorkGoogle Scholar
  13. 484.
    Johnson NL, Kotz S, Balakrishnan N (1995) Continuous univariate distributions, vol 2, 2nd edn. Wiley, New YorkGoogle Scholar
  14. 536.
    Klein JP, Moeschberger ML (2003) Survival analysis: techniques for censored and truncated data, 2nd edn. Springer, New YorkGoogle Scholar
  15. 561.
    Kundu D, Joarder A (2006b) Analysis of Type-II progressively hybrid censored data. Comput Stat Data Anal 50:2509–2528CrossRefMATHMathSciNetGoogle Scholar
  16. 631.
    Majumdar H, Sen PK (1978) Nonparametric tests for multiple regression under progressive censoring. J Multivariate Anal 8:73–95CrossRefMATHMathSciNetGoogle Scholar
  17. 640.
    Marshall AW, Olkin I (2007) Life distributions: structure of nonparametric, semiparametric, and parametric families. Springer, New YorkGoogle Scholar
  18. 676.
    Nelson W (1982) Applied life data analysis. Wiley, New YorkCrossRefMATHGoogle Scholar
  19. 805.
    Sinha AN, Sen PK (1982) Tests based on empirical processes for progressive censoring schemes with staggering entry and random withdrawal. Sankhyā, Ser B 44:1–18MATHMathSciNetGoogle Scholar
  20. 806.
    Sinha AN, Sen PK (1983) Staggering entry, random withdrawal and progressive censoring schemes: Some nonparametric procedures. In: Ghosh JK, Roy J (eds) Statistics applications and new directions: proceedings of the Indian statistical institute golden jubilee conference. Indian Statistical Institute, Calcutta, pp 531–547Google Scholar
  21. 875.
    Viveros R, Balakrishnan N (1994) Interval estimation of parameters of life from progressively censored data. Technometrics 36:84–91CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • N. Balakrishnan
    • 1
  • Erhard Cramer
    • 2
  1. 1.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada
  2. 2.Institute of StatisticsRWTH Aachen UniversityAachenGermany

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